8d practical problem solving

Eight Disciplines of Problem Solving (8D)

– Eight Disciplines of Problem Solving –

⇓   Introduction to 8D

⇓   What is 8D

⇓   Why Apply 8D

⇓   When to Apply 8D

⇓   How to Apply 8D

Introduction to Eight Disciplines of Problem Solving (8D)

The Eight Disciplines of Problem Solving (8D) is a problem solving methodology designed to find the root cause of a problem, devise a short-term fix and implement a long-term solution to prevent recurring problems. When it’s clear that your product is defective or isn’t satisfying your customers, an 8D is an excellent first step to improving Quality and Reliability.

Ford Motor Company developed this problem solving methodology, then known as Team Oriented Problem Solving (TOPS), in the 1980s. The early usage of 8D proved so effective that it was adopted by Ford as the primary method of documenting problem solving efforts, and the company continues to use 8D today.

8D has become very popular among manufacturers because it is effective and reasonably easy to teach. Below you’ll find the benefits of an 8D, when it is appropriate to perform and how it is performed.

What is Eight Disciplines of Problem Solving (8D)

The 8D problem solving process is a detailed, team oriented approach to solving critical problems in the production process. The goals of this method are to find the root cause of a problem, develop containment actions to protect customers and take corrective action to prevent similar problems in the future.

The strength of the 8D process lies in its structure, discipline and methodology. 8D uses a composite methodology, utilizing best practices from various existing approaches. It is a problem solving method that drives systemic change, improving an entire process in order to avoid not only the problem at hand but also other issues that may stem from a systemic failure.

8D has grown to be one of the most popular problem solving methodologies used for Manufacturing, Assembly and Services around the globe. Read on to learn about the reasons why the Eight Disciplines of Problem Solving may be a good fit for your company.

Why Apply Eight Disciplines of Problem Solving (8D)

The 8D methodology is so popular in part because it offers your engineering team a consistent, easy-to-learn and thorough approach to solving whatever problems might arise at various stages in your production process. When properly applied, you can expect the following benefits:

• Improved team oriented problem solving skills rather than reliance on the individual
• Increased familiarity with a structure for problem solving
• Creation and expansion of a database of past failures and lessons learned to prevent problems in the future
• Better understanding of how to use basic statistical tools required for problem solving
• Improved effectiveness and efficiency at problem solving
• A practical understanding of Root Cause Analysis (RCA)
• Problem solving effort may be adopted into the processes and methods of the organization
• Improved skills for implementing corrective action
• Better ability to identify necessary systemic changes and subsequent inputs for change
• More candid and open communication in problem solving discussion, increasing effectiveness
• An improvement in management’s understanding of problems and problem resolution

8D was created to represent the best practices in problem solving. When performed correctly, this methodology not only improves the Quality and Reliability of your products but also prepares your engineering team for future problems.

When to Apply Eight Disciplines of Problem Solving (8D)

The 8D problem solving process is typically required when:

• Safety or Regulatory issues has been discovered
• Customer complaints are received
• Warranty Concerns have indicated greater-than-expected failure rates
• Internal rejects, waste, scrap, poor performance or test failures are present at unacceptable levels

How to Apply Eight Disciplines of Problem Solving (8D)

The 8D process alternates inductive and deductive problem solving tools to relentlessly move forward toward a solution. The Quality-One approach uses a core team of three individuals for inductive activities with data driven tools and then a larger Subject Matter Expert (SME) group for the deductive activities through brainstorming, data-gathering and experimentation.

D0: Prepare and Plan for the 8D

Proper planning will always translate to a better start. Thus, before 8D analysis begins, it is always a good idea to ask an expert first for their impressions. After receiving feedback, the following criterion should be applied prior to forming a team:

Collect information on the symptoms

Use a Symptoms Checklist to ask the correct questions

Identify the need for an Emergency Response Action (ERA), which protects the customer from further exposure to the undesired symptoms

D1: Form a Team

A Cross Functional Team (CFT) is made up of members from many disciplines. Quality-One takes this principle one step further by having two levels of CFT:

• The Core Team Structure should involve three people on the respective subjects: product, process and data
• Additional Subject Matter Experts are brought in at various times to assist with brainstorming, data collection and analysis

Teams require proper preparation. Setting the ground rules is paramount. Implementation of disciplines like checklists, forms and techniques will ensure steady progress.  8D must always have two key members: a Leader and a Champion / Sponsor:

• The Leader is the person who knows the 8D process and can lead the team through it (although not always the most knowledgeable about the problem being studied)
• The Champion or Sponsor is the one person who can affect change by agreeing with the findings and can provide final approval on such changes

D2: Describe the Problem

The 8D method’s initial focus is to properly describe the problem utilizing the known data and placing it into specific categories for future comparisons. The “Is” data supports the facts whereas the “Is Not” data does not. As the “Is Not” data is collected, many possible reasons for failure are able to be eliminated. This approach utilizes the following tools:

• Problem Statement
• Affinity Diagram (Deductive tool)
• Fishbone/Ishikawa Diagram (Deductive tool)
• Problem Description

D3: Interim Containment Action

In the interim, before the permanent corrective action has been determined, an action to protect the customer can be taken. The Interim Containment Action (ICA) is temporary and is typically removed after the Permanent Correct Action (PCA) is taken.

• Verification of effectiveness of the ICA is always recommended to prevent any additional customer dissatisfaction calls

D4: Root Cause Analysis (RCA) and Escape Point

The root cause must be identified to take permanent action to eliminate it. The root cause definition requires that it can be turned on or off, at will. Activities in D4 include:

• Comparative Analysis listing differences and changes between “Is” and “Is Not”
• Development of Root Cause Theories based on remaining items
• Verification of the Root Cause through data collection
• Review Process Flow Diagram for location of the root cause
• Determine Escape Point, which is the closest point in the process where the root cause could have been found but was not

D5: Permanent Corrective Action (PCA)

The PCA is directed toward the root cause and removes / changes the conditions of the product or process that was responsible for the problem. Activities in D5 include:

• Establish the Acceptance Criteria which include Mandatory Requirements and Wants
• Perform a Risk Assessment /  Failure Mode and Effects Analysis (FMEA) on the PCA choices
• Based on risk assessment, make a balanced choice for PCA
• Select control-point improvement for the Escape Point
• Verification of Effectiveness for both the PCA and the Escape Point are required

D6: Implement and Validate the Permanent Corrective Action

To successfully implement a permanent change, proper planning is essential. A project plan should encompass: communication, steps to complete, measurement of success and lessons learned. Activities in D6 include:

• Develop Project Plan for Implementation
• Communicate the plan to all stakeholders
• Validation of improvements using measurement

D7: Prevent Recurrence

D7 affords the opportunity to preserve and share the knowledge, preventing problems on similar products, processes, locations or families. Updating documents and procedures / work instructions are expected at this step to improve future use. Activities in D7 include:

• Review Similar Products and Processes for problem prevention
• Develop / Update Procedures and Work Instructions for Systems Prevention
• Capture Standard Work / Practice and reuse
• Assure FMEA updates have been completed
• Assure Control Plans have been updated

D8: Closure and Team Celebration

Teams require feedback to allow for satisfactory closure. Recognizing both team and individual efforts and allowing the team to see the previous and new state solidifies the value of the 8D process. Activities in D8 include:

• Archive the 8D Documents for future reference
• Document Lessons Learned on how to make problem solving better
• Before and After Comparison of issue
• Celebrate Successful Completion

8D and Root Cause Analysis (RCA)

The 8D process has Root Cause Analysis (RCA) imbedded within it. All problem solving techniques include RCA within their structure. The steps and techniques within 8D which correspond to Root Cause Analysis are as follows:

• Problem Symptom is quantified and converted to “Object and Defect”
• Problem Symptom is converted to Problem Statement using Repeated Whys
• Possible and Potential Causes are collected using deductive tools (i.e. Fishbone or Affinity Diagram)
• Problem Statement is converted into Problem Description using Is / Is Not
• Problem Description reduces the number of items on the deductive tool (from step 3)
• Comparative Analysis between the Is and Is Not items (note changes and time)
• Root Cause theories are developed from remaining possible causes on deductive tool and coupled with changes from Is / Is Not
• Compare theories with current data and develop experiments for Root Cause Verification
• Test and confirm the Root Causes

Example: Multiple Why Technique

The Multiple / Repeated Why (Similar to 5 Why) is an inductive tool, which means facts are required to proceed to a more detailed level. The steps required to determine problem statement are:

• Problem Symptom is defined as an Object and Defect i.e. “Passenger Injury”
• Why? In every case “SUV’s Roll Over”
• Why? In every case, it was preceded by a “Blown Tire”
• Why? Many explanations may be applied, therefore the team cannot continue with another repeated why past “Blown Tire”
• Therefore, the Problem Statement is “Blown Tire”
• Why? Low (Air) Pressure, Tire Defect (Degradation of an Interface) and High (Ambient) Temperature
• Counter measures assigned to low pressure and tire defect

This example uses only 4 of the 5 Whys to determine the root causes without going further into the systemic reasons that supported the failure. The Repeated Why is one way to depict this failure chain. Fault Tree Analysis (FTA) could also be used.

Learn More About Eight Disciplines of Problem Solving (8D)

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Article • 8 min read

8D Problem Solving Process

Solving major problems in a disciplined way.

By the Mind Tools Content Team

(Also known as Global 8D Problem Solving)

When your company runs into a major problem, you need to address it quickly. However, you also need to deal with it thoroughly and ensure that it doesn't recur – and this can take a lot of effort and elapsed time.

The 8D Problem Solving Process helps you do both of these seemingly-contradictory things, in a professional and controlled way. In this article, we'll look at the 8D Problem Solving Process, and we'll discuss how you can use it to help your team solve major problems.

Origins of the Tool

The Ford Motor Company® developed the 8D (8 Disciplines) Problem Solving Process, and published it in their 1987 manual, "Team Oriented Problem Solving (TOPS)." In the mid-90s, Ford added an additional discipline, D0: Plan. The process is now Ford's global standard, and is called Global 8D.

Ford created the 8D Process to help teams deal with quality control and safety issues; develop customized, permanent solutions to problems; and prevent problems from recurring. Although the 8D Process was initially applied in the manufacturing, engineering, and aerospace industries, it's useful and relevant in any industry.

The eight disciplines are shown in figure 1, below:

Figure 1: The 8D Problem Solving Process

The 8D Process works best in teams tasked with solving a complex problem with identifiable symptoms. However, you can also use this process on an individual level, as well.

Applying the Tool

To use the 8D Process, address each of the disciplines listed below, in order. Take care not to skip steps, even when time is limited; the process is only effective when you follow every step.

Discipline 0: Plan

Before you begin to assemble a team to address the problem, you need to plan your approach. This means thinking about who will be on the team, what your time frame is, and what resources you'll need to address the problem at hand.

Discipline 1: Build the Team

You should aim to put together a team that has the skills needed to solve the problem, and that has the time and energy to commit to the problem solving process.

Keep in mind that a diverse team is more likely to find a creative solution than a team of people with the same outlook (although if outlooks are too diverse, people can spend so much time disagreeing that nothing gets done).

Create a team charter that outlines the team's goal and identifies each person's role. Then, do what you can to build trust and get everyone involved in the process that's about to happen.

If your team is made up of professionals who haven't worked together before, consider beginning with team-building activities to ensure that everyone is comfortable working with one another.

Discipline 2: Describe the Problem

Once your team has settled in, describe the problem in detail. Specify the who, what, when, where, why, how, and how many; and use techniques like CATWOE and the Problem-Definition Process to ensure that you're focusing on the right problem.

Start by doing a Risk Analysis – if the problem is causing serious risks, for example, to people's health or life, then you need to take appropriate action. (This may include stopping people using a product or process until the problem is resolved.)

If the problem is with a process, use a Flow Chart , Swim Lane Diagram , or Storyboard to map each step out; these tools will help your team members understand how the process works, and, later on, think about how they can best fix it.

Discovering the root cause of the problem comes later in the process, so don't spend time on this here. Right now, your goal is to look at what's going wrong and to make sure that your team understands the full extent of the problem.

Discipline 3: Implement a Temporary Fix

Once your team understands the problem, come up with a temporary fix. This is particularly important if the problem is affecting customers, reducing product quality, or slowing down work processes.

Harness the knowledge of everyone on the team. To ensure that each person's ideas are heard, consider using brainstorming techniques such as Round Robin Brainstorming or Crawford's Slip Writing Method , alongside more traditional team problem solving discussions.

Once the group has identified possible temporary fixes, address issues such as cost, implementation time, and relevancy. The short-term solution should be quick, easy to implement, and worth the effort.

Discipline 4: Identify and Eliminate the Root Cause

Once your temporary fix is in place, it's time to discover the root cause of the problem.

Conduct a Cause and Effect Analysis to identify the likely causes of the problem. This tool is useful because it helps you uncover many possible causes, and it can highlight other problems that you might not have been aware of. Next, apply Root Cause Analysis to find the root causes of the problems you've identified.

Once you identify the source of the problem, develop several permanent solutions to it.

If your team members are having trouble coming up with viable permanent solutions, use the Straw Man Concept to generate prototype solutions that you can then discuss, tear apart, and rebuild into stronger solutions.

Discipline 5: Verify the Solution

Once your team agrees on a permanent solution, make sure that you test it thoroughly before you fully implement it, in the next step.

• Conducting a Failure Mode and Effects Analysis (FMEA) to spot any potential problems.
• Using Impact Analysis to make sure that there will be no unexpected future consequences.
• Using Six Thinking Hats to examine the fix from several different emotional perspectives.

Last, conduct a Blind Spot Analysis to confirm that you and your team haven't overlooked a key factor, or made an incorrect assumption about this solution.

Discipline 6: Implement a Permanent Solution

Once your team reaches a consensus on the solution, roll your fix out. Monitor this new solution closely for an appropriate period of time to make sure that it's working correctly, and ensure that there are no unexpected side effects.

Discipline 7: Prevent the Problem From Recurring

When you're sure that the permanent solution has solved the problem, gather your team together again to identify how you'll prevent the problem from recurring in the future.

You might need to update your organization's standards, policies, procedures, or training manual to reflect the new fix. You'll likely also need to train others on the new process or standard. Finally, you'll need to consider whether to change your management practices or procedures to prevent a recurrence.

Discipline 8: Celebrate Team Success

The last step in the process is to celebrate and reward your team's success . Say "thank you" to everyone involved, and be specific about how each person's hard work has made a difference. If appropriate, plan a party or celebration to communicate your appreciation.

Before the team disbands, conduct a Post-Implementation Review to analyze whether your solution is working as you thought, and to improve the way that you solve problems in the future.

In the late 1980s, Ford Motor Company developed the 8D (8 Disciplines) Problem Solving Process to help manufacturing and engineering teams diagnose, treat, and eliminate quality problems. However, teams in any industry can use this problem solving process.

The eight disciplines are:

• Build the Team.
• Describe the Problem.
• Implement a Temporary Fix.
• Identify and Eliminate the Root Cause.
• Verify the Solution.
• Implement a Permanent Solution.
• Prevent the Problem From Recurring.
• Celebrate Team Success.

The 8D Problem Solving Process is best used with a team solving complex problems; however, individuals can also use it to solve problems on their own.

Ford is a registered trademark of the Ford Motor Company: https://www.ford.com/

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• Guide: 8D Problem Solving

Daniel Croft

Daniel Croft is an experienced continuous improvement manager with a Lean Six Sigma Black Belt and a Bachelor's degree in Business Management. With more than ten years of experience applying his skills across various industries, Daniel specializes in optimizing processes and improving efficiency. His approach combines practical experience with a deep understanding of business fundamentals to drive meaningful change.

• Last Updated: June 13, 2023
• Learn Lean Sigma

8D Problem Solving is a systematic and structured approach used to solve business related problems. It names has been given by the fact there are 8 steps or 8 disciplines that are followed to identify, correct and eliminate recurring problems.

8D Problem Solving is regarded as robust methodology that has proven its worth across multiple industries and manufacturing in particular. The methodology was Initially developed within the automotive industry, it has since been widely adopted in manufacturing, logistics and health care to name a few. The 8D approach goes beyond helping team just identify the root cause of problem but also provides a structured approach for implementing and verifying corrective actions.

Table of Contents

What is 8d problem solving.

The 8D Problem-Solving methodology was developed in the late 1980s  by Ford Motor Company. The term “8D” stands for “Eight Disciplines,” which represent the eight critical steps in problem-solving.

Initially it was only intended to resolve issues within the automotive manufacturing process. However, over the year since then the methodology has gained universal acceptance and is now applied across various sectors. The 8D approach was heavily influenced by quality management systems like Total Quality Management (TQM) and methodologies like Six Sigma and forms a key part of quality roles and Six sigma qualifications.

8D is also encourages collaborative team based approach to addressing issues in the workplace This methodology was purposefully designed to be a cross-functional effort, ensuring to bring together expertise from different departments or disciplines to comprehensively address an issue by looking at it from all point of view. Here are the key components:

Preparation : Before diving into problem-solving, the team gathers all necessary resources and tools.

Team Establishment : A cross-functional team is assembled, each member having a specific role and responsibility.

Problem Description : The issue at hand is clearly defined to ensure everyone has a shared understanding.

Interim Actions : Short-term solutions are implemented to contain the problem and prevent further damage.

Root Cause Analysis : Various tools and methods are used to identify the real cause of the problem.

Permanent Corrective Actions : Long-term solutions are selected and verified to eliminate the root cause.

Implementation : The long-term solutions are implemented across the board, including necessary changes to policies and procedures.

Prevent Recurrence : Measures are taken to ensure that the problem does not occur again.

Team Recognition : The team is congratulated and acknowledged for their efforts.

How does 8D Compare to over Problem-Solving Methods?

Between quality management systems and lean six sigma there are several problem-solving methodologies such as PDCA (Plan-Do-Check-Act), DMAIC (Define-Measure-Analyze-Improve-Control), and A3 . However the combination of the 8D steps results in a comprehensive frame work that is:

Team-Oriented : Unlike some methodologies that can be carried out by individuals, 8D strongly emphasizes team collaboration as a core principle as seen in steps D1 and D8.

Structured Framework : 8D provides a very detailed, step-by-step guide for solving complex problems, by breaking it down in to logical steps making it easier to manage and track progress.

Broad Applicability : While some methodologies like DMAIC are closely tied to Six Sigma, 8D can be applied in various contexts without being tied to a particular quality management system.

Focus on Prevention : 8D not only aims to solve the problem but also focuses on implementing changes to prevent its recurrence, making it a complete approach to problem solving.

The 8 Disciplines Explained

D0: prepare for the process.

Before you start 8D you should prepare for the 8D process. This phase sets the foundation for the entire methodology, ensuring that the team is able to tackle the problem effectively. Therefore, effective preparation helps in avoiding unnecessary delays and ensures that you’re not solving the wrong problem.

Within the initial preparation step you should also the time to think about what knowledge, expertise and experience you need within the team. Cross-functional teams are important, as they bring alternative perspectives and skills to the table rather than everyone looking at the problem from one point of view. Make sure you consider expertise, availability, and interest when selecting team members.

D1: Establish the Team

In D1 you should establish the team by clearly defining the roles and responsibilities for each team member. This includes assigning a team leader, subject matter experts, and roles for data collection , analysis, and communication this helps to provide the team members clarity on how they will be involved and contribute to the success of the problems solving activity.

Team Composition

Once roles are defined, where possible ensure that the team is balanced in terms of skills and expertise. A well-rounded team will be more effective in tackling various aspects of the problem.

Communication

Establish clear methods communication, both within the team and with external stakeholders. Such as deciding on regular meeting schedules that everyone can attend, reporting formats, and tools for collaboration.

D2: Describe the Problem

In D2 it is time to create a well formed problem statement. This step is key as it provides a foundation for understanding the problem which will lead to generally more successful problem-solving. It ensures that everyone clearly understands what needs to be addressed, setting the scope for the entire process. Ensure that the problem is clearly understood by everyone in the team at this stage to prevent confusion later on in the process.

5W1H Method of creating a Problem Definition

Use data gathering techniques such as observations, interviews, and document reviews can help to precisely identify the problem. A useful tool to use at this stage could be the 5W1H Problem definition method.

You can find out more about this method with our 5W1H guide .

Problem Definition – is / is not template

When creating your problem definition ensure to be specific, measurable, and unambiguous when stating the problem. You should avoid generalities and ensure that the problem statement is understandable to someone unfamiliar with the issue. If you are new to this process it may be helpful to give the statement to someone unfamiliar to the process and see if they understand it or if they have questions. You can then clarify any questions by adjusting the problem description to improve the claity.

D3: Implement and Verify Interim Actions

In D3 while the team is investigating the root cause, interim actions are must be implement to contain the problem and minimize its impact. This is particularly important in critical situations affecting safety, compliance, or customer satisfaction. 

In this step you should identify, plan, and execute short-term fixes that can quickly contain the problem. This could include quarantining the product to ensure it is not sent out to the customer or even pausing production lines that continue to product defects. Ensure these actions are documented for future reference.

Use metrics and KPIs to gauge the effectiveness of the interim actions. Make adjustments as necessary.

D4: Root Cause Analysis

D4 is where you start to understand what is causing the issue by identifying the underlying reason for the problem. The objective is to find the root cause, not just the symptoms.

At this stage there are a range of quality and lean six sigma tools that can be used to conduct root cause analysis , which can include the Fishbone Diagram for structured brainstorming and the 5 Whys technique for causal chain analysis.

We have a range of guides on all of these techniques for you to use.

Once identified, it is important validate the root cause through experimentation or additional data analysis to ensure it’s the actual cause and not a symptom, this can often be an overlook critical step in the root cause process.

D5: Choose and Verify Permanent Corrective Actions

In D5 you need to choose what actions to be taken to prevent the problem reoccurring and any solutions implemented should be verified that the actions correct the problem this can involve trial runs, further data collection and inspections of product or services being produced.

You should also consider factors like cost, impact, and feasibility when choosing a permanent corrective action and should also conduct a risk assessment to evaluate potential negative outcomes of the actions taken

An implementation or action plan is often useful to document at this stage to detail the steps for implementation, assign responsibilities, and set timelines.

D6: Implement Permanent Corrective Actions

Once verified, implement the corrective actions across all relevant departments or processes. This can involved documenting the new process and training out to all stakeholders involved to ensure the new process is followed and that the stakeholders understand the reason for the change.

At this point you should continue to regularly monitor the situation to ensure the corrective actions are sustained and effective, this could be for a period of 30, 60 or 90 days after the problem was resolved to ensure the new process has become a sustained and issues do not reoccur. 

D7: Prevent Recurrence

In D7 to prevent recurrent you should review and update organizational policies or standard operating procedures (SOPs) to prevent a recurrence of the problem and document the new standard process

It is important to conduct regular reviews to continuously monitor the process and ensure procedures are being followed but also to identify further opportunities for process improvement.

D8: Congratulate the Team

The final step D8, after the hard work and successful problem resolution, it is important to acknowledging and congratulating the team is vital for morale and future engagement. With the recognition of a successful 8D Problem-solving activity complete you are more likely to encourage future participation as the method gets a reputation as being useful and successful at solving problems. 

