ADR Times

Common Problem-Solving Models & How to Use Them

Problem – solving models are step-by-step processes that provide a framework for addressing challenges. Problems arise in every facet of life. From work. to home. to friends and family, problems and conflicts can make life difficult and interfere with our physical and mental well-being. Understanding how to approach problems when they arise and implementing problem-solving techniques can make the journey through a problem less onerous on ourselves and those around us.

By building a structured problem-solving process, you can begin to build muscle memory by repeatedly practicing the same approach, and eventually, you may even begin to find yourself solving complex problems . Building a problem-solving model for each of the situations where you may encounter a problem can give you a path forward, even when the most difficult of problems arise.

This article will explore the concept of problem-solving models and dive into examples of such models and how to use them. It will also outline the benefits of implementing a problem-solving model in each area of life and why these problem-solving methods can have a large impact on your overall well-being. The goal of this article is to help you identify effective problem-solving strategies and develop critical thinking to generate solutions for any problem that comes your way.

Problem-Solving Model Defined

The first step in creating a problem-solving plan is to understand what we mean when we say problem-solving models. A problem-solving model is a step-by-step process that helps a team identify and effectively solve problems that they may encounter. This problem-solving approach gives the team the muscle memory and guide to address a conflict and resolve disputes quickly and effectively.

There are common problem-solving models that many teams have implemented, but there is also the freedom to shape a method to fit the needs of a specific situation. These models often rely on various problem-solving techniques to identify the root cause of the issue and find the best solution. This article will explore some common problem-solving models as well as general problem-solving techniques to help a team engage with and solve problems effectively.

Benefits of Implementing Problem-Solving Models

Before we discuss the exact models for problem-solving, it can be helpful to discuss why problem-solving models are beneficial in the first place. There are a variety of benefits to having a plan in place when a problem arises, but a few important benefits are listed below.

Guide Posts

When a team encounters a problem and has a guide for how to approach and solve the problem, it can be a relief to know that they have a process to fall back on when the issue cannot be resolved quickly from the beginning. A problem-solving strategy will serve as a guide for the parties to know which steps to take next and how to identify the appropriate solution.

It can also clarify when the issue needs to stay within the team, and when the issue needs to be escalated to someone in a position with more authority. It can also help the entire team solve complex problems without creating an issue out of the way the team solves the problem. It gives the team a blueprint to work from and encourages them to find a good solution.

Creative Solutions That Last

When the team or family has a way to fall back on to solve a problem, it takes some of the pressure off of coming up with the process and allows the parties to focus on identifying the relevant information and coming up with various potential solutions to the issue. By using a problem-solving method, the parties can come up with different solutions and find common ground with the best solution. This can be stifled if the team is too focused on figuring out how to solve the problem.

Additionally, the solutions that the parties come up with through problem-solving tools will often address the root cause of the issue and stop the team from having to revisit the same problem over and over again. This can lead to overall productivity and well-being and help the team continue to output quality work. By encouraging collaboration and creativity, a problem-solving technique will often keep solving problems between the parties moving forward and possibly even address them before they show up.

Common Models to Use in the Problem-Solving Process

Several models can be applied to a complex problem and create possible solutions. These range from common and straightforward to creative and in-depth to identify the most effective ways to solve a problem. This section will discuss and break down the problem-solving models that are most frequently used.

Standard Problem-Solving Process

When you search for a problem-solving technique, chances are you will find the standard model for saving problems. This model identifies and uses several important steps that will often be used in other models as well, so it can be helpful to begin the model-building process with an understanding of this model as a base. Other models often draw from this process and adapt one or more of the steps to help create additional options. Each of these steps works to accomplish a specific goal in furtherance of a solution.

Define the Problem

The first step in addressing a problem is to create a clear definition of the issue at hand. This will often require the team to communicate openly and honestly to place parameters around the issue. As the team defines the problem, it will be clear what needs to be solved and what pieces of the conflict are ancillary to the major issue. It helps to find the root causes of the issue and begin a process to address that rather than the symptoms of the problem. The team can also create a problem statement, which outlines the parameters of the problem and what needs to be fixed.

In addition to open and honest communication, other techniques can help to identify the root cause and define the problem. This includes a thorough review of the processes and steps that are currently used in the task and whether any of those steps are directly or indirectly causing the problem.

This includes reviewing how tasks are done, how communication is shared, and the current partners and team members that work together to identify if any of those are part of the issue. It is also the time to identify if some of the easy fixes or new tools would solve the problem and what the impact would be.

It is also important to gain a wide understanding of the problem from all of the people involved. Many people will have opinions on what is going on, but it is also important to understand the facts over the opinions that are affecting the problem. This can also help you identify if the problem is arising from a boundary or standard that is not being met or honored. By gathering data and understanding the source of the problem, the process of solving it can begin.

Generate Solutions

The next step in the basic process is to generate possible solutions to the problem. At this step, it is less important to evaluate how each of the options will play out and how they may change the process and more important to identify solutions that could address the issue. This includes solutions that support the goals of the team and the task, and the team can also identify short and long-term solutions.

The team should work to brainstorm as many viable solutions as possible to give them the best options to consider moving forward. They cannot pick the first solution that is proposed and consider it a successful problem-solving process.

Evaluate and Select

After a few good options have been identified, the next step is to evaluate the options and pick the most viable option that also supports the goals of the team or organization. This includes looking at each of the possible solutions and determining how they would either encourage or hinder the goals and standards of the team. These should evaluated without bias toward the solution proposed or the person putting forward the solution. Additionally, the team should consider both actual outcomes that have happened in the past and predicted instances that may occur if the solution is chosen.

Each solution should be evaluated by considering if the solution would solve the current problem without causing additional issues, the willingness of the team to buy in and implement the solution, and the actual ability of the team to implement the solution.

Participation and honesty from all team members will make the process go more smoothly and ensure that the best option for everyone involved is selected. Once the team picks the option they would like to use for the specific problem, they should clearly define what the solution is and how it should be implemented. There should also be a strategy for how to evaluate the effectiveness of the solution.

Implement the Solution and Follow Up

Once a solution is chosen, a team will often assume that the work of solving problems is complete. However, the final step in the basic model is an important step to determine if the matter is resolved or if additional options are needed. After the solution has been implemented by the team, the members of the team must provide feedback and identify any potential obstacles that may have been missed in the decision-making process.

This encourages long-term solutions for the problem and helps the team to continue to move forward with their work. It also gives the team a sense of ownership and an example of how to evaluate an idea in the future.

If the solution is not working the way that it should, the team will often need to adapt the option, or they may get to the point where they scrap the option and attempt another. Solving a problem is not always a linear process, and encouraging reform and change within the process will help the team find the answer to the issues that they face.

GROW Method

Another method that is similar to the standard method is the G.R.O.W. method. This method has very similar steps to the standard method, but the catchiness of the acronym helps a team approach the problem from the same angle each time and work through the method quickly.

The first step in the method is to identify a goal, which is what the “g” stands for in “grow.” To establish a goal, the team will need to look at the issues that they are facing and identify what they would like to accomplish and solve through the problem-solving process. The team will likely participate in conversations that identify the issues that they are facing and what they need to resolve.

The next step is to establish the current reality that the group is facing. This helps them to determine where they currently are and what needs to be done to move them forward. This can help the group establish a baseline for where they started and what they would like to change.

The next step is to find any obstacles that may be blocking the group from achieving their goal. This is where the main crux of the issues that the group is facing will come out. This is also helpful in giving the group a chance to find ways around these obstacles and toward a solution.

Way Forward

After identifying the obstacles and potential ways to avoid them, the group will then need to pick the best way to move forward and approach their goal together. Here, they will need to create steps to move forward with that goal.

Divide and Conquer

Another common problem-solving method is the divide-and-conquer method. Here, instead of the entire team working through each step of the process as a large group, they split up the issue into smaller problems that can be solved and have individual members or small groups work through the smaller problems. Once each group is satisfied with the solution to the problem, they present it to the larger group to consider along with the other options.

This process can be helpful if there is a large team attempting to solve a large and complex problem. It is also beneficial because it can be used in teams with smaller, specialized teams within it because it allows each smaller group to focus on what they know best.

However, it does encourage the parties to shy away from collaboration on the overall issue, and the different solutions that each proposes may not be possible when combined and implemented.

For this reason, it is best to use this solution when approaching complex problems with large teams and the ability to combine several problem-solving methods into one.

Six Thinking Hats

The Six Thinking Hats theory is a concept designed for a team with a lot of differing conflict styles and problem-solving techniques. This method was developed to help sort through the various techniques that people may use and help a team find a solution that works for everyone involved. It helps to organize thinking and lead the conversation to the best possible solution.

Within this system, there are six different “hats” that identify with the various aspects of the decision-making process: the overall process, idea generation, intuition and emotions, values, information gathering, and caution or critical thinking. The group agrees to participate in the process by agreeing on which of the hats the group is wearing at a given moment. This helps set parameters and expectations around what the group is attempting to achieve at any moment.

This system is particularly good in a group with different conflict styles or where people have a hard time collecting and organizing their thoughts. It can be incredibly beneficial for complex problems with many moving parts. It can also help groups identify how each of the smaller sections relates to the big picture and help create new ideas to answer the overall problem.

However, it can derail if the group focuses too heavily or for too long on one of the “hats.” The group should ensure that they have a facilitator to guide them through the process and ensure that each idea and section is considered adequately.

Trial and Error

The trial and error process takes over the evaluation and selection process and instead chooses to try out each of the alternatives to determine what the best option would be. It allows the team to gather data on each of the options and how they apply practically. It also provides the ability for the team to have an example of each possible answer to help a decision-maker determine what the best option is.

Problem-solving methods that focus on trial and error can be helpful when a team has a simple problem or a lot of time to test potential solutions, gather data, and determine an answer to the issue.