Whether it’s a team lunch, certificates of achievement, or simply a public acknowledgment, celebrate the success in a way that resonates with your team.

Finally it is always important to conduct a lessons-learned session and document the insights gained during the process for future reference. This can be used as a future point of reference for problem solving activities.

Mastering the art of problem-solving is crucial in today’s complex and fast-paced environment. The 8D Problem-Solving methodology offers a structured, team-based approach to tackling challenges that can arise in any sector, be it manufacturing, public services, or logistics. This guide has walked you through each of the eight disciplines, offering best practices and highlighting common pitfalls to avoid. We’ve also enriched your understanding through real-world case studies that demonstrate the methodology’s versatility and effectiveness. Remember, the strength of 8D lies not just in identifying and resolving problems, but also in preventing their recurrence through systemic improvements. By adhering to the principles and steps outlined in this guide, you’re well on your way to becoming an adept problem solver, capable of driving continuous improvement in your organization.

• Zarghami, A. and Benbow, D.W., 2017.  Introduction to 8D problem solving . Quality Press.
• Camarillo, A., Ríos, J. and Althoff, K.D., 2017. CBR and PLM applied to diagnosis and technical support during problem solving in the Continuous Improvement Process of manufacturing plants .  Procedia Manufacturing ,  13 , pp.987-994.

Q: What is 8D problem solving?

A: 8D problem solving is a systematic approach used to address and resolve complex problems. It is widely utilized in various industries to identify the root causes of issues, develop effective solutions, and prevent their recurrence.

Q: Why is it called "8D" problem solving?

A: The name “8D” refers to the eight disciplines or steps involved in the problem-solving process. Each discipline represents a specific stage in the methodology, allowing for a structured and comprehensive approach to problem resolution.

Q: What are the eight disciplines (8D) in problem solving?

A: The eight disciplines in problem solving, often abbreviated as 8D, are as follows:

• D1: Form a team
• D2: Define the problem
• D3: Implement containment actions
• D4: Determine the root cause
• D5: Develop and implement corrective actions
• D6: Validate the effectiveness of corrective actions
• D7: Prevent recurrence
• D8: Congratulate the team

Q: What is the purpose of forming a team in the 8D problem-solving process?

A: Forming a team at the beginning of the 8D problem-solving process helps ensure that the right individuals with the necessary expertise are involved in addressing the problem. The team collaboratively works towards understanding the issue, analyzing data, and developing effective solutions.

Q: How is the root cause determined in the 8D problem-solving process?

A: Determining the root cause (D4) involves conducting a thorough analysis of the problem. Various tools and techniques, such as cause-and-effect diagrams, 5 Whys, and data analysis, are employed to identify the underlying factors contributing to the problem.

Q: Can the 8D problem-solving methodology be applied to any type of problem?

A: Yes, the 8D problem-solving methodology is a versatile approach that can be applied to various types of problems across different industries. It provides a structured framework for problem resolution and can be tailored to suit the specific needs and requirements of different situations.

Daniel Croft is a seasoned continuous improvement manager with a Black Belt in Lean Six Sigma. With over 10 years of real-world application experience across diverse sectors, Daniel has a passion for optimizing processes and fostering a culture of efficiency. He's not just a practitioner but also an avid learner, constantly seeking to expand his knowledge. Outside of his professional life, Daniel has a keen Investing, statistics and knowledge-sharing, which led him to create the website learnleansigma.com, a platform dedicated to Lean Six Sigma and process improvement insights.

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8D Problem Solving: Comprehensive Breakdown and Practical Applications

The 8D problem-solving process stands as a beacon of structured analysis and corrective action within the complexities of operational pitfalls and quality control discrepancies across industries. Originating from the automotive industry and since adopted widely, the methodology offers a meticulous step-by-step approach that fosters team cohesion, addresses problems at their roots, and implements sustainable solutions.

This article seeks to delve into the nuances of the 8D problem-solving framework, presenting a lucid exposition of its origins, a detailed foray into each step enriched by practical examples, and concluding with the unequivocal benefit bouquet it presents to the organization adopting it.

The Origins of the 8D Problem Solving Methodology

The 8D, or "Eight Disciplines," problem-solving approach germinated from the fertile grounds of collaborative efforts to ensure superior quality and reliability in manufacturing. Initially developed by the Ford Motor Company in the 1980s, this systematic method was a response to a confluence of quality and operational issues that were pervasive in the automotive industry. It drew broader appeal as its efficacy became apparent - functioning as an amalgam of logic, analytics, and teamwork to tackle problems methodically.

The wide reach of the 8D methodology is evident in industries ranging from manufacturing to healthcare, aerospace to IT, and beyond. Its universal applicability stems from a foundational adherence to principle over process, transcending the intricacies of industry-specific challenges. By combining reactive and proactive measures, the 8D method helps in not just extinguishing the fire, but also preventing its outbreak, making it an enduring asset in the organizational toolkit.

The 8 Steps of Problem Solving

An incursion into the 8D methodology reveals a framework that is both systematic and flexible. Each step is sequenced to ensure that issues are not merely patched but genuinely resolved, implementing robust preventive measures to curtail recurrences. This section expounds on each disciplinary step and serves as a substrate for practical implementation examples, supplementing theoretical insights with real-world applicability.

Step 1: Establish a Team

The cornerstone of any formidable 8D approach begins with assembling a competent team. The wisdom embedded in this initial phase is the recognition that effective problem-solving is not a solitary venture but a collaborative pursuit. A multidisciplinary team brings diverse perspectives that are critical in diagnosing issues accurately and devising solutions effectively.

When determining team composition, the emphasis should be on a mix of skills and expertise relevant to the problem at hand. Roles within the team should be clearly defined to streamline activities and foster accountability. Each member should be well-versed in their responsibilities, from those leading the problem-solving charge to those executing and tracking actions.

Step 2: Describe the Problem

Clarity is vital in the second step, which necessitates delineating the problem with precision. A meticulous description sets the foundation for targeted analysis and actionable solutions. It involves accruing information that is factual, quantifiable, and devoid of assumptions – the cornerstone of an accurate problem portrayal.

Techniques like '5W2H' (who, what, when, where, why, how, how much) can galvanize teams into crafting detailed problem descriptions. An exemplar of a well-articulated problem statement might state, "Machine X has experienced a 15% decline in output quality, resulting in a monthly loss of 200 units of product Y since January due to recurrent mechanical inaccuracies."

Step 3: Develop Interim Containment Actions

Addressing a problem's immediate impact is pivotal to prevent exacerbation as a root cause analysis is conducted. Interim containment actions can be likened to first aid – essential, though not the definitive cure. These measures should be rigorously designed to quell the problem's spread or intensification without creating new issues.

An interim action for the aforementioned issue with Machine X could involve adjusting the production schedule to mitigate output loss while the machine is under examination. This demonstrates a temperate solution, buying time for a comprehensive fix without severely disrupting the production chain.

Step 4: Define and Verify the Root Cause(s)

Singular in its focus yet pluralistic in its approach, this phase is committed to uncovering the underlying reasons for the problem. Root cause identification is a task of surgical precision, necessitating a deep dive into the problem without the constraints of predetermined notions.

Techniques such as the "5 Whys" and "Fishbone Diagram" guide problem solvers through a structured investigation of potential causes. Verification is as crucial as identification, ensuring that purported root causes stand up to scrutiny and testing.

Step 5: Verify Permanent Corrective Action(s)

Once root causes have been established, attention shifts to devising and validating long-term corrective actions. This step traverses the path from theory to practice. It requires a judicious appraisal of potential solutions with a clear-eyed view of their feasibility, effectiveness, and sustainability.

Best practices in this step incorporate piloting solutions on a smaller scale, enabling refinement before full-scale implementation. A well-considered corrective action for Machine X might involve upgrading mechanical components identified as failure points, subject to cost-benefit analysis and potential disruption to the production line.

Step 6: Implementing and Validating Permanent Corrective Actions

This step transitions the plan into reality, pushing the corrective actions beyond the threshold into the operational environment. Careful implementation is the linchpin, with detailed plans and schedules ensuring that actions are well-executed and efficacious.

The validation process is a keystone in affirming that corrective actions deliver the intended improvements. For Machine X, this could entail monitoring post-repair performance metrics over a defined period against pre-issue levels to authenticate the efficacy of the improvements.

Step 7: Preventive Measures

Armed with insights gleaned, the 7th step propels the methodology into preventative mode. Here, the onus is on forestalling a problem’s resurgence by ingraining the lessons learned into the organizational fabric. The aim is to encapsulate these insights in policies, procedures, or system changes.

This could mean revising maintenance schedules or worker training programs for Machine X to include the specific nuances that led to the mechanical inaccuracies, thereby shielding against repeat episodes.

Step 8: Congratulate Your Team

The final step encompasses a human-centered focus on recognition and commendation. Acknowledgment of the team’s efforts reinforces motivation, fosters a positive culture, and encourages engagement in future problem-solving initiatives.

Celebrating the success could manifest in a ceremonious recognition of the team’s achievements, an internal announcement of their contributions, or a tangible expression of appreciation. This not only cements the accomplishment but also propels a sense of camaraderie and collective purpose.

The Importance of the 8D Problem Solving Process

A mature consideration of the 8D problem-solving process corroborates its contributory significance in unraveling complex issues and instituting consequential improvements. The benefits it confers are manifest in enhanced product quality, heightened customer satisfaction, and the stimulation of a proactive problem-solving culture. Challenges do persist, mainly in the form of resistance to change or insufficient training; nevertheless, with a conscientious implementation, these can be navigated.

Moreover, the 8D approach aligns seamlessly with the pursuit of continuous improvement – a cornerstone of many business philosophies such as Lean and Six Sigma. It thus serves not only as a solution framework but also as a catalyst for organizational growth and learning.

In summary, the 8D problem-solving methodology stands out for its disciplined, team-driven, and methodical approach to tackling complex problems. From its historical roots in the automotive industry to its implementation in modern enterprises, its efficacy in achieving sustainable solutions is undoubted. Online certificate programs and problem-solving courses often feature 8D due to its relevance and value across industries.

As this article delineates each step, with practical applications and advice, the message is clear: mastery of 8D is not just for immediate problem resolution – it is a pathway to building a resilient and adaptive organization capable of facing the challenges of an ever-changing business landscape.

What are the key steps involved in the 8D Problem Solving process and how do they interact with each other?

Introduction to the 8d process.

The 8D Problem Solving process stands tall. It is a structured approach. Businesses use it widely. 8D tackles complex problems effectively. It drives teams towards lasting solutions. It also fosters quality and reliability. The "D" denotes eight disciplined steps. These steps guide teams. They identify, correct, and prevent issues.

8D Steps Explained

D1: establish the team.

Form a skilled team first. Diversity matters here. Each member brings insights. Their combined expertise is crucial. Team formation kicks off the process.

D2: Describe the Problem

Articulate the issue clearly. Use quantifiable data here. Understanding the scope matters. Have accurate problem statements ready. They pave the way forward.

D3: Develop Interim Containment Action

Ensure a temporary fix. It limits the problem's impact. Speed is of the essence. However, ensure the action is effective. The goal is to stabilize the situation.

D4: Determine Root Cause

Dig deep into causes. Use data-driven analysis. Techniques include fishbone diagrams. Five Whys is also popular. Root cause analysis is pivotal. It prepares the team for corrective actions.

D5: Design and Verify Permanent Corrective Actions

Choose the best corrective action. Rigorous selection criteria apply. Effectiveness and efficiency matter. Verify through testing. Make certain the solution fits.

D6: Implement and Validate Permanent Corrective Actions

Roll out the solution. Watch closely for results. Validation takes place here. Use performance indicators for this. They must indicate that the solution works.

D7: Prevent Recurrence

Embed the improvement. Update systems and policies. Training may be necessary. Maintain the gains. This step safeguards the future. Documentation is important here.

D8: Congratulate the Team

Never overlook recognition. Acknowledge everyone's efforts. Celebrate the success achieved. It boosts team morale. It also promotes a culture of quality.

Interplay Between Steps

The interdependence is strong. Each step builds on the previous one. For example, a strong team in D1 enhances problem understanding in D2. Similarly, effective interim actions in D3 set the stage for a thorough root cause analysis in D4.

The verification in D5 ensures the solution from D4 is sound. Implementation in D6 then relies on the verified action. To prevent recurrence (D7), one must understand the root cause. The entire process relies on clear communication. Team recognition (D8) closes the loop neatly. It paves the way for future problem-solving success.

In essence, the 8D steps are interlinked. Each step informs the next. Teams achieve the best results by following the sequence. They also adapt as needed. 8D enforces a discipline that leads to high-quality results. The interaction between steps ensures problems do not just disappear. They stay solved. This is the power of an integrated problem-solving approach.

Can you provide some practical examples of the effective application of 8D Problem Solving strategies in real-life settings?

Understanding 8d problem solving.

8D problem solving stands for Eight Disciplines. It involves steps that teams must follow. Starting from identifying problems , it goes until preventing reoccurrences . Companies use 8D to tackle complex issues. Its main goal remains quality improvement.

Here are practical examples where 8D shines.

Example 1: Automotive Industry

D0: Plan - An auto manufacturer formed a team. Their goal was clear: resolve brake failures.

D1: Team Formation - They gathered experts from diverse fields. Collaboration was key here.

D2: Describe the Problem - They identified specific issues. Customers reported brakes failing at high speeds.

D3: Develop Interim Containment - They distributed quick-fix kits to dealerships. This ensured immediate customer safety.

D4: Determine Root Causes - A deep dive ensued. The team discovered a faulty brake fluid line.

D5: Choose and Verify Permanent Corrective Actions (PCAs) - They redesigned the brake line. Then they tested it under rigorous conditions.

D6: Implement and Validate PCAs - The new design went into production. Ongoing assessments confirmed its effectiveness.

D7: Take Preventive Measures - They updated their design guidelines. Thus, they eliminated the possibility of similar failures.

D8: Congratulate Your Team - Management recognized the team's effort. This promoted a culture of problem-solving.

Example 2: Electronics Manufacturer

D0: Plan - A sudden surge in returned gadgets prompted action.

D1: Team Formation - A cross-functional team took charge. They had one aim: find the flaw.

D2: Describe the Problem - Devices were overheating during usage. Anxiety among customers grew.

D3: Develop Interim Containment - They halted the production line. Assessing risks was necessary.

D4: Determine Root Causes - Detailed analysis revealed a substandard battery component.

D5: Choose and Verify PCAs - They sourced a higher quality component. Subsequent tests showed promising results.

D6: Implement and Validate PCAs - They integrated the new component into production. Monitoring phases ensured it was a fix.

D7: Take Preventive Measures - They revamped their quality control protocols. Now they could avoid similar issues.

D8: Congratulate Your Team - The team's innovative approach earned praise. They set new standards in their processes.

Example 3: Food Packaging Company

D0: Plan - Reports of packaging leaks triggered an 8D.

D1: Team Formation - Experts from production to distribution joined forces. They understood the stakes were high.

D2: Describe the Problem - The leaks were sporadic but damaging. Food safety concerns escalated.

D3: Develop Interim Containment - They removed compromised products from shelves. Protecting the consumer was paramount.

D4: Determine Root Causes - Investigation exposed a sealing machine defect.

D5: Choose and Verify PCAs - Engineers redesigned the sealing mechanism. Trials followed, proving success.

D6: Implement and Validate PCAs - The updated machines replaced the old ones. Continuous evaluations followed to assure quality.

D7: Take Preventive Measures - They introduced more rigorous maintenance routines. They aimed to preempt future failures.

D8: Congratulate Your Team - The swift and thorough response earned accolades. They reinforced trust in their brand.

8D's Practical Value

Each example showcases 8D's potential. This problem-solving framework adapts to various scenarios. Through structured teamwork and analysis, it guides toward sustainable solutions. It helps in ensuring the same problem does not occur twice. Businesses across different sectors find 8D crucial for their continuous improvement efforts. It underlines that a methodical approach to problem-solving can yield significant long-term benefits.

How is the effectiveness and success of the 8D Problem Solving approach measured in practical applications?

Introduction to 8d problem solving.

The 8D Problem Solving approach stands as a structured methodology. It aims to address and resolve critical issues within an organization. Rooted in the team-oriented approach, 8D follows eight disciplined steps. These steps ensure a comprehensive and effective resolution process. The process includes identifying the problem, implementing interim controls, defining root causes, developing a corrective action plan, taking corrective actions, validating those actions, preventing recurrence, and finally congratulating the team.

Measuring Effectiveness and Success

Quantitative metrics.

Timeliness of Response

The promptness of the initial response is critical. It alerts stakeholders to the emergence and acknowledgment of the issue.

Problem Recurrence Rates

A key success indicator is the frequency of problem recurrence. A declining trend signifies effective corrective actions.

Financial Impact

Cost savings or avoidance measures the fiscal efficiency of the resolution. It counts both direct and indirect factors.

Cycle Time Reduction

Improvements in processes can lead to shorter cycle times. This reflects efficiency gains from the 8D implementation.

Qualitative Metrics

Quality of Documentation

Comprehensive documentation ensures thorough issue analysis. It captures the nuances of the problem-solving journey.

Stakeholder Satisfaction

Feedback from affected parties gauges the outcome’s acceptability. Satisfaction levels can direct future interventions.

Knowledge Transfer

Disseminating learnings enhances organizational capability. Sharing insights leads to broader, preventive measures.

Team Cohesion and Growth

Personal and team development signal process benefits. Such growth provides intangible value to the organization.

Practical Application and Continuous Improvement

In practical applications, tailoring metrics to contexts is vital. Unique business environments demand specific success criteria. Therefore, adapting the approach and its measurement system is necessary.

Organizations may employ a combination of tangible and intangible metrics. Aligning these to strategic goals ensures relevance. The 8D Process receives fine-tuning through iterative cycles. Each cycle offers an opportunity for enhanced problem-solving efficacy.

The Importance of Measure Standardization

Standardizing the measurement process ensures consistency. It aids in comparing and benchmarking against best practices. Homogeneity in measures facilitates clearer communication. It enhances the understanding of successes and areas for improvement.

Revisiting and Refining the 8D Process

Upon completion, a rigorous review of the 8D process is crucial. It ensures learnings lead to process refinement. Alterations in measures might follow to better reflect evolving business needs. This ongoing evolution drives the sustained value of the 8D methodology.

The 8D Problem Solving approach, with its disciplined steps, delivers a robust framework. Measuring its effectiveness requires a blend of quantitative and qualitative metrics. These metrics, when standardized and continually refined, offer a clear lens to assess the 8D process's success. They help organizations not just to solve problems but to evolve in their problem-solving capabilities.

He is a content producer who specializes in blog content. He has a master's degree in business administration and he lives in the Netherlands.

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An overview of the 8D problem-solving method

The 8D problem-solving method is a powerful tool in product management. It’s designed to help product managers tackle issues systematically and enhance product quality. This method follows eight steps in total, hence the name 8D.

The steps range from identifying problems to implementing long-term solutions. Today you’ll explore how you can effectively apply 8D to your products. You’ll also learn about the benefits of using this approach and analyze some real case studies.

What is 8D?

The 8D problem-solving method is designed to address and resolve problems by identifying, correcting, and eliminating recurring issues.

It involves eight different steps:

• Plan — Prepare for the problem-solving process
• Team selection — Assemble a team with the necessary knowledge and skills
• Problem definition — Clearly define the problem and its impact
• Interim containment action — Implement temporary measures to contain the problem
• Root cause identification — Identify the underlying cause(s) of the problem
• Permanent corrective action — Develop and implement a solution to address the root cause
• Preventive measures — Take steps to prevent the recurrence of the problem
• Team recognition — Acknowledge and reward the team’s efforts in resolving the issue

These steps focus on root cause analysis, preventive measures, and long-term solution implementation. The end goal is to improve product quality and operational efficiency.

The eight disciplines of 8D

The eight disciplines of the 8D method represent a comprehensive approach to solve problems within an organization. Each discipline is designed to guide teams through the process at each stage. Here’s a deeper look into each stage:

This initial step involves preparing for the problem-solving process. The goal here is to understand the problem’s magnitude and set up objectives. It’s about getting ready to tackle the issue systematically.

Team selection

In this step, a cross-functional team is formed. The team should consist of individuals with the necessary knowledge, skills, and experience to address the problem effectively. The team works together throughout the 8D process.

Problem definition

Next, the team has to describe the issue in specific terms. The goal here is to understand the impact and scope of the complication. A well-defined problem is easier to solve.

Interim containment

In the process of finding a solution, temporary measures are taken to contain the problem and prevent it from worsening. This reduces further damage or impact to the involved operations.

Root cause identification

In this phase, the team uses various tools and techniques to identify the underlying cause of the problem. An understanding of the root cause is essential for developing an effective, lasting solution.

Permanent corrective action

With the root cause identified, the team moves to develop a permanent corrective action plan to resolve the issue. Now, the team needs to choose the best solution, implement it, and monitor its effectiveness. This analysis will ensure that the problem is truly resolved.

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Preventive measures

With such vast processes, there is always a possibility of the problem recurring. To resolve this, the team identifies and implements measures that address the root cause. There might be a need for changes to different aspects of the overall approach.

Team recognition

The final stage focuses on acknowledging and rewarding the team’s efforts. Recognizing the team’s hard work and success in resolving the issue is important for morale. It also promotes a culture of continuous improvement.

By following these eight disciplines, product managers can solve problems more effectively. The other benefit is that it builds a proactive culture that addresses issues before they escalate.

Applying 8D in product management

Applying the 8D problem-solving method in product management involves leveraging its structured approach. This helps you eliminate problems and process improvement initiatives.

Problem identification

The 8D process begins with gathering data and feedback to quickly identify potential issues. After that, a diverse team from various departments works together to uncover issues. And finally, the team solves the problems efficiently.

Once a problem is spotted, quick fixes are applied to limit its impact. Simultaneously, you explore root causes of an issue using methods like the Five Whys . The final step is to implement the solution based on these insights. Occasionally, redesigns or process upgrades are also used to resolve the issue thoroughly.

Elimination

To eliminate recurring problems, it’s crucial to establish preventive measures. Several steps support the main goal of elimination including process adjustments, quality control improvements, and updates to design standards.

The insights gathered from each 8D cycle help with continuous improvement. It also aids in formulating strategies to avert future issues.

Benefits of the 8D method

The main benefit of using the 8D method is its impact on teamwork and continuous improvement. The more obvious benefits focus on root cause analysis and prevention of issues:

• Enhanced quality control
• Efficient problem resolution
• Systematic and thorough approach
• Teamwork and knowledge sharing
• Focus on root cause analysis
• Reduced recurrence of issues
• Cost reduction
• Improved customer satisfaction

The systematic approach to address issues ensures that no effort goes to waste. Eventually, it helps the teams to quickly propose long-term solutions to a range of problem patterns.

Challenges in implementing 8D

The 8D problem-solving method is extremely valuable when used in the right manner. However, there can be challenges at every stage of this process. Because of this, it’s beneficial for you to have an understanding of how to quickly identify these challenges.

These include:

• Resistance to change among team members
• Insufficient teamwork and collaboration
• Lack of training on the 8D methodology
• Difficulties in data collection and analysis

How to solve them?

• Clearly communicate benefits to overcome resistance
• Foster collaboration and teamwork among participants
• Provide targeted training on the 8D process
• Encourage data analysis for effective problem-solving

For a deeper understanding, let’s take a look at two case studies of how the 8D process can enhance the product management workflow.

Real-life examples of 8D

A leading tech company, (similar to Apple) faced public backlash over smartphones overheating and reduced battery life. In this context, the 8D method helped to quickly identify and contain the issues.

The root cause analysis helped it track the problem back to a battery design flaw. Collaborative efforts with the battery supplier led to a redesigned battery and an update to the operating system. This not only resolved the issue but also restored consumer trust. Eventually, the brand’s reputation for quality was restored.

Similarly, a major automaker found a software glitch in its driver-assistance systems. This issue was risking driver safety. Using the 8D method, it pinpointed outdated algorithms as the root cause. The solution was simple, it issued a software update and enhanced its development processes.

Both of these examples are evidence of how the 8D method can be utilized to prevent complications efficiently.

Key takeaways

In wrapping up, it’s clear that this approach is more than just a procedure. Think of it as a strategic framework designed for the product manager. The 8D method equips you with a robust toolkit for addressing and preempting issues, systematically.

On top of that it helps you to:

• Promote teamwork and continuous improvement
• Reduce problem recurrence through root cause analysis
• Overcome implementation challenges with effective communication

Feel free to comment with any questions you may have!

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8D Chess: How to Use The 8 Disciplines for Problem Solving

Hospitals have developed something of a reputation for being rife with bad processes . When processes aren’t adequate, the result is an abundance of “workarounds”.

For example, when equipment or supplies are missing, a nurse might waste time running around searching for what is needed, and once the item is found, return to their previous duties.

One study indicates that nurses spend 33 minutes of a 7.5-hour shift completing workarounds that are not part of their job description.

This may well “put out the fire” so-to-speak, but really it is just a hastily applied band-aid that does nothing to treat the root cause of the problem.

More time is wasted and more problems will arise in the future because nothing has been done to prevent the initial problem from happening again.

Individual nurses are not at fault here; workplace culture often values expertise in the form of those who “get the job done”, which tends to pull against the notion of spending time building good processes (time in which the job is perhaps not “getting done”).

So how to approach the problem of problem solving ?

In a lean context, problem solving can be distilled into two simple questions:

• What is the problem and how did it happen?
• How can we make sure that it doesn’t happen again?

The 8D, or eight disciplines methodology, is a problem solving process – most likely one of the most widely used problem solving processes out there. It is used by many different countries, in many different industries, and many different organizations.

8D is designed to help you put out those fires, and make sure they don’t happen again.

In this article, I’ll introduce you to the 8D problem solving methodology and provide you with an outline of the basic process that you can hopefully apply in your own business, plus how you can enhance 8D with other tools and methodologies like Six Sigma , FMEA , and Process Street .

Here’s what I hope you’ll take away after reading:

• An understanding of the basics of 8D
• Advantages of using 8D
• The purpose and objectives of each phase of the 8D process
• An understanding of how to use 8D for problem solving
• How 8D works with other problem solving tools
• How you can use Process Street to maximize the potential of the 8D framework

Let’s begin with the origins of 8D – what is it, and where did it come from?

What is 8D?

8D (sometimes Global 8D or G8D) stands for eight disciplines, and is a problem solving methodology. It’s basically a process for understanding and preventing problems.

Much like how risk management seeks to take a proactive, preventative stance, 8D aims to gain insight into the root causes of why the problems happen, so they won’t happen again.

The 8D process involves eight (sometimes nine) steps to solve difficult, recurring problems. It’s a transparent, team-based approach that will help you solve more problems in your business.

8D origins: Where did it come from?

Despite the popular story that 8D originated at Ford, it was in fact developed in 1974 by the US Department of Defence, ultimately taking the form of the military standard 1520 Corrective Action and Disposition System for Nonconforming Material .

Ford took this military standard, which was essentially a process for quality management , and expanded on it to include more robust problem solving methods.

In 1987, Ford Motor Company published their manual, Team Oriented Problem Solving (TOPS) , which included their first iteration of the 8D methodology.

Initially termed Global 8D (or G8D) standard, it is currently used by Ford and many other companies in the automotive supply chain.

8D, PDSA, & other problem solving processes

The disciplines of 8D follow the same logic as the Deming Cycle (also known as PDSA, and sometimes PDCA).

PDSA stands for Plan, Do, Study, Act (or Check, in the case of PDCA).

The similarity lies in the fact that both PDSA and 8D are designed to be used to improve processes. They’re both examples of cycles of continuous improvement.

Whereas 8D may be painted as a more generic problem-solving framework, structurally speaking both 8D and PDSA share a lot in common.

The simple idea of beginning with a clear objective, or desired output, and then testing, analyzing , and iteratively tweaking in a continuous cycle is the basis for both methodologies.

There are, of course, differences. We’ll cover the different applications of both 8D and PDSA in this article.

8D advantages

One of the main strengths of 8D is its focus on teamwork. 8D philosophy encourages the idea that teams, as a whole, are more powerful than the sum of the individual qualities of each team member.

It’s also an empirical methodology; that is to say that it is a fact-based problem solving process.

A branch of continuous improvement, proper use of 8D will help you coordinate your entire team for effective problem solving and improved implementation of just about all of the processes used in your business.

The 8 disciplines for problem solving

As you may have noticed, we’re starting with zero, which makes nine total disciplines. This “zero” stage was developed as an initial planning step.

D0: Plan adequately

Make comprehensive plans for solving the problem including any prerequisites you might determine.

Be sure to include emergency response actions.

D1: Establish your team

Establish your core team with relevant product or process knowledge. This team will provide you with the perspective and ideas needed for the problem solving process.

The team should consist of about five people, from various cross-functional departments. All individuals should have relevant process knowledge.

A varied group will offer you a variety of different perspectives from which to observe the problem.

It is advisable to establish team structure, roles, and objectives as far ahead in advance as possible so that corrective action can begin as quickly and effectively as possible.

D2: Describe the problem

Have your team gather information and data related to the problem or symptom. Using clear, quantifiable terms, unpack the problem by asking:

D3: Contain the problem (temporary damage control)

Depending on the circumstances, you may need to mobilize some kind of temporary fix, or “firefighting”.

The focus of this stage should be on preventing the problem from getting worse, until a more permanent solution can be identified and implemented.

D4: Identify, describe, and verify root causes

In preparation for permanent corrective action, you must identify, describe, and verify all possible causes that could contribute to the problem happening.

You can use various techniques for this, including a Failure Modes and Effects Analysis , or Ishikawa (fishbone) diagram .

It’s important that the root causes are systematically identified, described in detail, and promptly verified (or proved). How each cause is verified will depend on the data type and the nature of the problem.

Take a look at the section towards the end of this article for some more problem solving tools to help you decide the right approach.

D5: Identify corrective actions

You must verify that the corrective action you identified will in fact solve the problem and prevent it from happening again in the future (or whatever is your desired threshold of recurrence).

The best way to do this is to collect as much data as possible and by performing smaller-scale “pilot” tests to get an idea of the corrective action’s impact.

You can’t begin to identify the optimal corrective action until you have identified the root cause(s) of the problem.

D6: Implement and validate corrective actions

Carry out the corrective actions, and monitor short and long term effects. During this stage, you should assess and validate the corrective actions with empirical evidence.

Discuss and review results with your team.

D7: Take preventative measures (to avoid the problem happening again)

Here is where you make any necessary changes to your processes, standard operating procedures , policies , and anything else to make sure the problem does not happen again.

It may not be possible to completely eliminate any chance of the problem recurring; in that case, efforts should focus on minimizing possibility of recurrence as much as possible.

D8: Congratulate your team

It’s important to recognize the joint contribution of each and every one of the individuals that were involved in the process.

Team members should feel valued and rewarded for their efforts; this is crucial and perhaps the most important step – after all, without the team, the problem would not have been fixed.

Providing positive feedback and expressing appreciation helps to keep motivation high, which in turn improves the sense of process ownership and simply increases the likelihood your team will actually want to improve internal processes in the future.

How to use 8D for problem solving

The 8D method above outlines a proven strategy for identifying and dealing with problems. It’s an effective problem solving and problem prevention process.

In addition to avoiding long-term damage from recurring problems, 8D also helps to mitigate customer impact as much as possible.

More than just a problem-solving methodology, 8D sits alongside Six Sigma and other lean frameworks and can easily be integrated with them to minimize training and maximize efficacy.

8D is definitely a powerful framework on its own, but it really shines when combined with other synergistic concepts of lean and continuous improvement.

More problem solving tools that synergize well with 8D

8D has become a leading framework for process improvement, and in many ways it is more prescriptive and robust than other more simplistic Six Sigma approaches.

However, there are many Six Sigma methodologies, and even more frameworks for problem solving and process improvement .

The following improvement tools are often used within or alongside the 8D methodology.

DMAIC: Lean Six Sigma

DMAIC stands for:

The DMAIC process is a data-driven cycle of process improvement designed for businesses to help identify flaws or inefficiencies in processes.

Simply put, the goal with DMAIC is to improve and optimize existing processes.

Interestingly, the development of the DMAIC framework is credited to Motorola , whose work built upon the systems initially developed by Toyota .

In terms of working alongside 8D, you could use DMAIC to identify root causes as in D4; you could also implement the same techniques to better understand prospects for corrective actions as in D5, and D6.

We have a whole article on the DMAIC process, if you’re interested.

SWOT analysis

Strengths, Weaknesses, Opportunities, and Threats. You can use a SWOT analysis to gain insight into your organization as a whole, or on individual processes.

The main synergy with 8D is in the identification of opportunities, threats, and weaknesses.

These can represent opportunities for process improvements, weaknesses in your process that could produce problems further down the line, and threats, both internal and external, that may be out of your direct control but that could cause problems for you.

Here’s a SWOT analysis checklist you can use to structure your own analysis:

FMEA: Failure Mode and Effects Analysis

FMEA (Failure Mode and Effects Analysis) is a way of understanding the potential for problems and making preemptive preparations in order to avoid them. It is a method of risk management .

It is a type of preventative risk management process, and so works well in the context of identifying causes of problems so you can better deal with them.

FMEA and 8D work well together because:

• 8D can make use of information gathered during an FMEA process, like brainstorming sessions, to identify potential problems and their root causes.
• You can reuse possible cause information gathered during an FMEA process to feed into different representational diagrams like the Ishikawa (fishbone) diagram, which will help in the 8D process.
• 8D brainstorming data is useful for new process design. This allows the FMEA to take actual process failures into account, which produces more effective results.
• FMEA completed in the past can be used as databases of potential root causes of problems to inform 8D process development.

Here’s a free FMEA template for you to get started ASAP:

The Pareto Chart

The Pareto Chart helps us understand the impact of different variations of input on our output.

In relation to 8D, Pareto Charts can help us prioritize which root cause to target, based on which will have the greatest impact on improvement (where improvement is the desired output of the 8D process).

Here’s the Six Sigma Institute’s example Pareto Chart :

Here we have a simple deductive reasoning technique that asks “why?” five times to dig into the root cause of a problem.

The logic here is that by asking the same question five times, you work progressively “deeper” into the complexity of the problem from a single point of focus.

Ideally, by the fifth question you should have something that has a high likelihood of being a root cause.

This example from Wikipedia does a great job of conveying how the process works:

• The vehicle will not start. (the problem)
• Why? – The battery is dead. (First why)
• Why? – The alternator is not functioning. (Second why)
• Why? – The alternator belt has broken. (Third why)
• Why? – The alternator belt was well beyond its useful service life and not replaced. (Fourth why)
• Why? – The vehicle was not maintained according to the recommended service schedule. (Fifth why, a root cause)

Ishikawa diagrams (fishbone diagrams)

Sometimes called “cause-and-effect diagrams”, they are as such used to visualize the cause and effect of problems.

The approach takes six different categories and places information about the problem into different categories to help you understand what factors could be contributing to the problem.

One advantage over the 5 Whys approach is the way this method forces a more holistic perspective, as opposed to the potentially narrow vantage point offered by zooming in on a single aspect or question.

According to the Six Sigma Institute, the 6 key variables pertaining to root causes of problems are:

• Machine: Root causes related to tools used to execute the process.
• Material: Root causes related to information and forms needed to execute the process.
• Nature: Root causes related to our work environment, market conditions, and regulatory issues.
• Measure: Root causes related to the process measurement.
• Method: Root causes related to procedures, hand-offs, input-output issues.
• People: Root causes related people and organizations.

There’s also this useful illustration of a company using a fishbone diagram to better understand what factors contribute to a company’s high turn around time.

Gap analysis

A gap analysis is concerned with three key elements:

• The current situation, or “performance”
• The ideal situation, or “potential”
• What needs to be done in order to get from performance to potential, or “bridging the gap”

The “gap” is what separates your current situation from your ideal situation.

Businesses that perform a gap analysis can improve their efficiency and better understand how to improve processes and products.

They can help to better optimize how time, money, and human resources are spent in business.

There’s a lot that goes into a gap analysis, and quite a few different ways to approach it. Check out our article for a deeper dive into the gap analysis process.

Superpowered checklists

Checklists can be a great way to simplify a complex process into a series of smaller, easy-to-manage tasks. They’re one of the best ways to start using processes in your business.

By using checklists, you can reduce the amount of error in your workflow , while saving time and money by eliminating confusion and uncertainty.

What’s more, if you’re using Process Street, you have access to advanced features like conditional logic , rich form fields and streamlined template editing .

How to use Process Street for 8D problem solving

Good problem solving relies on good process. If you’re trying to solve problems effectively, the last thing you want is your tools getting in your way.

What you want is a seamless experience from start to finish of the 8D methodology.

The best kinds of processes are actionable. That’s why you should consider using a BPM software like Process Street to streamline recurring tasks and eliminate manual work with automation .

Process Street’s mission statement is to make recurring work fun, fast, and faultless. By breaking down a process into bite-sized tasks , you can get more done and stay on top of your workload.

Sign up today for a free Process Street trial!

Problem solving is an invaluable skill. What’s your go-to process for problem solving? We’d love to know how it compares with the 8D method. Let us know in the comments!

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Oliver Peterson

Oliver Peterson is a content writer for Process Street with an interest in systems and processes, attempting to use them as tools for taking apart problems and gaining insight into building robust, lasting solutions.

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What is 8D? A template for efficient problem-solving

How you respond when problems arise is one of the most defining qualities of a manager. Luckily, there are tools you can use to master problem-solving. The 8D method of problem-solving combines teamwork and basic statistics to help you reach a logical solution and prevent new issues from arising.

You’ve spent months overseeing the development of your company's newest project. From initiation, planning, and execution, you’re confident this may be your best work yet.

Until the feedback starts rolling in.

There’s no sugar-coating it—things don’t always go as planned. But production or process issues are hardly a signal to throw in the towel. Instead, focus on honing your problem-solving skills to find a solution that keeps it from happening again. 

The 8D method of problem solving emphasizes the importance of teamwork to not only solve your process woes but prevent new ones from occurring. In this guide, we’ll break down what 8D is, how to use this methodology, and the benefits it can give to you and your team. Plus, get an 8D template to make solving your issue easier. 

What is 8D?

The eight disciplines (8D) method is a problem-solving approach that identifies, corrects, and eliminates recurring problems. By determining the root causes of a problem, managers can use this method to establish a permanent corrective action and prevent recurring issues. 

How do you use the 8D method?

The 8D method is a proven strategy for avoiding long-term damage from recurring problems. If you’re noticing issues in your workflow or processes, then it’s a good time to give this problem-solving method a try. 

To complete an 8D analysis, follow “the eight disciplines” to construct a statistical analysis of the problem and determine the best solution.

The eight disciplines of problem-solving

8D stands for the eight disciplines you will use to establish an 8D report. As you may notice, this outline starts with zero, which makes nine total disciplines. The “zero stage” was developed later as an initial planning stage. 

To illustrate these steps, imagine your organization experienced a decline in team innovation and productivity this past year. Your stakeholders have noticed and want to see changes implemented within the next six months. Below, we’ll use the 8D process to uncover a morale-boosting solution.

D0: Prepare and plan

Before starting the problem-solving process, evaluate the problem you want to solve. Understanding the background of the problem will help you identify the root cause in later steps. 

Collect information about how the problem has affected a process or product and what the most severe consequences may be. Planning can include:

Gathering data

Determining the prerequisites for solving the problem

Collecting feedback from others involved

If we look back at our example, you may want to figure out whether this decline in morale is organization-wide or only applies to a few departments. Consider interviewing a few employees from different departments and levels of management to gain some perspective. Next, determine what knowledge and skills you will need to solve this lapse in productivity. 

D1: Form your team

Create a cross-functional team made up of people who have knowledge of the various products and workflows involved. These team members should have the skills needed to solve the problem and put corrective actions in place. 

Steps in this discipline may include:

Appointing a team leader

Developing and implementing team guidelines

Determining team goals and priorities

Assigning individual roles

Arranging team-building activities

From our example, a solid team would consist of people with first-hand experience with the issues—like representatives from all departments and key people close to workshop-level work. You may also want to pull someone in from your HR department to help design and implement a solution. Most importantly, make sure the people you choose want to be involved and contribute to the solution.

D2: Identify the problem

You may have a good understanding of your problem by now, but this phase aims to break it down into clear and quantifiable terms by identifying the five W’s a and two H’s (5W2H):

Who first reported the problem?

What is the problem about?

When did it occur and how often?

Where did it occur (relating to the sector, supplier, machine, or production line involved)?

Why is solving the problem important?

How was the problem first detected?

How many parts/units/customers are affected?

Use your team’s insights to answer these questions. From our example, your team may conclude that: 

Employees feel overwhelmed with their current workload. 

There is no real structure or opportunity to share new ideas.

Managers have had no training for meetings or innovation settings.

Disgruntled employees know they can achieve more—and want to achieve more—even if they seem disengaged.

Once you answer these questions, record an official problem statement to describe the issue. If possible, include photos, videos, and diagrams to ensure all parties have a clear understanding of the problem. It may also help to create a flowchart of the process that includes various steps related to the problem description.

D3: Develop an interim containment plan

Much like we can expect speedy first aid after an accident, your team should take immediate actions to ensure you contain the problem—especially if the problem is related to customer safety. 

An interim containment plan will provide a temporary solution to isolate the problem from customers and clients while your team works to develop a permanent corrective action. This band-aid will help keep your customers informed and safe—and your reputation intact.

Because your findings revealed workers were overworked and managers lacked training, your team suggests scheduling a few mandatory training sessions for leaders of each department covering time and stress management and combating burnout . You may also want to have a presentation outlining the topics of this training to get key managers and stakeholders interested and primed for positive upcoming changes. 

D4: Verify root causes and escape points

Refer back to your findings and consult with your team about how the problem may have occurred. The root cause analysis involves mapping each potential root cause against the problem statement and its related test data. Make sure to test all potential causes—fuzzy brainstorming and sloppy analyses may cause you to overlook vital information. 

In our example, focus on the “why” portion of the 5W2H. You and your team identify six root causes:

Managers have never had any training

There is a lack of trust and psychological safety

Employees don’t understand the objectives and goals

Communication is poor

Time management is poor

Employees lack confidence

In addition to identifying the root causes, try to pinpoint where you first detected the problem in the process, and why it went unnoticed. This is called the escape point, and there may be more than one. 

D5: Choose permanent corrective actions

Work with your team to determine the most likely solution to remove the root cause of the problem and address the issues with the escape points. Quantitatively confirm that the selected permanent corrective action(s) (PCA) will resolve the problem for the customer. 

Steps to choosing a PCA may include:

Determining if you require further expertise

Ensuring the 5W2Hs are defined correctly

Carrying out a decision analysis and risk assessment

Considering alternative measures

Collecting evidence to prove the PCA will be effective

Your team decides to roll out the training used in the interim plan to all employees, with monthly company-wide workshops on improving well-being. You also plan to implement meetings, innovation sessions, and team-coaching training for managers. Lastly, you suggest adopting software to improve communication and collaboration. 

D6: Implement your corrective actions

Once all parties have agreed on a solution, the next step is to create an action plan to remove the root causes and escape points. Once the solution is in effect, you can remove your interim containment actions.

After seeing success with the training in the interim phase, your stakeholders approve all of your team’s proposed PCAs. Your representative from HR also plans to implement periodic employee wellness checks to track employee morale .

To ensure your corrective action was a success, monitor the results, customer, or employee feedback over a long period of time and take note of any negative effects. Setting up “controls” like employee wellness checks will help you validate whether your solution is working or more needs to be done. 

D7: Take preventive measures

One of the main benefits of using the 8D method is the improved ability to identify necessary systematic changes to prevent future issues from occurring. Look for ways to improve your management systems, operating methods, and procedures to not only eliminate your current problem, but stop similar problems from developing later on.

Based on our example, the training your team suggested is now adopted in the new manager onboarding curriculum. Every manager now has a “meeting system” that all meetings must be guided by, and workloads and projects are managed as a team within your new collaboration software . Innovation is improving, and morale is at an all-time high!

D8: Celebrate with your team

The 8D method of problem-solving is impossible to accomplish without dedicated team members and first-class collaboration. Once notes, lessons, research, and test data are documented and saved, congratulate your teammates on a job well done! Make an effort to recognize each individual for their contribution to uncovering a successful solution.

8D report template and example

Check out our 8D report template below to help you record your findings as you navigate through the eight disciplines of problem solving. This is a formal report that can be used as a means of communication within companies, which makes for transparent problem-solving that you can apply to the entire production or process chain.

Benefits of using the 8D method

The 8D method is one of the most popular problem-solving strategies for good reason. Its strength lies in teamwork and fact-based analyses to create a culture of continuous improvement —making it one of the most effective tools for quality managers. The benefits of using the 8D method include: 

Improved team-oriented problem-solving skills rather than relying on an individual to provide a solution

Increased familiarity with a problem-solving structure

A better understanding of how to use basic statistical tools for problem-solving

Open and honest communication in problem-solving discussions

Prevent future problems from occurring by identifying system weaknesses and solutions

Improved effectiveness and efficiency at problem-solving

Better collaboration = better problem solving

No matter how good a manager you are, production and process issues are inevitable. It’s how you solve them that separates the good from the great. The 8D method of problem solving allows you to not only solve the problem at hand but improve team collaboration, improve processes, and prevent future issues from arising. 

Try Asana’s project management tool to break communication barriers and keep your team on track.

Related resources

What is stakeholder analysis and why is it important?

How Asana uses work management to optimize resource planning

Understanding dependencies in project management

Program manager vs. project manager: Key differences to know

Mastering the 8D Problem Solving Method: A Comprehensive Guide

It is often said that “a stitch in time saves nine.” Efficient problem-solving is an essential skill , especially in a professional environment.

When it comes to addressing complex issues, the 8D Problem Solving method has gained significant traction across various industries. In this comprehensive guide, we will explore the 8D Problem Solving method, its history, and its application across multiple sectors.

History of the 8D Problem Solving Method

The 8D Problem Solving approach has its origins in World War II when the American military was under intense pressure to produce reliable weapons as quickly as feasible.

The military established a methodical approach to problem-solving, focusing on quality control and continual improvement, to ensure that resources were used effectively.

This was the first instance of what would later develop into the 8D technique.

The writings of Walter Shewhart , W. Edwards Deming , and Joseph M. Juran , who set the groundwork for contemporary quality control and continuous improvement ideas, had a substantial impact on the development of the 8D Problem Solving approach.

These guidelines stress the value of data-driven decision-making and the necessity for businesses to take a pro-active approach to problem-solving.

The Ford Motor Company faced intense competition from Japanese automakers in the 1980s, which caused it to struggle.

Ford used quality control and continuous improvement as its guiding principles and included the 8D Problem Solving process into its business practices to regain its footing.

The automobile sector adopted the 8D methodology widely as a result of the initiative’s success.

The 8D Problem Solving approach gained popularity outside of the automobile industry as it showed continuous promise.

The 8D methodology is now being used by businesses in a variety of industries, such as manufacturing, healthcare, and technology, to solve complicated issues, enhance their operations, and guarantee customer happiness.

The 8D Problem Solving approach has attained widespread acceptance throughout a number of industries.

It is a potent tool for businesses looking to improve their problem-solving skills and promote long-term success due to its systematic approach, emphasis on teamwork, and emphasis on continual improvement.

The Eight Disciplines of 8D Problem Solving

D1: Form a Team

Assembling a diverse team with relevant expertise

The first phase in the 8D process is to put together a varied team of people with the necessary knowledge, making sure that all viewpoints and skill sets are represented. This multidisciplinary approach makes it easier to recognize problems and produce creative solutions.

Defining roles and responsibilities

The tasks and responsibilities of each team member must be established once the team has been constituted. Team members can work cooperatively and effectively by setting clear expectations, ensuring that everyone’s abilities are utilized to the utmost extent. It keeps the problem-solving process on track and upholds accountability.

D2: Define the Problem

Accurate problem description

Accurately characterizing the current problem is the second discipline of the 8D technique. In order to do this, the team must acquire pertinent data, analyze it, and create a clear, succinct statement describing the problem. A focused and efficient problem-solving approach is built on a well identified problem.

Gathering data and identifying root causes

To create long-lasting solutions, the problem’s underlying causes must be determined. The team must gather information from a variety of sources, such as consumer feedback, product testing, or process performance measurements, in order to accomplish this. The team is able to uncover patterns, trends, and potential fundamental causes thanks to this data-driven approach, which also ensures that the problem-solving procedure is unbiased and grounded in facts.

D3: Develop an Interim Containment Plan

Quick, temporary solutions

Minimizing the effects of a problem is crucial in the field of problem solving. Creating an interim containment strategy, which offers quick, temporary solutions to the issue, is the third discipline in the 8D technique. These quick fixes aid in limiting the harm, stopping more problems, and buying the team some time while they produce a more long-term fix.

Mitigating damage and preventing further issues

It is essential to keep an eye on the interim containment plan’s efficacy and adjust as necessary as you go. This guarantees that the short-term fix works to contain the harm and stop the issue from getting worse. Any lessons learnt during this phase should also be recorded by the team because they will be helpful in creating the ultimate corrective action.

D4: Identify Root Causes

Root cause analysis techniques

The fourth discipline of the 8D technique entails examining the issue more closely in order to determine its underlying causes. Various root cause analysis methods, including the Five Whys, Fishbone Diagram, and Fault Tree Analysis, must be used in this situation. The team may create focused solutions that address the issue at its source rather than just treating its symptoms by determining the fundamental causes of the problem.

Verifying root causes through data

Verifying potential root causes with data is crucial after the team has discovered them. Taking this step, the team can avoid being misled by assumptions or unrelated elements and instead concentrate on the real core cause. The team may be confident that their suggested remedies will be successful in tackling the problem by validating the main causes using data.

D5: Choose and Verify Permanent Corrective Actions

Developing and evaluating potential solutions

The team can now consider various solutions after determining the root reasons. “Two heads are better than one,” as the saying goes, and this collaborative process frequently produces innovative and useful ideas. The team should assess each alternative after producing a list of potential corrective actions based on elements including feasibility, cost, and potential impact. This makes it more likely that the selected solution will be both workable and efficient.

Implementing and verifying chosen solution

It’s crucial to assess the effectiveness of the chosen solution before fully applying it. A small-scale trial or a pilot program can be used to accomplish this. The team may be certain that their selected corrective action will be successful when used on a bigger scale by confirming the solution’s success in resolving the issue.

D6: Implement Permanent Corrective Actions

Developing a detailed action plan

The team must create a thorough action plan for putting the selected solution into practice when it has been verified. This strategy should specify the actions, materials, and timetable required for a full integration of the solution into the organization’s operations. A comprehensive action plan makes for an effective implementation that minimizes any hiccups or setbacks.

Monitoring implementation and adjusting as needed

It’s essential to keep an eye on the permanent remedial action’s development and adjust, as necessary. The team may make sure that the solution is properly integrated and produces the required results by remaining alert and reacting to any unforeseen obstacles.

D7: Prevent Recurrence

Identifying potential future issues

The 8D method’s seventh discipline focuses on predicting prospective problems that might develop in the future from comparable underlying causes. The team can help to prevent repeat incidences and continuously enhance the organization’s procedures by foreseeing and addressing these possible issues.

Adjusting processes and procedures to prevent recurrence

The team should analyze and make any necessary modifications to the organization’s systems and procedures to stop the issue from happening again. This can entail creating new quality control procedures, updating the documentation, or changing the training materials. Implementing these changes, the company can promote a climate of continuous development and make sure that the lessons discovered throughout the problem-solving procedure are incorporated into every aspect of its day-to-day work.

D8: Congratulate the Team

Recognizing team achievements

It’s important to acknowledge the team’s effort and commitment when the 8D technique has been implemented successfully. Celebrating their accomplishments promotes a sense of ownership, boosts morale, and encourages continuing commitment to ongoing growth.

Sharing lessons learned with the organization

The team should share their lessons learned with the broader organization. Doing so, they can help to disseminate the knowledge gained during the problem-solving process, fostering a culture of learning and improvement throughout the company.

Practical Application of the 8D Problem Solving Method

Numerous industries, including aerospace, automotive, healthcare, manufacturing, and technology, have successfully used the 8D Problem Solving method. These actual instances show how adaptable and successful the system is at solving a variety of challenging issues .

Although the 8D method offers a structured approach to problem-solving, it is crucial to customize the procedure to the particular requirements and context of the current problem.

This could entail modifying the chronology, modifying the root cause analysis methods, or adding new data sources.

The team can ensure the most efficient problem-solving procedure by continuing to be adaptable and flexible.

Tips for Successful 8D Problem Solving Implementation

Emphasizing clear communication

Clear communication is the lifeblood of effective problem-solving.

Throughout the 8D process, the team should prioritize open and honest communication, ensuring that all members have a thorough understanding of the problem, the chosen solution, and their individual responsibilities.

Fostering a culture of collaboration and continuous improvement

A collaborative and improvement-focused culture is key to the success of the 8D method.

Encouraging open dialogue, mutual support, and ongoing learning, the organization can create an environment in which the 8D method can thrive.

Employing project management tools and techniques

Project management tools and techniques can be invaluable in facilitating the 8D process.

Using tools such as Gantt charts, project management software, or Kanban boards, the team can better track progress, allocate resources, and manage timelines.

These tools can help to keep the problem-solving process organized and efficient, ensuring that the team stays on track and achieves their goals.

Final Thoughts

The 8D Problem Solving method is an effective and adaptable way for tackling complicated challenges in a variety of industries.

Organizations may methodically identify and address problems, stop them from happening again, and promote a culture of continuous improvement and adhering to the eight disciplines.

As we’ve seen, the 8D method’s effectiveness depends on putting together a varied team, upholding clear communication, customizing the procedure for particular circumstances, and using efficient project management tools and approaches.

We urge you to use the 8D Problem Solving method inside your organization now that you have a thorough understanding of it.

Doing this, you may not only address issues more quickly, but also unleash the long-term growth potential of your company.

If you can master the 8D approach, your business will have a better future and you’ll be well-equipped to traverse the waters of problem-solving.

Q: What is the 8D Problem Solving method?

A : A systematic strategy for addressing complicated challenges across multiple industries is the 8D Problem Solving method. It consists of eight disciplines that help firms recognize problems, find solutions, stop them from happening again, and promote a continuous improvement culture.

Q: What are the origins of the 8D Problem Solving method?

A : The United States military created a systematic approach to problem-solving during World War II that was centered on quality control and continual improvement, and this is where the 8D technique got its start. The Ford Motor Company later adopted and promoted the technique in the 1980s.

Q: What are the eight disciplines of the 8D Problem Solving method?

A : The eight disciplines of the 8D method are

• Form a Team
• Define the Problem
• Develop an Interim Containment Plan
• Identify Root Causes
• Choose and Verify Permanent Corrective Actions
• Implement Permanent Corrective Actions
• Prevent Recurrence
• Congratulate the Team

Q: How can the 8D method be applied across different industries?

A : The 8D method is adaptable and may be used to solve a wide variety of complicated problems in a number of different industries, including manufacturing, aerospace, automotive, healthcare, and technology. Organizations should modify the process to match the particular requirements and context of the current challenge in order to utilize the 8D technique effectively.

Q : What are some tips for successfully implementing the 8D Problem Solving method?

A : To ensure the success of the 8D method, organizations should

• Emphasize clear communication.
• Foster a culture of collaboration and continuous improvement.
• Employ effective project management tools and techniques .

Q: What is the role of root cause analysis in the 8D method?

A : The 8D method’s key element is root cause analysis, which identifies the root reasons of an issue. Organizations can create focused solutions that solve the issue at its foundation rather than just masking the symptoms by addressing the root causes.

Q: How can the 8D method help prevent the recurrence of problems?

A : By recognizing potential future issues that may result from comparable root causes and modifying processes and procedures accordingly, the 8D technique aids in preventing the recurrence of problems. This proactive strategy assists companies in making continuous improvements and reducing the possibility that similar issues will arise again.

Ronnie Patterson

Ronnie Patterson, founder of MagnÜron, is a multifaceted entrepreneur with a diverse background in music, electronics engineering, and engineering management. Drawing on experience across various industries, He offers expertise in SEO, operations, and strategy to help businesses thrive. Possessing a unique perspective and unwavering commitment to collaboration, and ideal partner for growth and success.

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Mastering 8d problem solving: a comprehensive guide for businesses.

Table of contents

• What is 8D Problem Solving?
• The 8 Disciples of Problem Solving
• Implementing 8D Problem Solving Methodology

Example of Successful 8D Problem Solving

• Common Challenges and Best Practices

Measuring the Effectiveness of 8D Problem-Solving Efforts

Problem solving is a vital skill for any business that wants to survive and thrive in today’s competitive and dynamic environment. However, not all problems are created equal. Some are simple and straightforward, while others are complex and multifaceted. How can businesses effectively tackle these challenging problems and prevent them from recurring?

One of the most powerful and proven problem-solving methodologies is 8D problem solving. 8D stands for eight disciplines, which are a series of steps that guide teams through the process of identifying, analyzing, resolving, and preventing problems. 8D problem solving can help businesses improve their quality, reduce their costs, and enhance their customer satisfaction.

What is 8D Problem Solving

8D problem solving is a structured and systematic approach to solving complex problems that require cross-functional collaboration and root cause analysis. It was developed by Ford Motor Company in the late 1980s as a way to address customer complaints and improve product quality. Since then, it has been widely adopted by many organizations across various sectors.

The core principles and objectives of 8D problem solving are:

• Focus on the customer’s needs and expectations
• Involve a multidisciplinary team with relevant expertise and authority
• Use data and facts to support decision making
• Identify and eliminate the root causes of the problem
• Implement corrective actions that prevent reoccurrence
• Document and communicate the problem-solving process and results

The 8D methodology differs from other problem-solving approaches in several ways. First, it emphasizes team-oriented problem-solving. Second, it follows a sequential and logical order of steps that ensures thoroughness and consistency. Third, it uses various tools and techniques to facilitate analysis and action. Fourth, it incorporates feedback loops and verification methods to ensure effectiveness and sustainability.

The Eight Disciples of Problem Solving

D1: establish the team.

The first step in the 8D approach is to form a team that will work on the problem. The team should consist of members who have knowledge, experience, or involvement in the problem area. The team should also have a leader who will coordinate the activities and communicate with stakeholders.

The purpose of establishing the team is to:

• Define the roles and responsibilities of each team member
• Establish the scope and boundaries of the problem
• Set the goals and expectations for the problem-solving process
• Allocate the resources and time required for the process

D2: Describe the Problem

The second step in this problem-solving method is to define and describe the problem in detail. The team should use data and facts to describe the problem as accurately as possible. The team should also use tools such as the 5W2H method (who, what, where, when, why, how, how much), Six Sigma, or an IS/IS NOT matrix to clarify the aspects of the problem.

Defining and describing the problem allows businesses to:

• Establish a common understanding of the problem among the team members
• Identify the symptoms, effects, and impacts of the problem
• Quantify the magnitude and frequency of the problem
• Specify the criteria for evaluating potential solutions

D3: Develop Interim Containment Actions

The third step in 8D problem solving is to develop interim containment actions that will prevent or minimize the negative consequences of the problem until a permanent solution is found. The team should identify and implement actions that will isolate, control, or eliminate the causes or sources of variation that contribute to the problem.

When you develop interim containment actions, you:

• Protect the customer from defective products or services
• Reduce the risk of further damage or harm
• Maintain operational continuity and stability
• Buy time for root cause analysis and corrective actions

D4: Determine Root Causes

The fourth step in the 8D method is to determine the root causes responsible for creating or allowing the problem to occur. The team should use data analysis tools such as Pareto charts, histograms, scatter plots, or fishbone diagrams to identify possible causes. The team should also use root cause analysis techniques such as 5 Whys, fault tree analysis, or Failure Modes and Effect Analysis (FMEA) to verify or validate the causes.

The purpose of determining root causes is to:

• Understand why the problem happened
• Identify all possible factors that influence or contribute to the problem
• Eliminate superficial or symptomatic causes
• Prevent jumping to conclusions or making assumptions

D5: Choose Permanent Corrective Actions

The fifth step in 8D problem solving is to choose permanent corrective actions that will address or remove root causes permanently. The team should generate multiple possible solutions using brainstorming techniques such as SCAMPER (substitute, combine, adapt, modify, put to another use, eliminate, reverse) or TRIZ (theory of inventive problem solving). The team should also evaluate each solution using criteria such as feasibility, effectiveness, cost, risk, or impact.

Choosing permanent corrective actions helps to:

• Select the best solution that meets customer needs and expectations
• Ensure that root causes are eliminated or prevented from recurring
• Consider trade-offs between different solutions
• Plan for implementation challenges or barriers

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D6: implement permanent corrective actions.

The sixth step in 8D problem solving is to implement permanent corrective actions that were chosen in D5. The team should develop an action plan that specifies who will do what by when using tools such as Gantt charts or PDCA cycles (plan-do-check-act). The team should also execute the action plan according to schedule using tools such as checklists or standard operating procedures.

The purpose of implementing permanent corrective actions is to:

• Put the chosen solution into practice
• Monitor progress and performance during implementation
• Resolve any issues or problems that arise during the implementation
• Document changes or modifications made during implementation

D7: Prevent Recurrence

The seventh step in 8D problem solving is to prevent recurrence by ensuring that permanent corrective actions are effective and sustainable. The team should verify that root causes have been eliminated using tools such as control charts or statistical process control (SPC). The team should also validate that customer requirements have been met using tools such as surveys or audits.

Preventing reoccurrence helps to:

• Confirm that permanent corrective actions have solved the problem
• Evaluate customer satisfaction with products or services after implementation
• Identify opportunities for further improvement or optimization
• Standardize best practices or lessons learned from implementation

D8: Recognize Team Efforts

The eighth step in 8D problem solving is recognizing team efforts by acknowledging their contributions and achievements throughout the process. The team should celebrate their success by sharing their results with stakeholders using tools such as reports or presentations. The team should also appreciate their efforts by rewarding them with recognition or incentives.

The purpose of recognizing team efforts is to:

• Motivate team members for future challenges
• Build trust and rapport among team members
• Enhance team morale and cohesion
• Promote a culture of continuous improvement

Implementing 8D Problem-Solving Methodology

Implementing an 8D problem-solving methodology can be challenging for many businesses due to various factors such as organizational culture, resources, or complexity. However, with proper planning, preparation, and execution, it can be done successfully.

Here is some practical guidance on how businesses can effectively implement the 8D process:

Define clear roles & responsibilities for each discipline

One of the key factors for successful implementation is having clear roles & responsibilities for each discipline within the 8D process. Each discipline requires specific skills, knowledge, or authority that may not be available within a single person or department.

Therefore, it is important to assign appropriate roles & responsibilities for each discipline based on their expertise & involvement in the problem area.

Some examples of roles & responsibilities are:

By defining clear roles & responsibilities for each discipline, businesses can ensure accountability, transparency, and collaboration throughout the process.

Establish a common language & framework for communication

Another key factor for successful implementation is having a common language & framework for communication among team members & stakeholders. Communication is essential for sharing information, ideas, or feedback during the process.

However, communication can also be challenging due to different backgrounds, perspectives, or expectations among team members & stakeholders. Therefore, it is important to establish a common language & framework for communication that can facilitate understanding, alignment, and agreement throughout the process. Some examples of common language & framework are:

• Using standard terminology & definitions for the 8D process
• Implementing visual tools & templates to document & present the 8D process
• Using common metrics & criteria to measure & evaluate the 8D process
• Establishing feedback mechanisms & channels to communicate & collaborate during the 8D process

By establishing a common language & framework for communication, businesses can ensure clarity, consistency, and quality throughout the process.

Provide adequate training & support for team members

A third key factor for successful implementation is providing adequate training & support for team members who are involved in the 8D process. Team members need to have sufficient knowledge, skills, or confidence to perform their roles & responsibilities effectively. However, team members may not have prior experience or exposure to the 8D process or its tools & techniques. Therefore, it is important to provide adequate training & support for team members that can enhance their competence & capability during the process. Some examples of training & support are:

• Providing formal training sessions or workshops on the 8D process or its tools & techniques
• Offering coaching or mentoring from experts or experienced practitioners on the 8D process or its tools & techniques
• Contributing access to resources or references on the 8D process or its tools & techniques
• Maintaining feedback or recognition of team members’ performance or improvement during the 8D process

By providing adequate training & support for team members, businesses can ensure effectiveness, efficiency, and engagement throughout the process.

To illustrate the versatility and applicability of 8D problem solving across different industries and contexts, here is a hypothetical example of successful 8D problem solving:

Example: Reducing Customer Complaints in a Food Manufacturing Company

A food manufacturing company was facing a high rate of customer complaints due to foreign materials found in their products. The company used 8D problem solving to address this issue and improve product quality. Here are the steps they took within each discipline:

The company formed a cross-functional team consisting of representatives from quality assurance, production, engineering, and customer service. The team leader was the quality assurance manager who had the authority and responsibility to coordinate the activities and communicate with stakeholders.

The team defined and described the problem using data and facts from customer complaints and product inspection records. The team used the 5W2H method to clarify the aspects of the problem. The problem statement was: “In the past six months, we have received 25 customer complaints due to foreign materials such as metal shavings, plastic pieces, or wood chips found in our products.”

The team developed interim containment actions that would prevent or minimize the occurrence of foreign materials in their products until a permanent solution was found. The team identified and implemented measures such as increasing the frequency and intensity of product inspection, installing additional metal detectors and filters in the production line, and segregating and quarantining any products that were suspected or confirmed to contain foreign materials.

The team determined the root causes that were responsible for creating or allowing foreign materials to enter their products. They then used data analysis tools such as Pareto charts and fishbone diagrams to identify potential causes. Root cause analysis techniques such as 5 Whys to verify or validate the causes were also implemented.

Ultimately, they found that there were three main root causes:

• inadequate maintenance of equipment that resulted in metal shavings or plastic pieces falling off during operation;
• improper handling of raw materials that resulted in wood chips or other contaminants being mixed in during storage or transportation;
• lack of awareness or training of staff on how to prevent or detect foreign materials in products.

The team chose permanent corrective actions that would address or remove root causes permanently. The team generated multiple possible solutions using brainstorming techniques such as SCAMPER and TRIZ. They also evaluated each solution using criteria such as feasibility, effectiveness, cost, risk, or impact. Eventually, they selected the best solutions that met customer needs and expectations.

The solutions were:

• implementing a preventive maintenance program for equipment that included regular inspection, cleaning, and replacement of parts;
• establishing a quality control system for raw materials that included verification, testing, and labeling of incoming materials;
• conducting a training program for staff on how to prevent, detect, and report foreign materials in products.

The team implemented permanent corrective actions that were chosen in D5. An action plan that specified who would do what by when using tools such as Gantt charts and PDCA cycles was then developed. They then executed the action plan according to schedule using tools such as checklists and standard operating procedures.

The team prevented recurrence by ensuring that permanent corrective actions were effective and sustainable. They first verified that root causes had been eliminated using tools such as control charts and statistical process control (SPC). Next, they validated that customer requirements had been met using tools such as surveys and audits. After implementing permanent corrective actions, the rate of customer complaints due to foreign materials dropped by 90%.

Team efforts were recognized by acknowledging their contributions and achievements throughout the process. The team celebrated their success by sharing their results with stakeholders using tools such as reports and presentations. Management also appreciated their efforts by rewarding them with recognition or incentives such as certificates, gift cards, or bonuses.

Common Challenges and Best Practices in 8D Problem Solving

Despite its benefits and advantages,

8D problem solving can also pose some challenges for businesses that want to implement it effectively. Some of these challenges are:

• Resistance to change from staff or management who are used to existing processes or practices
• Lack of commitment or support from senior leaders who do not see the value or urgency of problem-solving
• Difficulty in defining or measuring problems
• Insufficient data or information to support analysis or decision making
• Conflicts or disagreements among team members or stakeholders due to different opinions or interests

To overcome these challenges and ensure successful 8D problem solving, businesses can adopt some best practices such as:

• Communicating the benefits and objectives of 8D problem solving to staff and management
• Securing the buy-in and sponsorship of senior leaders who can provide direction and resources
• Using clear and objective criteria to define and measure problems
• Collecting and analyzing relevant and reliable data or information
• Resolving conflicts or disagreements through constructive dialogue and compromise

To ensure that 8D problem-solving efforts are not wasted or forgotten, businesses need to measure the effectiveness and impact of their initiatives. Measuring the effectiveness of 8D problem-solving efforts can help businesses:

• Assess whether they have achieved their goals and expectations
• Evaluate whether they have improved their performance and customer satisfaction
• Identify areas for further improvement or optimization
• Demonstrate their value and credibility to stakeholders

To measure the effectiveness of 8D problem-solving efforts, businesses can use various methods such as:

• Key performance indicators (KPIs) that can be used to quantify the results or outcomes of 8D problem-solving initiatives. Some examples of KPIs are customer satisfaction scores, defect rates, cycle times, or cost savings.
• Data collection and analysis tools that can be used to gather and interpret data or information related to 8D problem-solving initiatives. Some examples of data collection and analysis tools are surveys, audits, control charts, or statistical process control (SPC).
• Periodic reviews and feedback mechanisms can be used to monitor and evaluate the progress and performance of 8D problem-solving initiatives. Some examples of periodic reviews and feedback mechanisms are reports, presentations, meetings, or feedback forms.

By measuring the effectiveness of 8D problem-solving efforts, businesses can ensure that they are continuously improving their quality, efficiency, and customer satisfaction.

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8D Problem Solving

Learn to identify, correct and eliminate recurring problems.

Next available: London, 07 Nov 2024

Members: £ 550 + VAT Non-members: £ 650 + VAT

8D is a team-based problem-solving methodology that was originally used in the automotive industry but is now used in a wide range of industry applications. It is designed to put a short-term fix in place, find the real root cause of a problem and implement a permanent long-term solution.

This highly practical and interactive course focuses on ensuring you can implement the 8D methodology and problem-solving tools immediately and apply it in a variety of scenarios, from shop floor staff needing to use the tools as part of problem-solving teams; to managers looking to drive improvements.

Who should attend?

How will i benefit.

• Have greater knowledge of the principles of problem solving 
• Understand the nine steps of 8D and the importance of working as a team
• Understand the importance of using data to support 8D problem solving
• Be able to implement the 8D approach to problem solving to support your work activity
• The importance of a structured problem-solving approach
• Overview of 8D and its aims and objectives
• A detailed view of each level of the 8D methodology
• Common aspects of problem solving that link to 8D
• Considerations for roll out of the 8D approach in your organisation

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• Design and development of processes, systems, services and products - For Chartered Engineers: ‘Apply appropriate theoretical and practical methods to the analysis and solution of mechanical engineering problems’ For Incorporated Engineers ‘Apply appropriate theoretical and practical methods to design, develop, manufacture, construct commission, operate, maintain, decommission and re-cycle mechanical engineering processes, systems, services and products’
• Professional commitment - For Incorporated and Chartered Engineers: ‘Demonstrate a personal commitment to professional standards, recognising obligations to society, the profession and the environment’

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Practical Problem Solving Tools for Factory and Office

February 5, 2022

Many tools exist to address deviations and defects, but only a few are simple yet effective to address daily issues in manufacturing, development, administration.

When starting systematic trouble-shooting, it is important to choose the right approach. Using a comprehensive method that requires 50 pages to solve a simple problem is a waste of time, while solving a complex problem with a simple tool will most likely not reveal the hidden causes. The optimal choice of Problem Solving Tools depends on the type of issues to be addressed. Before going into details, let’s first review the most common methods used today.

Comparing Popular Methods: 3W, PDCA, 8D, A3, DMAIC, 7STEP

At their core, all scientific approaches follow a similar logic: take quick action to prevent the problem from getting worse and then define the gap, analyze the gap, identify causes, take action, evaluate impact, and embed the solution so that the problem will not reoccur. 

• 3W : When the issue is small and the solution is obvious, a formal analysis is not required. The 3W-method defines  What  to do,  Who  to do it, by  When . This “quick-fix” or “just-do-it” is commonly applied at daily team meetings to contain and correct snags and minor issues.
• PDCA : The Deming or Shewhart cycle “Plan-Do-Check-Act” is the classic method, used by over 80% companies that practice systematic problem solving. PDCA is effective for medium-size problems that require a systematic analysis to uncover underlying causes.
• 8D : The eight disciplines (8D) are commonly used in automotive, and the problem-solving process (PSP) in avionics. Both methods are similar, using 8 steps to address complex problems with focus on a fast reaction to non-conformances, completing the first three steps within three days.
• A3 : The A3-report, developed by Toyota, is an 8-step improvement and problem-solving process that fits on one sheet of paper. The A3-report is most effective to address small- to medium-size problems, and to structure improvement projects.
• DMAIC : The 5-step Six Sigma process “Define-Measure-Analyze-Improve-Control” is a data-centric solving method. DMAIC is used to structure projects and solve complex situations that require statistical analysis to develop the solution, e.g. adjust process parameters to reduce yield loss.
• 7STEP : This seven-step (7S) problem-solving process shares elements with the A3 and 8D, but does not include a formal step for containment. Because of this weakness, the 7STEP process is rarely used today, replaced by 8D to address major deviations and PDCA for smaller issues.

Comparing the most-popular processes for trouble-shooting and root-cause analysis shows how similar they are. For example, the PDCA planning phase covers the first three steps in DMAIC and the first five steps in A3 and 8D. Of all those processes, there are two that stick out, that all others are based on – PDCA and 8D – they are therefore considered the “mother” and “father” of practical problem solving tools used today.

Answer 5 Questions to Select the Best Method

When it comes to choosing the right process, it merely depends on the complexity of the situation to address. The more complex or severe, the more formal steps should be applied to make sure no step is missed. Here are five questions that will help you selecting the best process:

• Is the issue small, medium, or large?
• Is the solution obvious or unknown?
• Is it reoccurring or a single incident?
• Is it a single cause or multiple causes?
• Is statistical data analysis required?

3 Practical Problem Solving Tools: Fix, Fish, Tree

There are three practical, yet effective tools to address daily issues in factory and office: The 3W or “Fix” because it is quick, simple, informal;, the PDCA or “Fish” because it is based on the Ishikawa or Fishbone diagram;, and the 8D or “Tree” because it uses logical trees to analyze complex root causes.

• Fix: use 3W (What-Who-When) for informal trouble-shooting , finding a quick action to fix a small issue within a day .
• Fish: use PDCA (Plan-Do-Check-Act) to analyze simple and repeat issues within a week , using the fishbone diagram.
• Tree: use 8D (Eight Disciplines) to systematically eliminate multiple root-causes or complex problems within a month .

Tools and Templates to Eliminate Root Causes

To encourage people to go beyond containment and quick fixes, the method they use must be simple and practical, but also effective and efficient. Over the course of several years, we have tested dozens of different templates and found that the following two forms work best by far. Why? Because the user is given a clear structure, enhanced with pictograms, and the entire solving process can be completed on a single sheet, the key for broad adoption.

The PDCA and 8D templates have proven to be extremely effective in addressing non-conformances; they are practical problem solving tools for teams in manufacturing, quality control, product development, healthcare, back office, and corporate administration to successfully resolve daily issues and prevent them from coming back. You can download the free toolkit in 22 languages here .

Use PDCA Template to Solve Simple Problems

4 Steps to Eliminate Simple Causes

• Plan-1 Record Problem : Describe what happened, where and when, and who is involved solving it.
• Plan-2 Analyze Problem : Assign potential causes to categories: Man, Method, Machine, Material, Management, Milieu (Environment).
• Plan-3 Identify Causes : Ask “why” to drill down to root causes; for complex problems, use several forms, one per branch or issue.
• Do Implement Actions : Create and implement an action plan to contain, correct, and prevent the problem from reoccurring.
• Check Results and Act : Review impact, standardize solution; close the case or initiate further actions by starting a new PDCA cycle.

Use 8D Template to Solve Complex Problems

8 Steps to Eliminate Complex Causes

• D0 Plan : Register problem and define emergency response.
• D1 Team : Identify team members to address the problem.
• D2 Problem : Grasp the situation and describe the problem.
• D3 Containment : Prevent the problem from spreading.
• D4 Diagnostics : Identify direct causes and root causes.
• D5 Correction : Define and prioritize corrective actions.
• D6 Validation : Implement actions and evaluate effectiveness.
• D7 Prevention : Systemize solutions to prevent reoccurrence.
• D8 Completion : Transfer knowledge and recognize contributors.

Become an Effective Problem Solver by Applying Practical Tools and Learning Battle-Tested Methods

Examples Of 8D Problem-Solving

Product defects are not uncommon but an organization must act quickly to eliminate them. This will ensure customers have a…

Product defects are not uncommon but an organization must act quickly to eliminate them. This will ensure customers have a good experience and the brand doesn’t suffer. In the event of a complaint, an organization can rely on the analysis of an 8D report sample to address errors and improve quality.

The 8D methodology is a structured and systematic approach to problem-solving. From an 8D problem-solving example it’s clear that it not only identifies a problem but also recognizes the weaknesses in the system. Analysis of an 8D report example prevents future occurrences of similar issues.

Examples Of 8D Reports

8d problem-solving report example, 8d problem-solving example.

An 8D problem-solving example shows the strength of this model lies in its methodology, structure and discipline. Organizations can effectively use an 8D report example to analyze defects, its root causes and ways to implement corrective actions.

Let’s have a look at these 8D reports.  

An organization had a problem with holes appearing in its metal cast toy parts. They found that about 3% of their last batch received complaints after operations due to pin-hole defects. An analysis was submitted after the purchase head asked for a full 8D report example . Here’s a look at the 8D report sample that was submitted.

D1 : Names of team members, team leader and manager.

D2 : The problem reported by the customer is described by answering the following questions:

• What is the problem? A pin-hole defect
• Who reported it? Tulip Pvt Ltd
• When did it occur? Seen in the last batch
• Why did it happen? Due to a defect in the casting base
• How much production is affected? 3% of the products are defective.

  These questions aim to simplify their approach to problem-solving.

D3 : Once the problem is defined, the defective parts are segregated.

D4 : The root cause of the problem is identified by answering the following questions:

• Why is there a pin-hole defect?
• Why are core problems arising?
• Why wasn’t the core cured properly?
• Why was drying/curing time not modified?

These questions reveal that curing time was not validated and that was the root cause of the problem.  

D5 : A permanent corrective plan is recommended to the quality assurance engineer. It is proposed that product and process should be validated for new drying time.

D6 : Permanent corrective actions are implemented. 10 samples are collected. Product and process characteristics of each sample are checked.

D7 : Preventive measures are recommended to ensure the problem doesn’t recur.

D8 : Team and individual contributions are recognized by the manager. The team leader and team members are rewarded for their efforts.  

An organization received customer complaints about shrinkage on an automobile part. The management demanded a thorough analysis based on an 8D problem-solving example . Here’s the 8D report sample that was submitted:

D1 : A team is created with supply team members, team leader and manager.

D2 : A customer complaint is used to describe the problem. The problem is established by answering the following questions:

• What is the complaint? Shrinkage on sump.
• When was it seen? In the last batch.
• Why did it happen? Due to a defect in the entrance area.
• Who reported the problem? Albert D’Souza
• How much production is affected? Nearly 2%

These questions allow the team to devise a containment plan.  

D3 : As a containment action the team decides to stop consignments and segregate the good parts immediately.

D4 : To identify the root cause, the team has to answer the questions defining the problem. They are:

• Why was there a shrinkage at the ingate area?
• Why were high pouring temperatures used?
• Why was the pyrometer reading incorrect?
• Why was the pyrometer condition not checked?

The root cause of the problem is revealed to be a faulty pyrometer.

D5 : As a permanent corrective plan, periodic checking of the pyrometer is suggested to the maintenance supervisor.

D6 : Permanent corrective action is implemented and pyrometers are scheduled for weekly checks.

D7 : Periodic checking and proper maintenance of pyrometers are factors to prevent a recurrence.

D8 : The team effort is recognized. The manager and team are praised for solving the problem.

An 8D report example will show that Root Cause Analysis (RCA) is an integral part of the 8D process. It helps managers establish problem statements, identify potential causes, compare theories and confirm the main cause of a problem. You can establish the root cause in an 8D report example by asking the most relevant questions related to the defect.

Harappa’s Structuring Problems course equips learners with frameworks to strengthen problem-solving skills. Explore the various causes behind a problem before solving it. Learn how to simplify problems, manage them better and scrutinize them in depth. The course helps professionals, managers and team leaders master logic trees, impact analysis, MECE principle and PICK framework.  Take the team to newer heights with Harappa.

Explore Harappa Diaries to learn more about topics such as What Is Problem Solving , Different Problem Solving Methods , Common Barriers To Problem Solving , and What are the essential Problem Solving Skills to classify problems and solve them efficiently.

Solving the uncapacitated facility location problem under uncertainty: a hybrid tabu search with path-relinking simheuristic approach

• Open access
• Published: 24 April 2024

Cite this article

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• David Peidro   ORCID: orcid.org/0000-0001-8678-6881 1 ,
• Xabier A. Martin 1 ,
• Javier Panadero 2 &
• Angel A. Juan 1  

The uncapacitated facility location problem (UFLP) is a well-known combinatorial optimization problem that finds practical applications in several fields, such as logistics and telecommunication networks. While the existing literature primarily focuses on the deterministic version of the problem, real-life scenarios often involve uncertainties like fluctuating customer demands or service costs. This paper presents a novel algorithm for addressing the UFLP under uncertainty. Our approach combines a tabu search metaheuristic with path-relinking to obtain near-optimal solutions in short computational times for the determinisitic version of the problem. The algorithm is further enhanced by integrating it with simulation techniques to solve the UFLP with random service costs. A set of computational experiments is run to illustrate the effectiveness of the solving method.

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1 Introduction

The facility location problem (FLP) was initially addressed by Stollsteimer [ 1 ], Kuehn and Hamburger [ 2 ], Manne [ 3 ] and Balinski [ 4 ] to determine a set of facilities that minimizes the aggregation of two inversely correlated costs: (i) the cost of opening facilities; (ii) the cost related to servicing customers from the opened facilities. In most formulations of the problem, a set of customers and a set of potential facility locations are known in advance. Likewise, the opening costs associated with each facility and the costs of servicing each customer from every potential facility are also known. Hence all inputs are deterministic insofar as they are static inputs that are given from the very beginning. So the FLP is a frequent optimization problem used in very diverse application fields, from logistics and inventory planning ( e.g. , where to allocate distribution or retailing centers in a supply chain) to telecommunication and computing networks ( e.g. , where to allocate cloud service servers in a distributed network, cabinets in optical fiber networks, etc.).

Illustrative example of a solution for the UFLP under uncertainty

As one of the most frequent optimization problems in the logistics and supply chain management area, several versions of the FLP have been analyzed in the scientific literature. The uncapacitated FLP (UFLP) assumes that each facility’s capacity is virtually unlimited or is, at least, far beyond expected customer demands. Despite being known as the simple facility location problem, the simple warehouse location problem, or the simple plant location problem for its apparent simplicity [ 5 ], the UFLP has been proved to be NP-hard [ 6 ]. Therefore, heuristic and metaheuristic approaches become a natural choice for solving large-scale instances of the UFLP in reasonably short computing times. This is because exact and approximate methods are unable to accurately solve large instances during short periods of time. Another variant is the capacitated FLP (CFLP), where each open facility has a limited servicing capacity; i.e., there is limit to customers’ demand that can be served by any single facility. According to Silva and de la Figuera [ 7 ], both Lagrangian-based heuristics and metaheuristics have been demonstrated as effective methods for solving the CFLP. The single-source CFLP (SSCFLP) also requires each customer having to be supplied by exactly one facility. As stated by Klose and Drexl [ 8 ], the SSCFLP is generally more difficult to solve than the multiple-source CFLP. In fact the SSCFLP also belongs to the class of NP-hard problems [ 9 ]. Therefore, heuristic approaches become a natural choice for solving large-scale instances of the SSCFLP in reasonably short computing times.

Uncertainty permeates all real-world systems, including supply chain management, logistics and facility locations. The inherent unpredictability of various variables poses a significant challenge in designing efficient and cost-effective solutions. Correia and Saldanha-da Gama [ 10 ] reviewed the FLP with stochastic components by exploring different methods proposed in the recent literature to optimize the FLP under uncertainty. These stochastic components arise when inputs, such as customer demands or service costs, are random variables instead of deterministic values. Effectively recognizing and accounting for this uncertainty become crucial in providing optimal solutions for real-life combinatorial optimization problems. Simulation-based optimization approaches have been proposed to tackle such problems [ 11 , 12 ]. These approaches encompass diverse optimization methods, including mathematical programming, metaheuristics, and even machine learning. In recent decades, the hybridization of metaheuristics with simulation has emerged as a popular and effective approach for solving stochastic optimization problems [ 12 ]. Simheuristics, a simulation-optimization method that combines simulation with metaheuristics, has been widely used to address various combinatorial optimization problems with stochastic elements [ 13 , 14 ]. This work proposes a novel simheuristic algorithm to address the UFLP under uncertainty by specifically considering stochastic components in the form of random service costs. These service costs can be modeled using probability distributions that can be either theoretical or empirical. Figure  1 provides an illustrative example of a solution for the UFLP under uncertainty. The example depicts the locations where facilities have been opened (indicated by red squares) and the closed facilities (represented by white squares). Customers, depicted by blue circles, are served by the open facilities to which they are actively connected. Each facility has a fixed opening cost, and servicing a customer throughout an open facility has an associated service cost, which is uncertain and, therefore, modeled as a random variable.

Accordingly, the main contributions of this paper can be summarized as follows: (i) a tabu search metaheuristic [ 15 ] to efficiently solve the UFLP in short computational times; (ii) a path-relinking approach to obtain near-optimal solutions by exploring paths that connect good quality solutions; (iii) a simheuristic algorithm that integrates the tabu search metaheuristic and path-relinking approach with simulation techniques to efficiently solve the aforementioned problem. Note that the tabu search and path-relinking algorithms are shown to be highly effective in practice for finding near-optimal or optimal solutions to large-scale optimization instances in short computational times [ 16 , 17 ]. However, without the support of simulation-based extensions like that introduced in this paper, these techniques do not account for the inherent unpredictability found in real-life systems when solving the UFLP under uncertainty.

The remainder of this paper is structured as follows: Section  2 formulates the mathematical model for the UFLP with random service costs. Section  3 reviews the literature on the UFLP under uncertainty. Section  4 presents a tabu search metaheuristic with path-relinking as a solving method for the UFLP, and how the algorithm can be extended into a simheuristic one to solve the UFLP under uncertainty. Section  5 describes the computational study performed to test the proposed solving method. Finally, Section  6 discusses the main conclusions of this work and open research lines.

2 Model formulation

By following the mixed-integer linear programming model for the deterministic UFLP proposed by Erlenkotter [ 18 ], the stochastic version of the problem can be modeled using the following set of parameters and variables

I - Set of m alternative facility locations, indexed by i .

J - Set of n customer zones, indexed by j .

\(f_i\) - Fixed cost of establishing a facility at location i .

\(C_{ij}\) - Random variable that models the cost of servicing customer j

from facility i .

\(x_{ij}\) - It takes the value 1 if the demand of customer j is supplied from

facility i , and 0 otherwise.

\(y_{i}\) - It takes the value 1 if facility i is open, and 0 otherwise.

Then the stochastic UFLP considered in this work is formulated as follows:

The objective function ( 1 ) represents the minimization of the sum of the expected total cost of servicing customers and the total fixed costs of facility establishment.

Constraint ( 2 ) ensures that the demand for each customer zone is met. Constraint ( 3 ) makes sures that customer demand can only be produced and shipped where the facility is established. Constraint ( 4 ) features probabilistic constraints. These constraints add a probabilistic aspect to the model by ensuring that the cost of serving each customer from each facility falls within a certain threshold \(c_{max}\) with a specified level of confidence \(p_0\) . This allows the model to account for the uncertainty in the cost values and helps more robust decisions to be made that consider the risk associated with the random variable \(C_{ij}\) . As discussed later, this can be considered a soft constraint, which will generate a penalty cost every time it is violated. Finally, Constraints ( 5 ) and ( 6 ) define the binary decision variables. The deterministic version of this model (considering constant costs \(c_{ij}\) instead of variable ones \(C_{ij}\) ) was implemented using Python and solved with commercial solver Gurobi to calculate the optimal values for different instances of the deterministic UFLP. In this way, the performance of the metaheuristic proposed in this work can be compared to the mathematical approach. Additionally, a simheuristic was developed to solve the stochastic version of the problem at different uncertainty levels, which is a very common situation in real-life problems.

3 Related work on the UFLP under uncertainty

The FLP was initially introduced as the plant location problem by Stollsteimer [ 1 ] and Balinski [ 4 ]. Traditionally, the FLP has been approached from several perspectives, including worst-case analysis, probabilistic analysis and empirical heuristics. Although exact algorithms for the problem can be found in the existing literature, the NP-hard nature of the FLP makes heuristics a more practical approach for quickly obtaining solutions, especially for larger and more realistic instances. One of the first works on the FLP was carried out by Efroymson and Ray [ 19 ], who developed a branch-and-bound algorithm. They utilize a compact formulation of the FLP by leveraging the fact that its linear programming relaxation could be solved through inspection. However, this linear programming relaxation is known to be weak and does not, therefore, provide tight lower bounds. Another early approach was proposed by Spielberg [ 20 ], which employs a direct search or implicit enumeration method. The authors present two different algorithms based on the same directed search: one considering the facilities to be initially open and another one contemplating initially closed ones. Later Erlenkotter [ 18 ] proposed a dual-based exact approach that differed from previous approaches by considering a dual objective function. An improved version of this work was presented by Körkel [ 21 ]. Although exact approaches provide optimal solutions for small or medium instances, they are unsuitable for solving large-scale real-world problems in reasonable computational times. Therefore, employing approximate methods is advisable. One of the earliest approximation methods was that by Hochbaum [ 22 ], and it consists of a simple and fast greedy heuristic. More recently, Ghosh [ 23 ] put forward a neighborhood search heuristic by incorporating a tabu search as the local search component. This approach yields competitive solutions in significantly shorter computational times compared to exact algorithms. A similar approach with a tabu search was proposed by Michel and Van Hentenryck [ 24 ]. This algorithm shows competitive performance compared to previous literature results. The algorithm utilizes a linear neighborhood approach, where a single facility is flipped at each iteration. Resende and Werneck [ 25 ] introduced an algorithm based on the GRASP metaheuristic. This algorithm incorporates a greedy construction phase combined with a local search operator and path-relinking. It obtains results that come close to the lower bound values for a wide range of different instances. Recently, Martins et al. [ 26 ] introduced an ‘agile optimization’ framework for the UFLP. This framework combines a biased-randomized algorithm with parallel programming techniques to offer real-time solutions. The key feature of this approach is its ability to react and swiftly adapt to rapidly changing customer demands. It achieves this by re-optimizing the system whenever new information is incorporated into the model.

The FLP was initially introduced as the plant location problem by Stollsteimer [ 1 ] and Balinski [ 4 ]. Traditionally, the FLP has been approached through various perspectives, including worst-case analysis, probabilistic analysis, and empirical heuristics. While exact algorithms for the problem can be found in the existing literature, the NP-hard nature of the FLP makes heuristics a more practical approach for obtaining solutions quickly, especially for larger and more realistic instances. One of the first works on the FLP was carried out by Efroymson and Ray [ 19 ] who developed a branch-and-bound algorithm. They utilized a compact formulation of the FLP, leveraging the fact that its linear programming relaxation could be solved through inspection. However, this linear programming relaxation is known to be weak and therefore does not provide tight lower bounds. Another early approach was proposed by Spielberg [ 20 ], which employed a direct search or implicit enumeration method. The authors present two different algorithms based on the same directed search, one considering the facilities initially open and another one considering the facilities initially closed. Later, Erlenkotter [ 18 ] propose a dual-based exact approach, differing from previous approaches by considering a dual objective function. An improved version of this work was presented by Körke [ 21 ]. Although exact approaches provide optimal solutions for small or medium instances, they are unsuitable for solving large-scale real-world problems in reasonable computational time. Therefore, it is advisable to employ approximate methods. One of the earliest approximation methods was proposed by Hochbaum [ 22 ], consisting of a simple and fast greedy heuristic. More recently, Ghosh [ 23 ] proposed a neighborhood search heuristic, incorporating tabu search as the local search component. This approach yields competitive solutions within significantly reduced computational times compared to exact algorithms. A similar approach using a tabu search was proposed by Michel and Van Hentenryck [ 24 ]. This algorithm has shown competitive performance compared to previous literature results. The algorithm utilizes a linear neighborhood approach, where a single facility is flipped at each iteration. Resende and Werneck [ 25 ] introduced an algorithm based on the GRASP metaheuristic. This algorithm incorporates a greedy construction phase combined with a local search operator, and a path-relinking. It achieved results close to the lower bound values for a wide range of different instances. Recently, Martins et al. [ 27 ] introduced an Agile Optimization framework [ 26 ] for the UFLP. This framework combines a biased-randomized algorithm with parallel programming techniques to offer real-time solutions. The key feature of this approach is its ability to react and adapt swiftly to rapidly changing customer demands. It achieves this by re-optimizing the system whenever new information is incorporated

A wide range of variants of the FLP have been extensively addressed in the literature, regardless of the employed solution method. One of the most studied variants is the SSCFLP. Similarly to the original version of the FLP, several exact methods have also been proposed to solve small instances of this problem. For example, Holmberg et al. [ 28 ] described a matching algorithm incorporated into a Lagrangian heuristic. In another study, Díaz and Fernández [ 29 ] developed an exact algorithm that integrates a column generation procedure for finding upper and lower bounds within a branchand-price framework. Similarly, Yang et al. [ 9 ] introduced an exact algorithm based on a cut-and-solve framework designed explicitly for the SSCFLP. Regarding the use of approximate methods, Chen and Ting [ 30 ] proposed a hybrid algorithm that combines a Lagrangian-based heuristic with an ant colony method. This approach aims to leverage the strengths of both techniques to solve the problem. Ahuja et al. [ 31 ] presented a large-scale neighborhood search algorithm, which focuses on efficiently exploring the solution space of the problem. This approach allows large-scale instances to be effectively handled in a reasonable computational time. Filho and Galvão [ 32 ] proposed a tabu search metaheuristic that is also able to handle large instances, while Delmaire et al. [ 33 ] put forward a more sophisticated algorithm also based on a tabu search, which combines a reactive GRASP algorithm with a tabu search. This algorithm incorporates elements of both techniques to enhance search capabilities and to find high-quality solutions. Finally, Estrada-Moreno et al. [ 34 ] presented a biased-randomized iterated local search metaheuristic to solve the SSCFLP with soft capacity constraints. This variant of the SSCFLP assumes that the maximum capacity at each facility can be potentially exceeded by incurring a penalty cost, which increases with the constraint-violation gap. For a more comprehensive literature review on the FLP and its variants, readers are referred to [ 8 , 35 ], and the book edited by Eiselt and Marianov [ 36 ] covers many relevant works on the FLP.

In real life, the inputs of combinatorial optimization problems are typically nondeterministic. This means that they are subject to random events; i.e.., random failures of some components, stockouts due to random demands, etc. Therefore, Simulation-based optimization approaches are required. These methods aim to find a solution that performs well for any possible realization of the random variables, i.e., a robust solution that can handle variations and fluctuations in the problem parameters that may occur in real-world scenarios s [ 37 ]. Although the stochastic FLP has not been paid significant attention in the literature, we can find several works, some of which have been published only a few years after the problem’s definition. For example, Balachandran and Jain [ 38 ] presented a stochastic FLP model with piece-wise linear production. This model takes demands to be random and continuous variables. Later Correia and Saldanha-da Gama [ 10 ] examined distinct modeling frameworks for facility location under uncertain conditions, which specifically distinguish among robust optimization, stochastic programming and chance-constrained models. Another simulation-optimization approach to address this problem is the simheuristics [ 39 ], which is a promising approach based on the combination of simulation with metaheuristics, used for solving efficiency different combinatorial optimization problems with stochastic elements. Indeed simheuristics has been used by different authors to solve the UFLP under uncertainty. De Armas et al. [ 40 ] proposed a simheuristic approach to address the UFLP with random service costs. This simheuristics combines an ILS metaheuristic with Monte Carlo simulation to deal with uncertainty by providing flexibility to consider diverse optimization objectives beyond minimizing the expected cost. A similar approach is that proposed in Quintero-Araujo et al. [ 41 ], which proposes a SimILS framework, a simheuristic algorithm that combines Monte Carlo simulation with a biased-randomized metaheuristic algorithm to solve the capacitated location routing problem (CLRP) with stochastic demands. Another interesting approach i that reported Bayliss and Panadero [ 42 ], where a learnheuristic algorithm [ 43 ] is presented to solve the temporary-facility location and queuing problem. It integrates a biased randomization algorithm with simulation and a machine-learning component to tackle not only uncertain components, but also dynamics components of problems.

To further extend the landscape of facility location problems under uncertainty, other methodological approaches have emerged in recent years. Marques and Dias [ 44 ] introduced a dynamic UFLP by considering uncertainty in fixed and assignment costs, customer and facility locations. They aimed to minimize the expected total cost, while explicitly considering regret. Regret, as a measure of loss for not choosing an optimal scenario solution, is upper-bounded. Their mixed integer programming model and solution approach demonstrates potential through illustrative examples and computational results. Another exciting approach was that proposed by Zhang et al. [ 45 ], which tackles another variant, the squared metric two-stage stochastic FLP by focusing on uncertainty in client sets and facility costs with squared metric connection costs. They proposed a new integer linear programming formulation and evaluated two algorithms’ performance by analyzing approximation ratios and per-scenario bounds. Moreover, Ramshani et al. [ 46 ] explored disruptions in two-level UFLPs by including additional facilities between customers and the main facilities, and by acknowledging disruptions’ impact on facility reliability for meeting customer demands. They developed mathematical formulations and algorithms, such as a tabu search and a problem-specific heuristic, to address disruptions in a two-level distribution chain scenario. By extending this research, Koca et al. [ 47 ] addressed two-stage stochastic UFLPs by emphasizing system nervousness. They introduced models to consider uncertain location and allocation decisions adaptable to realizations of uncertain parameters. Their proposed models incorporated restricted recourse to control deviations between first-stage and scenario-dependent allocation decisions by showcasing Benders-type decomposition algorithms and computational enhancements.

4 Proposed methodology

Simulation methods are frequently employed by experts to address stochastic uncertainty because they enable several scenarios to be analyzed to support decision-making processes. However, it is important to note that simulation itself is not an optimization tool. Therefore, hybrid simulation-optimization methodologies have been proposed to efficiently cope with large-scale optimization problems under uncertainty. One such simulation-optimization method is simheuristics, which combines metaheuristics with simulation [ 48 ]. Its efficiency as a method for solving different combinatorial optimization problems with stochastic elements has been shown in several studies [ 43 ]. This success can be attributed to the method’s ability to evaluate solutions using simulation and problem-specific analytical expressions. Simheuristic algorithms are ‘white-box’ approaches designed specifically to solve large-scale and NP-hard combinatorial optimization problems with stochastic elements, which can come in the form of stochastic objective functions or probabilistic constraints [ 49 ]. The proposed simheuristic method combines a tabu search metaheuristic with path-relinking, which is then integrated with Monte Carlo simulation (MCS) to solve the UFLP with random service costs. Using the tabu search metaheuristic with path-relinking combination allows us to obtain near-optimal solutions to the deterministic version of the problem in short computational times. This combination is successfully employed to solve NP-hard optimization problems in vehicle routing and scheduling domains [ 50 , 51 ]. The algorithm is further combined with simulation techniques to guide the algorithm during the search for near-optimal solutions to the stochastic version of the problem.

4.1 Tabu search with path-relinking

The algorithm for a tabu search with path-relinking is now described. We represent a state in the tabu search by vector \(y_i\) as defined in the model formulation. It is a natural choice seeing that the facility locations are the only combinatorial component. To solve the UFLP, it is enough to know the set of open facilities because customer zones are connected to the cheapest open facilities.

As shown in Algorithm 1, three sections can be identified. The first section applies the tabu search metaheuristic N times to the same problem instance, but uses different seeds. The best solutions are stored in a pool of elite solutions of size L . Subsequently, the path-relinking technique is applied for each pair of elements in the elite solution pool. The new solutions produced to create the next pool of elite solutions are employed (new generation pool). Only those solutions that improve the two used in the path-relinking process are considered the candidates to be inserted into the new generation pool of size L . Note that the best solution found so far is inserted directly into the new generation of elite solutions (1-elitism). The criterion for inserting a new solution into the elite solutions pool is the lowest total cost. The creation of new pools is repeated as long as new generation pools of at least two solutions are produced. After the path-relinking phase, the algorithm begins a local search process around \(sol_{best}\) . This procedure consists of applying a well-known 2-opt local search to every possible combination of two facility locations in the solution.

Tabu search with path-relinking

• Tabu search

The tabu search is presented in Algorithm 2. First, a random solution is generated to provide each facility location with an opening probability. The neighborhood consists in flipping the state of a facility from open to closed, or vice versa. After scanning the neighborhood, if there is an improvement is calculated. Then the facility location involved in the improvement is added to the tabu list to prevent it from being chosen for a defined number of iterations (tenure). The tabu list is implemented by associating a simple counter tabu [ i ] for each facility i . When a facility is inserted on the tabu list, the counter tabu [ i ] is updated by adding the actual iteration count, plus the tenure ( \(tabu[i] = iteration+tenure\) ). This expression states that the facility will remain in the tabu search memory for as many iterations as the value of the tenure parameter. The algorithm can quickly check if a facility is on the tabu list if \(tabu[i] > iteration\) . If there is no improvement in the solution, the algorithm randomly closes a previously open facility location. If only one site remains to be closed, a new one is randomly opened. Tenure is adjusted during the search process. If the algorithm finds improvements in the neighborhood, it decreases tenure to improve exploitation. On the contrary, if it does not find improvements when changing the state of any of the facility locations of a solution, tenure is increased to improve search diversification (never without exceeding a given maximum value). The process is repeated until the stopping criterion is met, which consists in exceeding a number M of iterations without finding an improvement in the solution. The tabu search algorithm uses three different pieces of information for each customer zone j : the number of open facilities that offer the cheapest connection to j, the cost of that connection, and the cost of the second cheapest connection to an open facility. These details allow the gains from opening and closing a facility to be incrementally updated by eliminating the need to compute the entire objective function for a new solution (line 10). A similar approach is used in Michel and Van Hentenryck [ 24 ].

• Path-relinking

The path-relinking subroutine is comprehensively described in Algorithm 3. Given the origin and reference solutions, we first calculate which one gives the best cost and store it in \(sol_{best}\) . Then cardinality is calculated as the number of differences between the origin and reference solutions. Next, the algorithm starts from \(sol_O\) and gradually transforms into \(sol_R\) by flipping the facilities that are different between the two solutions. During this transformation process, intermediate solutions are evaluated to see if they improve the overall result. Finally, the best found solution is returned.

The algorithm’s computational complexity is next reported. For the tabu search component, the complexity per iteration is \(O(n \cdot log(m))\) , where n represents the number of clients and m denotes the number of facilities. This complexity accounts for the calculation of the cost of flipping each facility in a solution, while tracking the best and second-best facilities to assign clients to. These operations are repeated until a number of failed runs is reached, which contributes to the constant factor of the computational complexity. In other words, as the number of iterations is constant (not dependent on the size of the problem), the overall computational complexity of the tabu search component is expressed as \(O(n \cdot log(m))\) . The path-relinking component has a similar complexity per iteration of \(O(n \cdot log(m))\) . This also involves updates to the best and second-best facilities assigned to clients, because intermediate solutions have to be evaluated to see if they improve current solutions. Similar to the tabu search component, the actual number of iterations performed by the path-relinking component depends on the cardinality of solutions along with the number of elite generations, which are not dependent on the size of the instance. Thus, the overall computational complexity of the path-relinking component is \(O(n \cdot log(m))\) . The local search component, the computational complexity per iteration is associated with the process of exploring the neighborhood of the current solution. This involves flipping each facility in the solution and checking if the new solution is improved, whose computational complexity is \(O(n \cdot log(m))\) . This process is repeated until no further improvements are found, so the overall computational complexity of the local search is \(O(n \cdot log(m))\) . Finally, as the three components discussed are executed in a serial manner, we can conclude the proposed algorithm has a worst-case computational complexity of \(O(n \cdot log(m))\) .

Flowchart of the simheuristic methodology

4.2 The simheuristic framework

Figure  2 illustrates a flow chart of our simheuristic methodology for dealing with the UFLP under stochastic uncertainty. Every time a new solution is generated by the tabu search, path-relinking or a local search, it is simulated with a few runs to obtain an estimate of the solution’s average stochastic cost. On the one hand, regarding the tabu search, all the N times when the algorithm reaches the stopping criterion and finds the best solution (Algorithm 1), the fast simulation is run. On the other hand, the simulations of the path-relinking solutions are the most important in the proposed simheuristic. Path-relinking as an intensive process done on a set of elite solutions allows a sufficiently large set of potential solutions to be explored that could perform well in a stochastic environment. For this reason, every time a new solution is generated during the gradual transformation of \(sol_O\) into \(sol_R\) , it is simulated regardless of whether it improves the deterministic solution. In addition, whenever the local search procedure reaches a new improved solution, this is also simulated. The solutions with the best-estimated cost are stored in a pool of elite stochastic solutions. Once an overall stopping criterion is met, a limited set of elite stochastic solutions is sent to a more intensive simulation stage to obtain accurate estimates on their behavior in a stochastic scenario. The general stopping criterion consists of satisfying the stopping criteria of each section of the proposed metaheuristic ( M failed tabu search runs, a new pool generation with < than 2 solutions during path-relinking and no new improvements during the local search).

Algorithm 4 depicts the main characteristics of our simheuristic algorithm. The code is similar to that shown in Algorithm 1. The solutions obtained by the tabu search are quickly simulated, while those with the lowest expected cost are included in the pool of elite stochastic solutions (lines 13-17). Then when the path-relinking ( PR-SIMH ) and local search ( LS-SIMH ) functions are called, the pool is passed as an argument to be updated according to the simulations of the newly generated solutions (as explained above). In lines 34-38, intensive simulation is performed to obtain better estimates of the elite solutions. The best solutions are selected according to the lowest expected cost. However, other estimates, such as risk or reliability, may also be used as discussed in Chica et al. [ 52 ].

Simheuristic for the UFLP

5 Computational study

Several computational experiments were carried out to evaluate and assess the performance of our solving method. To comprehensively illustrate the experiments conducted in this section, a detailed presentation of the utilized benchmark instances, that outlines their characteristics, is first provided. Next the presented benchmark instances are extended to consider random service costs, which model the uncertainty that is inherent in practical scenarios, and penalty costs, by addressing several real-world situations. Then Section  5.4 identifies the significantly affected parameters and decides the optimal parameter settings for the algorithm through the Design of Experiments (DoE). Last, the obtained results and the discussion are presented in Section 5.5. All the numerical experiments were implemented using the C++ programming language. The code was compiled on a Manjaro Linux machine with the GCC version 12.3 compiler and executed on a computer with an Intel Core i5-9600K 3.7 GHz and 16 GB RAM.

5.1 Description of benchmark instances

In order to evaluate the performance of the proposed simheuristic algorithm for the UFLP with random service costs, we used the classic instances originally proposed for the p -median problem by Ahn et al. [ 53 ], later employed in the UFLP context by Barahona and Chudak [ 54 ]. This set of large instances is called MED, which is the most used set of instances in the UFLP literature for being the most challenging ones to solve. To the best of our knowledge, the results of these instances have not been improved from 2006 [ 25 ]. This makes them the perfect benchmarks to test the quality of our algorithm. Each instance is composed of a set of n points picked uniformly at random in the unit square. A point represents both a user and facility, and the corresponding Euclidean distance determines service costs. Additionally, each instance is characterized by the following nomenclature \(x - y\) , where x represents the number of facilities and customers, while y refers to the opening cost scheme. The set of instances consists of six different subsets, each with a different number of facilities and customers (500, 1000, 1500, 2000, 2500 and 3000), and three different opening cost schemes per subset ( \(\sqrt{n}/10\) , \(\sqrt{n}/100\) , and \(\sqrt{n}/1000\) corresponding to 10, 100, and 1000 instance suffixes, respectively). The larger instances and those with suffix 1000 are the most difficult to solve. As they have lower opening costs, the number of open facilities in the solution is bigger, which increases the number of possible combinations and, thus, the complexity of finding the optimal solution.

5.2 Extending benchmark to address uncertainty

To the best of our knowledge, there are no stochastic FLP instances that employ random service costs to be used as a benchmark. So instead of assuming constant service costs \(c_{ij}\) ( \(\forall i\in I, \forall j\in J\) ), we consider a more realistic scenario in which service costs are modeled as random variables \(C_{ij}\) . The service cost represents the cost required to service a customer zone \(j \in J\) throughout a facility location \(i \in I\) under perfect conditions. Accordingly, we extend the previously described set of instances called MED to assess both the performance and quality of the proposed simheuristic algorithm. The dataset construction process involves transforming the deterministic service costs into random service costs following a probability distribution function. Specifically, the deterministic service costs are transformed into stochastic ones when solutions are sent to the simulation phase. Hence the service costs \(c_{ij}\) found in instances are used as the expected values of the random service costs \(C_{ij}\) , which are modeled to follow a log-normal probability distribution. The log-normal distribution is a natural choice for describing nonnegative random variables, such as service costs [ 55 ]. The log-normal distribution has two parameters: the location parameter, \(\mu _{ij}\) , and the scale parameter,  \(\sigma _{ij}\) , which relate to the expected value \(E[C_{ij}]\) and to variance \(Var[C_{ij}]\) , respectively. Equations  7 - 8 define how these parameters have been modeled. We assume service cost \(C_{ij} \sim LogNormal(\mu _{ij}, \sigma _{ij})\) with \(E[C_{ij}] = c_{ij}\) , where \(c_{ij}\) is the deterministic service delay found in instances, and variance \(Var[C_{ij}] = k \cdot E[C_{ij}]\) . Parameter k is a design parameter that allows us to set up the uncertainty level. It determines how much stochastic costs deviate from their expected values ( \(c_{ij}\) derived from deterministic costs) and, therefore, influences the degree of randomness or uncertainty in the simulated costs. So as k converges to zero, the more the results will move toward the deterministic state, and by increasing the value of k , the results will converge to the stochastic state. The selection of k values depends on the uncertainty level desired in stochastic costs. We consider three different uncertainty levels: low ( \(k = 5\) ), medium ( \(k = 10\) ) and high ( \(k = 20\) ). The main objective of setting different k values is to simulate a range of real-world scenarios for the variability and unpredictability of service costs. By employing multiple k values, the algorithm’s performance can be evaluated under diverse conditions, which allows for a comprehensive assessment of its robustness and adaptability to varying cost uncertainty levels.

This approach enables us to test the effectiveness of our simheuristic algorithm in handling UFLP instances with varying uncertainty levels, and to showcase its adaptability at different degrees of random service costs without having to create brand-new datasets.

5.3 Extend benchmark with penalty costs

In order to address real-world situations where certain facilities’ costs need to be controlled or limited, a nonlinear penalty cost is added. This approach aligns the optimization process with practical considerations and allows decision makers to make more informed choices regarding facility selection and cost management. Note in the basic UFLP under uncertainty with a linear objective function that the solution which minimizes the total expected cost will be the same as the optimal solution for the deterministic UFLP. This property will not hold if, for instance, a nonlinear penalty cost is added in the objective function to account for facilities with a total higher service cost than a threshold, etc. Thus we introduce a non linear penalty cost that is twice the cost of opening a facility if the instance maximum service cost of a deterministic solution is exceeded. This parameter, denoted as \(c_{\text {max}} = \max {c_{ij}}\) , represents the maximum \(c_{ij}\) value between all the facilities opened in the best-found deterministic solution. It is worth noting that when this nonlinear penalty is incorporated into the objective function of the UFLP under uncertainty, the solution that minimizes the total expected cost may no longer be the same as the optimal solution for the deterministic UFLP. This deviation from linearity arises because the penalty cost is included. In other words, the best-known deterministic solution, which will still be optimal in a deterministic scenario for not being affected by the \(c_{\text {max}}\) threshold, will perform quite poorly in a stochastic scenario because in many simulation runs there will be service costs that will exceed the \(c_{\text {max}}\) threshold, which will result in a severe penalty. Furthermore, the simheuristic algorithm tends to open some more facilities than those in the deterministic solution to avoid the number of times that the threshold is exceeded. Therefore, the simheuristic approach aims to search for solutions that mitigate the impact of penalties associated with exceeding the \(c_{\text {max}}\) threshold in multiple simulation runs.

5.4 Parameter analysis by design of experiments

In this section, we use DoE to identify the significantly affected parameters and decide the best combination of each parameter for the TS+PR algorithm. As shown in Table  1 , a two-level full factorial design with three replications [ 56 ] is adopted to investigate the significant effect of four parameters of the TS+PR algorithm on both the objective value and the calculation time. The following parameters are considered: N (maximum runs of the algorithm with different seeds), M (maximum number of the tabu iterations without improvement), L (elite pool length) and Tenure (number of iterations a move is considered to be tabu, expressed as a percentage of the number of facility locations of the problem). The high and low levels of each parameter are displayed in Fig.  4 .

The results are shown in Table  1 for a randomly generated test problem of size ( \(|I| = |J|=2000\) ). The problem was created following the same structure as the large instances called MED. The selected opening cost scheme was \(\sqrt{n}/1000\) because, as previously mentioned, it is the most challenging. The response variable AVG GAP (%) is the average gap of 30 different independent runs compared to the optimal solution obtained with Gurobi for the generated test problem. The response variable AVG TIME is the average execution time for the 30 independent runs. In all, 3 * \(2^{4}\) * 30 = 1440 trials were conducted in this experiment. Table  1 shows the average (best) values for the 30 runs and displays 48 trials.

Pareto chart for AVG GAP(%)

Main effect plot for AVG GAP(%)

According to the ANOVA results (Table  2 ) and the Pareto chart (Fig.  3 ) for the response AVG GAP (%), only parameters M and L are statistically significant for the proposed problem. The values RSquare = 92.21%, RSquare(Adj) = 88.19%, and Square(Pred) = 81.33% obtained in Statgraphics mean that this model fits the data well and can be used to accordingly determine the suitable parameters (Fig.  4 ).

For the response AVG TIME (see Fig.  5 ), all the parameters except Tenure are the algorithm’s most significant and critical parameters at \(\alpha = 0.05\) . The model fits the data very well (RSquare = 99.25%, RSquare(Adj) = 98.86%, and Square(Pred) = 98.20%).

Pareto chart for AVG TIME(s)

Main effect plot for AVG TIME(s)

To find the best parameters for the algorithm, we focus mainly on the response AVG GAP (%). The best parameter settings on N , M , L and Tenure , according to AVG GAP(%), are 64, 500, 10 and 10%, respectively (see Fig.  4 ). Although M and L prolong the computation time (see Fig.  6 ), they are statistically significant and their higher values are necessary. Coosing a value of 64 vs. 32 for N negatively affects the execution time (it increases by more than 40%) and is not statistically significant. Furthermore, the best gap for \(N=64\) is 0.02% and 0.03% for \(N=32\) , a minimal difference for the longer computational time required. Finally, Tenure does not statistically affect either AVG GAP or AVG TIME. As explained previously, the reason lies in the algorithm’s capacity to adjust the tenure value as the search progresses. So it does not affect starting with a slightly higher or lower value.

The main objective of this paper is not to obtain the best possible solutions in the deterministic environment. So we explore the possibility of considering \(N=64\) and of even analyzing the results of larger values for the most significant factors, such as M and L . This paper focuses on uncertain conditions using a simulation optimization approach, such as the simheuristics concept. For this reason, having a good deterministic search algorithm (i.e. 0.03% gap) with reasonable computation times is sufficient. In this way, the algorithm can be efficiently combined with Monte Carlo simulations to search for the best solutions under uncertainty. For all these reasons, the values chosen for the adjustment of the TS+PR algorithm, used later within the simheuristic framework, are \(N = 32, M = 1000, L = 10\) and \(Tenure = 10\%\) .

Three more parameters are defined by applying the simheuristic approach described in Algorithm 2, which are longSim , shortSim and L 2. The first parameter is defined as being large enough to have a full, meaningful simulation of a solution under stochastic uncertainty. The second parameter attempts to quickly evaluate a solution in an uncertain environment to guide the search for better ones. The last parameter consists of a pool of elite solutions (quickly evaluated) to be finally validated in the complete simulation. This pool is ordered from the best to the worst result of the fast simulation. A solution in a lower position may obtain a better result in the long simulation than another in a higher initial position. For this reason, pool size must be large enough to capture the best possible solution in the global simulation. The exploratory studies indicate that the best final solution after the full simulation appears before the first five positions of the elite pool. To ensure that the best solution is obtained in the complete simulation, a value higher than five is finally chosen.

Table  3 summarizes all the parameters and the values selected for the following computational experiments applied to the benchmark instances described in the previous points (Table 4 ).

5.5 Results and discussion

Table  5 includes the results obtained for four different approaches to solve the UFLP with the MED benchmark instances. The first column displays instances, whose names are combinations of the number of demand points and the opening cost scheme. The next two columns show the solutions obtained using the Gurobi Optimizer solver, along with the corresponding computational time required to reach those solutions. The subsequent three columns present the best-found solutions obtained from our tabu search with the path-relinking approach, along with the computational time needed to obtain them. Each instance is run 30 times using a different seed for the random number generator, and the best and average results are reported. Furthermore, the three columns that follow depict the best-found solutions achieved using the multi-start heuristic proposed by Resende and Werneck [ 25 ], along with the computational time required for each solution. The next three columns illustrate the best-found solutions obtained with the ILS-based approach proposed by De Armas et al. [ 40 ], along with the computational time taken to achieve those results. Finally, the last three columns display the best-found solutions obtained using the multi-wave algorithm approach by Glover et al. [ 57 ], plus the computational time taken to reach these solutions. To deal with the different CPU performance times for each previous method found in the literature, the results can be refactored in time using the performance characteristics of the employed CPUs. We used the tables published on specialized websites; i.e., http://www.techarp.com and https://www.userbenchmark.com , which evaluate CPU performance, to complete the conversion and normalisation for fair results. Based on the PLUS column, in Table  4 we include the number of times that our computer was faster than each computer used in the literature. It should be noted that it was not possible to normalize the times reported in Resende and Werneck [ 25 ] due to lack of comparative information and the difficulty of the conversion process when employing a CPU with a different architecture (RISC). However, it is reasonable to assume that the normalized times of their work would be very competitive.

Table  6 presents the results obtained for the uncertainty levels considered using the MED benchmark instances. Each instance was run 10 times using our simheuristic algorithm with different seeds for the random number generator, and the best results are reported. The first column identifies the instances, while the following three display the results obtained by our approach for the deterministic UFLP. First, the column labeled BKS reports the best-known solutions provided by the Gurobi Optimizer solver, along with our best-found deterministic solutions labeled OBD . We also calculate the percentage gaps of the best-found deterministic solutions compared to the best-known solutions. The remaining columns showcase the results obtained for three different uncertainty levels. In the second section of the table, we report the results obtained for the low uncertainty level. The OBD-S column displays the expected cost obtained when evaluating the best deterministic solution ( OBD ) in a stochastic scenario with a low uncertainty level. To compute the expected cost, an intensive simulation process is applied to the OBD . This process aims to assess the quality of our best-found deterministic solutions at varying uncertainty levels. The next column (OBS) shows the expected cost obtained using our simheuristic approach for the stochastic version of the problem. This approach considers the random service costs during the solution search. The subsequent section of the table presents the results for the medium uncertainty level. In the OBD-S column, we report the expected cost obtained when evaluating the best deterministic solution ( OBD ) in a stochastic scenario with medium uncertainty. Similarly, the next column ( OBS ) displays the expected cost obtained using our simheuristic algorithm. Finally, the last section of the table exhibits the results for the high uncertainty level. The OBD-S column shows the expected cost obtained when evaluating the best deterministic solution ( OBD ) in a stochastic scenario with high uncertainty. The last column ( OBS ) displays the expected cost obtained with our simheuristic approach.

For the sake of completeness, Table  7 covers the additional details of the computational results omitted in Table  6 . The first column identifies the instances, while the following four columns display the facilities open cost, the related nonlinear penalty cost, the threshold defined as the instance maximum service cost and the number of open facilities of the best-found solution, respectively. The remaining columns showcase the percentage gaps obtained for three different uncertainty levels, along with the number of open facilities of the best-found stochastic solutions. In the second section of the table, we report the results obtained for the low uncertainty level. The OBD-S GAP (%) column displays the percentage gap obtained when comparing the best deterministic solutions simulated in a low uncertainty scenario with the best-known solutions ( BKS ). The next column ( OBS GAP (%) ) shows the percentage gap obtained when comparing our simheuristic approach. The subsequent column ( OPEN ) presents the number of open facilities of the best-found stochastic solution. The subsequent section of the table offers the results for the medium uncertainty level. In the OBD-S GAP (%) column, we report the percentage gap obtained when comparing the best deterministic solution at a medium uncertainty level to the best-known solutions ( BKS ). The next column ( OBS (%) ) displays the percentage gap obtained using our simheuristic algorithm. Moreover, the subsequent column ( OPEN ) presents the number of open facilities of the best-found stochastic solution. Finally, the last section of the table exhibits the results for the high uncertainty level. The OBD-S GAP (%) column depicts the percentage gap obtained when comparing the best deterministic solution at a high uncertainty level. The next column ( OBS GAP (%) ) displays the percentage gap obtained using our simheuristic algorithm. The last column (OPEN) displays the number of open facilities of the best-found stochastic solution.

Gaps of \(\sqrt{n}/10\) opening cost scheme instances w.r.t the BKS

Gaps of \(\sqrt{n}/100\) opening cost scheme instances w.r.t the BKS

Gaps of \(\sqrt{n}/1000\) opening cost scheme instances w.r.t the BKS

Figures  7 ,  8 and  9 depict an overview of Table  6 by showing our algorithm’s performance for all the considered uncertainty levels. In these box plots, the horizontal and vertical axes represent the three uncertainty levels and the percentage gap obtained in relation to the BKS reported by the Gurobi Optimization solver, respectively. Note for the deterministic version of the UFLP, that our tabu search with the path re-linking approach nearly reaches the BKS for the \(\sqrt{n}/10\) , \(\sqrt{n}/100\) , and \(\sqrt{n}/1000\) opening cost schemes, with a gap of approximately \(0.00\%\) , \(0.03\%\) , and \(0.04\%\) , respectively. These results highlight the quality of our algorithm because our approach provides highly competitive solutions. Regarding the stochastic version of the UFLP, which is the main contribution of this paper, the obtained results show that the solutions provided by our heuristic approach for the three different uncertainty levels clearly outperform the solutions for the deterministic UFLP when they are simulated at the corresponding uncertainty level. In other words, our best-found solutions for the deterministic version of the problem ( OBD ) might be suboptimal when uncertainty is considered. Hence the importance of integrating simulation methods when dealing with optimization problems with uncertainty. Note also that the OBD can be seen as a reference lower bound in an ideal scenario with perfect information (i.e., without uncertainty) for the expected cost under uncertainty conditions. Similarly, OBD-S can be seen as an upper bound for the expected cost at the different uncertainty levels. As expected, the gaps for all three opening cost schemes worsen as the uncertainty level of k increases. For the specific case of the \(\sqrt{n}/10\) opening cost scheme, gaps increase more than for others. As shown in Table  7 , this is because the penalty cost (opening cost) is higher in this case. The penalty amounts to 3-5% of the total costs, but is less than 1.5% for the \(\sqrt{n}/100\) opening cost scheme and less than 0.5% for the remaining one. In addition, the number of open facilities is much smaller. These are cases in which a few facilities with high capacity serve many customers. The average number of open facilities for this opening cost scheme is around 18 in the best-found deterministic solutions, but rises to over 430 for the instances with suffix 1000. In this high opening cost scheme, where there are few viable facilities to open and with a high cost penalty, the OBD-S result is that which obtains the worst values on average, with a gap of 8.99%, 15.42% and 30.56% for all three uncertainty levels. In this environment, our simheuristic approach is able to achieve a 3 to 5 times better improvement (1.81%, 3.80%, and 10.71%). For the remaining cases (suffixes 100 and 1000) where the penalty costs are lower and the number of open installations is bigger, and the gaps shown in Table  7 and Figs.  7 ,  8 and  9 are smaller. It is not surprising that the OBD solutions better perform under uncertainty when the penalty cost is lower. Our OBS solutions improve the deterministic model’s performance for all the different k uncertainty levels, and also for all the opening cost schemes, which demonstrates the validity of the proposed approach.

When taking everything into account, the findings validate the significance of factoring in uncertainty while searching for a solution because it can greatly affect the quality of our best-found solutions. For instance, when our best deterministic solution is simulated in a stochastic scenario, it yields a much higher expected cost. Conversely, our best-found stochastic solution ( OBS ) provides a lower expected cost. Therefore, incorporating uncertainty aspects during the search process produces better results than when simulating uncertainty elements after finding a solution for the deterministic version of the problem.

6 Conclusions

In this paper, we analyze the UFLP under uncertainty, which occurs in several real-life systems. This uncertainty arises when inputs, such as customer demands or service costs, are random variables instead of deterministic values. To solve this optimization problem, we propose a novel solving methodology that combines a tabu search metaheuristic with path-relinking. The proposed algorithm is tested on the largest instances from the literature because they are the most challenging ones. The results show that our approach is capable of obtaining near-optimal solutions in short computational times. Additionally, the results are compared to the BKS from the literature, along with other competitive approaches, to validate our algorithm’s effectiveness in the deterministic scenario. Then the algorithm is converted into a simheuristic by integrating it with a simulation component to solve the UFLP with random service costs. The log-normal probability distribution is employed to model the random service costs. The obtained results show our simheuristic approach outperforms the simulated deterministic solutions when uncertainty is considered. Thus our simheuristic approach constitutes a general methodology that can be employed to efficiently solve several FLP variants under uncertainty.

One of the limitations of the present work is that it considers only uncertainty of a stochastic nature. Thus extending the simheuristic algorithm to address the UFLP in a more general setting, including stochastic and nonstochastic uncertainty elements like type-2 fuzzy systems [ 58 ] and rough sets [ 59 ], is a future research line. Another limitation is that simulations are performed on a single CPU core. As a future research line, it would be interesting to consider a parallel version of the simheuristic algorithm to obtain optimal solutions in an even shorter time, which may allow fast decision making in time-sensitive scenarios. Finally, another possible extension for this paper is to develop a similar combination of a tabu search metaheuristic with a path-relinking simheuristic to obtain near-optimal solutions in short computational times for other optimization problems under uncertainty, for example, vehicle routing problems, arc routing problems and scheduling problems.

Data availability statement

Data sharing is not applicable to this article because no datasets were generated or analyzed during the present study.

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Acknowledgements

This work has been partially supported by the Spanish Ministry of Science (PDC2022-133957-I00, PID2022-138860NB-I00 and RED2022-134703-T) and by the Generalitat Valenciana (PROMETEO/2021/065).

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Conceptualization: Angel A. Juan, David Peidro; Methodology: Angel A. Juan, Xabier A. Martin, Javier Panadero; Software: David Peidro; Validation: Angel A. Juan, Xabier A. Martin, David Peidro, Javier Panadero; Software: David Peidro; Writing-original draft preparation: Xabier A. Martin, David Peidro, Javier Panadero; Writing-review and editing: Angel A. Juan, David Peidro. All authors have read and agreed to the published version of the manuscript.

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Peidro, D., Martin, X.A., Panadero, J. et al. Solving the uncapacitated facility location problem under uncertainty: a hybrid tabu search with path-relinking simheuristic approach. Appl Intell (2024). https://doi.org/10.1007/s10489-024-05441-x

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A hybrid particle swarm optimization algorithm for solving engineering problem

• Jinwei Qiao 1 , 2 ,
• Guangyuan Wang 1 , 2 ,
• Zhi Yang 1 , 2 ,
• Xiaochuan Luo 3 ,
• Jun Chen 1 , 2 ,
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Scientific Reports volume  14 , Article number:  8357 ( 2024 ) Cite this article

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To overcome the disadvantages of premature convergence and easy trapping into local optimum solutions, this paper proposes an improved particle swarm optimization algorithm (named NDWPSO algorithm) based on multiple hybrid strategies. Firstly, the elite opposition-based learning method is utilized to initialize the particle position matrix. Secondly, the dynamic inertial weight parameters are given to improve the global search speed in the early iterative phase. Thirdly, a new local optimal jump-out strategy is proposed to overcome the "premature" problem. Finally, the algorithm applies the spiral shrinkage search strategy from the whale optimization algorithm (WOA) and the Differential Evolution (DE) mutation strategy in the later iteration to accelerate the convergence speed. The NDWPSO is further compared with other 8 well-known nature-inspired algorithms (3 PSO variants and 5 other intelligent algorithms) on 23 benchmark test functions and three practical engineering problems. Simulation results prove that the NDWPSO algorithm obtains better results for all 49 sets of data than the other 3 PSO variants. Compared with 5 other intelligent algorithms, the NDWPSO obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function ( \({f}_{1}-{f}_{13}\) ) with 3 kinds of dimensional spaces (Dim = 30,50,100) and 80% of the best optimal solutions for 10 fixed-multimodal benchmark functions. Also, the best design solutions are obtained by NDWPSO for all 3 classical practical engineering problems.

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Neural operators for accelerating scientific simulations and design

Physics-informed machine learning

Principal component analysis

Introduction.

In the ever-changing society, new optimization problems arise every moment, and they are distributed in various fields, such as automation control 1 , statistical physics 2 , security prevention and temperature prediction 3 , artificial intelligence 4 , and telecommunication technology 5 . Faced with a constant stream of practical engineering optimization problems, traditional solution methods gradually lose their efficiency and convenience, making it more and more expensive to solve the problems. Therefore, researchers have developed many metaheuristic algorithms and successfully applied them to the solution of optimization problems. Among them, Particle swarm optimization (PSO) algorithm 6 is one of the most widely used swarm intelligence algorithms.

However, the basic PSO has a simple operating principle and solves problems with high efficiency and good computational performance, but it suffers from the disadvantages of easily trapping in local optima and premature convergence. To improve the overall performance of the particle swarm algorithm, an improved particle swarm optimization algorithm is proposed by the multiple hybrid strategy in this paper. The improved PSO incorporates the search ideas of other intelligent algorithms (DE, WOA), so the improved algorithm proposed in this paper is named NDWPSO. The main improvement schemes are divided into the following 4 points: Firstly, a strategy of elite opposition-based learning is introduced into the particle population position initialization. A high-quality initialization matrix of population position can improve the convergence speed of the algorithm. Secondly, a dynamic weight methodology is adopted for the acceleration coefficients by combining the iterative map and linearly transformed method. This method utilizes the chaotic nature of the mapping function, the fast convergence capability of the dynamic weighting scheme, and the time-varying property of the acceleration coefficients. Thus, the global search and local search of the algorithm are balanced and the global search speed of the population is improved. Thirdly, a determination mechanism is set up to detect whether the algorithm falls into a local optimum. When the algorithm is “premature”, the population resets 40% of the position information to overcome the local optimum. Finally, the spiral shrinking mechanism combined with the DE/best/2 position mutation is used in the later iteration, which further improves the solution accuracy.

The structure of the paper is given as follows: Sect. “ Particle swarm optimization (PSO) ” describes the principle of the particle swarm algorithm. Section “ Improved particle swarm optimization algorithm ” shows the detailed improvement strategy and a comparison experiment of inertia weight is set up for the proposed NDWPSO. Section “ Experiment and discussion ” includes the experimental and result discussion sections on the performance of the improved algorithm. Section “ Conclusions and future works ” summarizes the main findings of this study.

Literature review

This section reviews some metaheuristic algorithms and other improved PSO algorithms. A simple discussion about recently proposed research studies is given.

Metaheuristic algorithms

A series of metaheuristic algorithms have been proposed in recent years by using various innovative approaches. For instance, Lin et al. 7 proposed a novel artificial bee colony algorithm (ABCLGII) in 2018 and compared ABCLGII with other outstanding ABC variants on 52 frequently used test functions. Abed-alguni et al. 8 proposed an exploratory cuckoo search (ECS) algorithm in 2021 and carried out several experiments to investigate the performance of ECS by 14 benchmark functions. Brajević 9 presented a novel shuffle-based artificial bee colony (SB-ABC) algorithm for solving integer programming and minimax problems in 2021. The experiments are tested on 7 integer programming problems and 10 minimax problems. In 2022, Khan et al. 10 proposed a non-deterministic meta-heuristic algorithm called Non-linear Activated Beetle Antennae Search (NABAS) for a non-convex tax-aware portfolio selection problem. Brajević et al. 11 proposed a hybridization of the sine cosine algorithm (HSCA) in 2022 to solve 15 complex structural and mechanical engineering design optimization problems. Abed-Alguni et al. 12 proposed an improved Salp Swarm Algorithm (ISSA) in 2022 for single-objective continuous optimization problems. A set of 14 standard benchmark functions was used to evaluate the performance of ISSA. In 2023, Nadimi et al. 13 proposed a binary starling murmuration optimization (BSMO) to select the effective features from different important diseases. In the same year, Nadimi et al. 14 systematically reviewed the last 5 years' developments of WOA and made a critical analysis of those WOA variants. In 2024, Fatahi et al. 15 proposed an Improved Binary Quantum-based Avian Navigation Optimizer Algorithm (IBQANA) for the Feature Subset Selection problem in the medical area. Experimental evaluation on 12 medical datasets demonstrates that IBQANA outperforms 7 established algorithms. Abed-alguni et al. 16 proposed an Improved Binary DJaya Algorithm (IBJA) to solve the Feature Selection problem in 2024. The IBJA’s performance was compared against 4 ML classifiers and 10 efficient optimization algorithms.

Improved PSO algorithms

Many researchers have constantly proposed some improved PSO algorithms to solve engineering problems in different fields. For instance, Yeh 17 proposed an improved particle swarm algorithm, which combines a new self-boundary search and a bivariate update mechanism, to solve the reliability redundancy allocation problem (RRAP) problem. Solomon et al. 18 designed a collaborative multi-group particle swarm algorithm with high parallelism that was used to test the adaptability of Graphics Processing Units (GPUs) in distributed computing environments. Mukhopadhyay and Banerjee 19 proposed a chaotic multi-group particle swarm optimization (CMS-PSO) to estimate the unknown parameters of an autonomous chaotic laser system. Duan et al. 20 designed an improved particle swarm algorithm with nonlinear adjustment of inertia weights to improve the coupling accuracy between laser diodes and single-mode fibers. Sun et al. 21 proposed a particle swarm optimization algorithm combined with non-Gaussian stochastic distribution for the optimal design of wind turbine blades. Based on a multiple swarm scheme, Liu et al. 22 proposed an improved particle swarm optimization algorithm to predict the temperatures of steel billets for the reheating furnace. In 2022, Gad 23 analyzed the existing 2140 papers on Swarm Intelligence between 2017 and 2019 and pointed out that the PSO algorithm still needs further research. In general, the improved methods can be classified into four categories:

Adjusting the distribution of algorithm parameters. Feng et al. 24 used a nonlinear adaptive method on inertia weights to balance local and global search and introduced asynchronously varying acceleration coefficients.

Changing the updating formula of the particle swarm position. Both papers 25 and 26 used chaotic mapping functions to update the inertia weight parameters and combined them with a dynamic weighting strategy to update the particle swarm positions. This improved approach enables the particle swarm algorithm to be equipped with fast convergence of performance.

The initialization of the swarm. Alsaidy and Abbood proposed 27 a hybrid task scheduling algorithm that replaced the random initialization of the meta-heuristic algorithm with the heuristic algorithms MCT-PSO and LJFP-PSO.

Combining with other intelligent algorithms: Liu et al. 28 introduced the differential evolution (DE) algorithm into PSO to increase the particle swarm as diversity and reduce the probability of the population falling into local optimum.

Particle swarm optimization (PSO)

The particle swarm optimization algorithm is a population intelligence algorithm for solving continuous and discrete optimization problems. It originated from the social behavior of individuals in bird and fish flocks 6 . The core of the PSO algorithm is that an individual particle identifies potential solutions by flight in a defined constraint space adjusts its exploration direction to approach the global optimal solution based on the shared information among the group, and finally solves the optimization problem. Each particle \(i\) includes two attributes: velocity vector \({V}_{i}=\left[{v}_{i1},{v}_{i2},{v}_{i3},{...,v}_{ij},{...,v}_{iD},\right]\) and position vector \({X}_{i}=[{x}_{i1},{x}_{i2},{x}_{i3},...,{x}_{ij},...,{x}_{iD}]\) . The velocity vector is used to modify the motion path of the swarm; the position vector represents a potential solution for the optimization problem. Here, \(j=\mathrm{1,2},\dots ,D\) , \(D\) represents the dimension of the constraint space. The equations for updating the velocity and position of the particle swarm are shown in Eqs. ( 1 ) and ( 2 ).

Here \({Pbest}_{i}^{k}\) represents the previous optimal position of the particle \(i\) , and \({Gbest}\) is the optimal position discovered by the whole population. \(i=\mathrm{1,2},\dots ,n\) , \(n\) denotes the size of the particle swarm. \({c}_{1}\) and \({c}_{2}\) are the acceleration constants, which are used to adjust the search step of the particle 29 . \({r}_{1}\) and \({r}_{2}\) are two random uniform values distributed in the range \([\mathrm{0,1}]\) , which are used to improve the randomness of the particle search. \(\omega\) inertia weight parameter, which is used to adjust the scale of the search range of the particle swarm 30 . The basic PSO sets the inertia weight parameter as a time-varying parameter to balance global exploration and local seeking. The updated equation of the inertia weight parameter is given as follows:

where \({\omega }_{max}\) and \({\omega }_{min}\) represent the upper and lower limits of the range of inertia weight parameter. \(k\) and \(Mk\) are the current iteration and maximum iteration.

Improved particle swarm optimization algorithm

According to the no free lunch theory 31 , it is known that no algorithm can solve every practical problem with high quality and efficiency for increasingly complex and diverse optimization problems. In this section, several improvement strategies are proposed to improve the search efficiency and overcome this shortcoming of the basic PSO algorithm.

Improvement strategies

The optimization strategies of the improved PSO algorithm are shown as follows:

The inertia weight parameter is updated by an improved chaotic variables method instead of a linear decreasing strategy. Chaotic mapping performs the whole search at a higher speed and is more resistant to falling into local optimal than the probability-dependent random search 32 . However, the population may result in that particles can easily fly out of the global optimum boundary. To ensure that the population can converge to the global optimum, an improved Iterative mapping is adopted and shown as follows:

Here \({\omega }_{k}\) is the inertia weight parameter in the iteration \(k\) , \(b\) is the control parameter in the range \([\mathrm{0,1}]\) .

The acceleration coefficients are updated by the linear transformation. \({c}_{1}\) and \({c}_{2}\) represent the influential coefficients of the particles by their own and population information, respectively. To improve the search performance of the population, \({c}_{1}\) and \({c}_{2}\) are changed from fixed values to time-varying parameter parameters, that are updated by linear transformation with the number of iterations:

where \({c}_{max}\) and \({c}_{min}\) are the maximum and minimum values of acceleration coefficients, respectively.

The initialization scheme is determined by elite opposition-based learning . The high-quality initial population will accelerate the solution speed of the algorithm and improve the accuracy of the optimal solution. Thus, the elite backward learning strategy 33 is introduced to generate the position matrix of the initial population. Suppose the elite individual of the population is \({X}=[{x}_{1},{x}_{2},{x}_{3},...,{x}_{j},...,{x}_{D}]\) , and the elite opposition-based solution of \(X\) is \({X}_{o}=[{x}_{{\text{o}}1},{x}_{{\text{o}}2},{x}_{{\text{o}}3},...,{x}_{oj},...,{x}_{oD}]\) . The formula for the elite opposition-based solution is as follows:

where \({k}_{r}\) is the random value in the range \((\mathrm{0,1})\) . \({ux}_{oij}\) and \({lx}_{oij}\) are dynamic boundaries of the elite opposition-based solution in \(j\) dimensional variables. The advantage of dynamic boundary is to reduce the exploration space of particles, which is beneficial to the convergence of the algorithm. When the elite opposition-based solution is out of bounds, the out-of-bounds processing is performed. The equation is given as follows:

After calculating the fitness function values of the elite solution and the elite opposition-based solution, respectively, \(n\) high quality solutions were selected to form a new initial population position matrix.

The position updating Eq. ( 2 ) is modified based on the strategy of dynamic weight. To improve the speed of the global search of the population, the strategy of dynamic weight from the artificial bee colony algorithm 34 is introduced to enhance the computational performance. The new position updating equation is shown as follows:

Here \(\rho\) is the random value in the range \((\mathrm{0,1})\) . \(\psi\) represents the acceleration coefficient and \({\omega }{\prime}\) is the dynamic weight coefficient. The updated equations of the above parameters are as follows:

where \(f(i)\) denotes the fitness function value of individual particle \(i\) and u is the average of the population fitness function values in the current iteration. The Eqs. ( 11 , 12 ) are introduced into the position updating equation. And they can attract the particle towards positions of the best-so-far solution in the search space.

New local optimal jump-out strategy is added for escaping from the local optimal. When the value of the fitness function for the population optimal particles does not change in M iterations, the algorithm determines that the population falls into a local optimal. The scheme in which the population jumps out of the local optimum is to reset the position information of the 40% of individuals within the population, in other words, to randomly generate the position vector in the search space. M is set to 5% of the maximum number of iterations.

New spiral update search strategy is added after the local optimal jump-out strategy. Since the whale optimization algorithm (WOA) was good at exploring the local search space 35 , the spiral update search strategy in the WOA 36 is introduced to update the position of the particles after the swarm jumps out of local optimal. The equation for the spiral update is as follows:

Here \(D=\left|{x}_{i}\left(k\right)-Gbest\right|\) denotes the distance between the particle itself and the global optimal solution so far. \(B\) is the constant that defines the shape of the logarithmic spiral. \(l\) is the random value in \([-\mathrm{1,1}]\) . \(l\) represents the distance between the newly generated particle and the global optimal position, \(l=-1\) means the closest distance, while \(l=1\) means the farthest distance, and the meaning of this parameter can be directly observed by Fig.  1 .

Spiral updating position.

The DE/best/2 mutation strategy is introduced to form the mutant particle. 4 individuals in the population are randomly selected that differ from the current particle, then the vector difference between them is rescaled, and the difference vector is combined with the global optimal position to form the mutant particle. The equation for mutation of particle position is shown as follows:

where \({x}^{*}\) is the mutated particle, \(F\) is the scale factor of mutation, \({r}_{1}\) , \({r}_{2}\) , \({r}_{3}\) , \({r}_{4}\) are random integer values in \((0,n]\) and not equal to \(i\) , respectively. Specific particles are selected for mutation with the screening conditions as follows:

where \(Cr\) represents the probability of mutation, \(rand\left(\mathrm{0,1}\right)\) is a random number in \(\left(\mathrm{0,1}\right)\) , and \({i}_{rand}\) is a random integer value in \((0,n]\) .

The improved PSO incorporates the search ideas of other intelligent algorithms (DE, WOA), so the improved algorithm proposed in this paper is named NDWPSO. The pseudo-code for the NDWPSO algorithm is given as follows:

The main procedure of NDWPSO.

Comparing the distribution of inertia weight parameters

There are several improved PSO algorithms (such as CDWPSO 25 , and SDWPSO 26 ) that adopt the dynamic weighted particle position update strategy as their improvement strategy. The updated equations of the CDWPSO and the SDWPSO algorithm for the inertia weight parameters are given as follows:

where \({\text{A}}\) is a value in \((\mathrm{0,1}]\) . \({r}_{max}\) and \({r}_{min}\) are the upper and lower limits of the fluctuation range of the inertia weight parameters, \(k\) is the current number of algorithm iterations, and \(Mk\) denotes the maximum number of iterations.

Considering that the update method of inertia weight parameters by our proposed NDWPSO is comparable to the CDWPSO, and SDWPSO, a comparison experiment for the distribution of inertia weight parameters is set up in this section. The maximum number of iterations in the experiment is \(Mk=500\) . The distributions of CDWPSO, SDWPSO, and NDWPSO inertia weights are shown sequentially in Fig.  2 .

The inertial weight distribution of CDWPSO, SDWPSO, and NDWPSO.

In Fig.  2 , the inertia weight value of CDWPSO is a random value in (0,1]. It may make individual particles fly out of the range in the late iteration of the algorithm. Similarly, the inertia weight value of SDWPSO is a value that tends to zero infinitely, so that the swarm no longer can fly in the search space, making the algorithm extremely easy to fall into the local optimal value. On the other hand, the distribution of the inertia weights of the NDWPSO forms a gentle slope by two curves. Thus, the swarm can faster lock the global optimum range in the early iterations and locate the global optimal more precisely in the late iterations. The reason is that the inertia weight values between two adjacent iterations are inversely proportional to each other. Besides, the time-varying part of the inertial weight within NDWPSO is designed to reduce the chaos characteristic of the parameters. The inertia weight value of NDWPSO avoids the disadvantages of the above two schemes, so its design is more reasonable.

Experiment and discussion

In this section, three experiments are set up to evaluate the performance of NDWPSO: (1) the experiment of 23 classical functions 37 between NDWPSO and three particle swarm algorithms (PSO 6 , CDWPSO 25 , SDWPSO 26 ); (2) the experiment of benchmark test functions between NDWPSO and other intelligent algorithms (Whale Optimization Algorithm (WOA) 36 , Harris Hawk Algorithm (HHO) 38 , Gray Wolf Optimization Algorithm (GWO) 39 , Archimedes Algorithm (AOA) 40 , Equilibrium Optimizer (EO) 41 and Differential Evolution (DE) 42 ); (3) the experiment for solving three real engineering problems (welded beam design 43 , pressure vessel design 44 , and three-bar truss design 38 ). All experiments are run on a computer with Intel i5-11400F GPU, 2.60 GHz, 16 GB RAM, and the code is written with MATLAB R2017b.

The benchmark test functions are 23 classical functions, which consist of indefinite unimodal (F1–F7), indefinite dimensional multimodal functions (F8–F13), and fixed-dimensional multimodal functions (F14–F23). The unimodal benchmark function is used to evaluate the global search performance of different algorithms, while the multimodal benchmark function reflects the ability of the algorithm to escape from the local optimal. The mathematical equations of the benchmark functions are shown and found as Supplementary Tables S1 – S3 online.

Experiments on benchmark functions between NDWPSO, and other PSO variants

The purpose of the experiment is to show the performance advantages of the NDWPSO algorithm. Here, the dimensions and corresponding population sizes of 13 benchmark functions (7 unimodal and 6 multimodal) are set to (30, 40), (50, 70), and (100, 130). The population size of 10 fixed multimodal functions is set to 40. Each algorithm is repeated 30 times independently, and the maximum number of iterations is 200. The performance of the algorithm is measured by the mean and the standard deviation (SD) of the results for different benchmark functions. The parameters of the NDWPSO are set as: \({[{\omega }_{min},\omega }_{max}]=[\mathrm{0.4,0.9}]\) , \(\left[{c}_{max},{c}_{min}\right]=\left[\mathrm{2.5,1.5}\right],{V}_{max}=0.1,b={e}^{-50}, M=0.05\times Mk, B=1,F=0.7, Cr=0.9.\) And, \(A={\omega }_{max}\) for CDWPSO; \({[r}_{max},{r}_{min}]=[\mathrm{4,0}]\) for SDWPSO.

Besides, the experimental data are retained to two decimal places, but some experimental data will increase the number of retained data to pursue more accuracy in comparison. The best results in each group of experiments will be displayed in bold font. The experimental data is set to 0 if the value is below 10 –323 . The experimental parameter settings in this paper are different from the references (PSO 6 , CDWPSO 25 , SDWPSO 26 , so the final experimental data differ from the ones within the reference.

As shown in Tables 1 and 2 , the NDWPSO algorithm obtains better results for all 49 sets of data than other PSO variants, which include not only 13 indefinite-dimensional benchmark functions and 10 fixed-multimodal benchmark functions. Remarkably, the SDWPSO algorithm obtains the same accuracy of calculation as NDWPSO for both unimodal functions f 1 –f 4 and multimodal functions f 9 –f 11 . The solution accuracy of NDWPSO is higher than that of other PSO variants for fixed-multimodal benchmark functions f 14 -f 23 . The conclusion can be drawn that the NDWPSO has excellent global search capability, local search capability, and the capability for escaping the local optimal.

In addition, the convergence curves of the 23 benchmark functions are shown in Figs. 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 and 19 . The NDWPSO algorithm has a faster convergence speed in the early stage of the search for processing functions f1-f6, f8-f14, f16, f17, and finds the global optimal solution with a smaller number of iterations. In the remaining benchmark function experiments, the NDWPSO algorithm shows no outstanding performance for convergence speed in the early iterations. There are two reasons of no outstanding performance in the early iterations. On one hand, the fixed-multimodal benchmark function has many disturbances and local optimal solutions in the whole search space. on the other hand, the initialization scheme based on elite opposition-based learning is still stochastic, which leads to the initial position far from the global optimal solution. The inertia weight based on chaotic mapping and the strategy of spiral updating can significantly improve the convergence speed and computational accuracy of the algorithm in the late search stage. Finally, the NDWPSO algorithm can find better solutions than other algorithms in the middle and late stages of the search.

Evolution curve of NDWPSO and other PSO algorithms for f1 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f2 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f3 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f4 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f5 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f6 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f7 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f8 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f9 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f10 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f11(Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f12 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f13 (Dim = 30,50,100).

Evolution curve of NDWPSO and other PSO algorithms for f14, f15, f16.

Evolution curve of NDWPSO and other PSO algorithms for f17, f18, f19.

Evolution curve of NDWPSO and other PSO algorithms for f20, f21, f22.

Evolution curve of NDWPSO and other PSO algorithms for f23.

To evaluate the performance of different PSO algorithms, a statistical test is conducted. Due to the stochastic nature of the meta-heuristics, it is not enough to compare algorithms based on only the mean and standard deviation values. The optimization results cannot be assumed to obey the normal distribution; thus, it is necessary to judge whether the results of the algorithms differ from each other in a statistically significant way. Here, the Wilcoxon non-parametric statistical test 45 is used to obtain a parameter called p -value to verify whether two sets of solutions are different to a statistically significant extent or not. Generally, it is considered that p  ≤ 0.5 can be considered as a statistically significant superiority of the results. The p -values calculated in Wilcoxon’s rank-sum test comparing NDWPSO and other PSO algorithms are listed in Table  3 for all benchmark functions. The p -values in Table  3 additionally present the superiority of the NDWPSO because all of the p -values are much smaller than 0.5.

In general, the NDWPSO has the fastest convergence rate when finding the global optimum from Figs. 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 and 19 , and thus we can conclude that the NDWPSO is superior to the other PSO variants during the process of optimization.

Comparison experiments between NDWPSO and other intelligent algorithms

Experiments are conducted to compare NDWPSO with several other intelligent algorithms (WOA, HHO, GWO, AOA, EO and DE). The experimental object is 23 benchmark functions, and the experimental parameters of the NDWPSO algorithm are set the same as in Experiment 4.1. The maximum number of iterations of the experiment is increased to 2000 to fully demonstrate the performance of each algorithm. Each algorithm is repeated 30 times individually. The parameters of the relevant intelligent algorithms in the experiments are set as shown in Table 4 . To ensure the fairness of the algorithm comparison, all parameters are concerning the original parameters in the relevant algorithm literature. The experimental results are shown in Tables 5 , 6 , 7 and 8 and Figs. 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 and 36 .

Evolution curve of NDWPSO and other algorithms for f1 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f2 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f3(Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f4 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f5 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f6 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f7 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f8 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f9(Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f10 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f11 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f12 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f13 (Dim = 30,50,100).

Evolution curve of NDWPSO and other algorithms for f14, f15, f16.

Evolution curve of NDWPSO and other algorithms for f17, f18, f19.

Evolution curve of NDWPSO and other algorithms for f20, f21, f22.

Evolution curve of NDWPSO and other algorithms for f23.

The experimental data of NDWPSO and other intelligent algorithms for handling 30, 50, and 100-dimensional benchmark functions ( \({f}_{1}-{f}_{13}\) ) are recorded in Tables 8 , 9 and 10 , respectively. The comparison data of fixed-multimodal benchmark tests ( \({f}_{14}-{f}_{23}\) ) are recorded in Table 11 . According to the data in Tables 5 , 6 and 7 , the NDWPSO algorithm obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function ( \({f}_{1}-{f}_{13}\) ) in the search space of three dimensions (Dim = 30, 50, 100), respectively. In Table 8 , the NDWPSO algorithm obtains 80% of the optimal solutions in 10 fixed-multimodal benchmark functions.

The convergence curves of each algorithm are shown in Figs. 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 and 36 . The NDWPSO algorithm demonstrates two convergence behaviors when calculating the benchmark functions in 30, 50, and 100-dimensional search spaces. The first behavior is the fast convergence of NDWPSO with a small number of iterations at the beginning of the search. The reason is that the Iterative-mapping strategy and the position update scheme of dynamic weighting are used in the NDWPSO algorithm. This scheme can quickly target the region in the search space where the global optimum is located, and then precisely lock the optimal solution. When NDWPSO processes the functions \({f}_{1}-{f}_{4}\) , and \({f}_{9}-{f}_{11}\) , the behavior can be reflected in the convergence trend of their corresponding curves. The second behavior is that NDWPSO gradually improves the convergence accuracy and rapidly approaches the global optimal in the middle and late stages of the iteration. The NDWPSO algorithm fails to converge quickly in the early iterations, which is possible to prevent the swarm from falling into a local optimal. The behavior can be demonstrated by the convergence trend of the curves when NDWPSO handles the functions \({f}_{6}\) , \({f}_{12}\) , and \({f}_{13}\) , and it also shows that the NDWPSO algorithm has an excellent ability of local search.

Combining the experimental data with the convergence curves, it is concluded that the NDWPSO algorithm has a faster convergence speed, so the effectiveness and global convergence of the NDWPSO algorithm are more outstanding than other intelligent algorithms.

Experiments on classical engineering problems

Three constrained classical engineering design problems (welded beam design, pressure vessel design 43 , and three-bar truss design 38 ) are used to evaluate the NDWPSO algorithm. The experiments are the NDWPSO algorithm and 5 other intelligent algorithms (WOA 36 , HHO, GWO, AOA, EO 41 ). Each algorithm is provided with the maximum number of iterations and population size ( \({\text{Mk}}=500,\mathrm{ n}=40\) ), and then repeats 30 times, independently. The parameters of the algorithms are set the same as in Table 4 . The experimental results of three engineering design problems are recorded in Tables 9 , 10 and 11 in turn. The result data is the average value of the solved data.

Welded beam design

The target of the welded beam design problem is to find the optimal manufacturing cost for the welded beam with the constraints, as shown in Fig.  37 . The constraints are the thickness of the weld seam ( \({\text{h}}\) ), the length of the clamped bar ( \({\text{l}}\) ), the height of the bar ( \({\text{t}}\) ) and the thickness of the bar ( \({\text{b}}\) ). The mathematical formulation of the optimization problem is given as follows:

Welded beam design.

In Table 9 , the NDWPSO, GWO, and EO algorithms obtain the best optimal cost. Besides, the standard deviation (SD) of t NDWPSO is the lowest, which means it has very good results in solving the welded beam design problem.

Pressure vessel design

Kannan and Kramer 43 proposed the pressure vessel design problem as shown in Fig.  38 to minimize the total cost, including the cost of material, forming, and welding. There are four design optimized objects: the thickness of the shell \({T}_{s}\) ; the thickness of the head \({T}_{h}\) ; the inner radius \({\text{R}}\) ; the length of the cylindrical section without considering the head \({\text{L}}\) . The problem includes the objective function and constraints as follows:

Pressure vessel design.

The results in Table 10 show that the NDWPSO algorithm obtains the lowest optimal cost with the same constraints and has the lowest standard deviation compared with other algorithms, which again proves the good performance of NDWPSO in terms of solution accuracy.

Three-bar truss design

This structural design problem 44 is one of the most widely-used case studies as shown in Fig.  39 . There are two main design parameters: the area of the bar1 and 3 ( \({A}_{1}={A}_{3}\) ) and area of bar 2 ( \({A}_{2}\) ). The objective is to minimize the weight of the truss. This problem is subject to several constraints as well: stress, deflection, and buckling constraints. The problem is formulated as follows:

Three-bar truss design.

From Table 11 , NDWPSO obtains the best design solution in this engineering problem and has the smallest standard deviation of the result data. In summary, the NDWPSO can reveal very competitive results compared to other intelligent algorithms.

Conclusions and future works

An improved algorithm named NDWPSO is proposed to enhance the solving speed and improve the computational accuracy at the same time. The improved NDWPSO algorithm incorporates the search ideas of other intelligent algorithms (DE, WOA). Besides, we also proposed some new hybrid strategies to adjust the distribution of algorithm parameters (such as the inertia weight parameter, the acceleration coefficients, the initialization scheme, the position updating equation, and so on).

23 classical benchmark functions: indefinite unimodal (f1-f7), indefinite multimodal (f8-f13), and fixed-dimensional multimodal(f14-f23) are applied to evaluate the effective line and feasibility of the NDWPSO algorithm. Firstly, NDWPSO is compared with PSO, CDWPSO, and SDWPSO. The simulation results can prove the exploitative, exploratory, and local optima avoidance of NDWPSO. Secondly, the NDWPSO algorithm is compared with 5 other intelligent algorithms (WOA, HHO, GWO, AOA, EO). The NDWPSO algorithm also has better performance than other intelligent algorithms. Finally, 3 classical engineering problems are applied to prove that the NDWPSO algorithm shows superior results compared to other algorithms for the constrained engineering optimization problems.

Although the proposed NDWPSO is superior in many computation aspects, there are still some limitations and further improvements are needed. The NDWPSO performs a limit initialize on each particle by the strategy of “elite opposition-based learning”, it takes more computation time before speed update. Besides, the” local optimal jump-out” strategy also brings some random process. How to reduce the random process and how to improve the limit initialize efficiency are the issues that need to be further discussed. In addition, in future work, researchers will try to apply the NDWPSO algorithm to wider fields to solve more complex and diverse optimization problems.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by Key R&D plan of Shandong Province, China (2021CXGC010207, 2023CXGC01020); First batch of talent research projects of Qilu University of Technology in 2023 (2023RCKY116); Introduction of urgently needed talent projects in Key Supported Regions of Shandong Province; Key Projects of Natural Science Foundation of Shandong Province (ZR2020ME116); the Innovation Ability Improvement Project for Technology-based Small- and Medium-sized Enterprises of Shandong Province (2022TSGC2051, 2023TSGC0024, 2023TSGC0931); National Key R&D Program of China (2019YFB1705002), LiaoNing Revitalization Talents Program (XLYC2002041) and Young Innovative Talents Introduction & Cultivation Program for Colleges and Universities of Shandong Province (Granted by Department of Education of Shandong Province, Sub-Title: Innovative Research Team of High Performance Integrated Device).

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School of Mechanical and Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, China

Jinwei Qiao, Guangyuan Wang, Zhi Yang, Jun Chen & Pengbo Liu

Shandong Institute of Mechanical Design and Research, Jinan, 250353, China

School of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

Xiaochuan Luo

Fushun Supervision Inspection Institute for Special Equipment, Fushun, 113000, China

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Z.Y., J.Q., and G.W. wrote the main manuscript text and prepared all figures and tables. J.C., P.L., K.L., and X.L. were responsible for the data curation and software. All authors reviewed the manuscript.

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Correspondence to Zhi Yang .

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Qiao, J., Wang, G., Yang, Z. et al. A hybrid particle swarm optimization algorithm for solving engineering problem. Sci Rep 14 , 8357 (2024). https://doi.org/10.1038/s41598-024-59034-2

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Received : 11 January 2024

Accepted : 05 April 2024

Published : 10 April 2024

DOI : https://doi.org/10.1038/s41598-024-59034-2

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