It can also be helpful when the team has a sense of the best guess for a solution but wants to test it out to determine if the data supports that option, or if they have several viable options and would like to identify the best one. However, it can be incredibly time-consuming to test each of the options and evaluate how they went. Time can often be saved by evaluating each option and selecting the best to test.

Other Problem-Solving Skills

In addition to the methods outlined above, other problem-solving skills can be used regardless of the model that is used. These techniques can round out the problem-solving process and help address either specific steps in the overall method or alter the step in some way to help it fit a specific situation.

Ask Good Questions

One of the best ways to work through any of the problem-solving models is to ask good questions. This will help the group find the issue at the heart of the problem and address that issue rather than the symptoms. The best questions will also help the group find viable solutions and pick the solution that the group can use to move forward. The more creative the questions , the more likely that they will produce innovative solutions.

Take a Step Back

Occasionally, paying attention to a problem too much can give the group tunnel vision and harm the overall processes that the group is using. Other times, the focus can lead to escalations in conflict. When this happens, it can be helpful to set aside the problem and give the group time to calm down. Once they have a chance to reconsider the options and how they apply, they can approach the issue with a new sense of purpose and determination. This can lead to additional creative solutions that may help the group find a new way forward.

Final Thoughts

Problem-solving can be a daunting part of life. However, with a good problem-solving method and the right techniques, problems can be addressed well and quickly. Applying some of these options outlined in this article can give you a head start in solving your next problem and any others that arise.

To learn more about problem-solving models, problem-solving activities, and more, contact ADR Times !

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35 problem-solving techniques and methods for solving complex problems

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

  • Tips for more effective problem-solving

Complete problem-solving methods

  • Problem-solving techniques to identify and analyze problems
  • Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

example of problem solving model

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

  • Six Thinking Hats
  • Lightning Decision Jam
  • Problem Definition Process
  • Discovery & Action Dialogue
Design Sprint 2.0
  • Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

  • The Creativity Dice
  • Fishbone Analysis
  • Problem Tree
  • SWOT Analysis
  • Agreement-Certainty Matrix
  • The Journalistic Six
  • LEGO Challenge
  • What, So What, Now What?
  • Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

  • Improved Solutions
  • Four-Step Sketch
  • 15% Solutions
  • How-Now-Wow matrix
  • Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

  • Check-in/Check-out
  • Doodling Together
  • Show and Tell
  • Constellations
  • Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

  • One Breath Feedback
  • Who What When Matrix
  • Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

example of problem solving model

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

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thank you very much for these excellent techniques

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Certainly wonderful article, very detailed. Shared!

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Status.net

What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

  • Identify the issue : Recognize the problem that needs to be solved.
  • Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
  • Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
  • Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
  • Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
  • Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
  • Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

  • Brainstorming with others
  • Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
  • Analyzing cause and effect
  • Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

  • Creating a list of potential ideas to solve the problem
  • Grouping and categorizing similar solutions
  • Prioritizing potential solutions based on feasibility, cost, and resources required
  • Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

  • SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
  • Decision-making matrices
  • Pros and cons lists
  • Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

  • Communicating the solution to relevant parties
  • Setting timelines and milestones
  • Assigning tasks and responsibilities
  • Monitoring the solution and making adjustments as necessary
  • Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

  • Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
  • Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
  • SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
  • Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

  • Generate a diverse range of solutions
  • Encourage all team members to participate
  • Foster creative thinking

When brainstorming, remember to:

  • Reserve judgment until the session is over
  • Encourage wild ideas
  • Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

  • 5 Whys : Ask “why” five times to get to the underlying cause.
  • Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
  • Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

  • List your problem’s strengths, such as relevant resources or strong partnerships.
  • Identify its weaknesses, such as knowledge gaps or limited resources.
  • Explore opportunities, like trends or new technologies, that could help solve the problem.
  • Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

  • Write the problem in the center of a blank page.
  • Draw branches from the central problem to related sub-problems or contributing factors.
  • Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

  • Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
  • Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
  • Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

  • Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
  • Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
  • Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

  • Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
  • Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
  • Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
  • How to Resolve Employee Conflict at Work [Steps, Tips, Examples]
  • How to Write Inspiring Core Values? 5 Steps with Examples
  • 30 Employee Feedback Examples (Positive & Negative)

How to master the seven-step problem-solving process

In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.

Podcast transcript

Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.

Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].

Charles and Hugo, welcome to the podcast. Thank you for being here.

Hugo Sarrazin: Our pleasure.

Charles Conn: It’s terrific to be here.

Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”

You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”

I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.

I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.

Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.

Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.

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Simon London: So this is a concise problem statement.

Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.

Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.

How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.

Hugo Sarrazin: Yeah.

Charles Conn: And in the wrong direction.

Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?

Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.

What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.

Simon London: What’s a good example of a logic tree on a sort of ratable problem?

Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.

If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.

When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.

Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.

Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.

People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.

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Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?

Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.

Simon London: Not going to have a lot of depth to it.

Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.

Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.

Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.

Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.

Both: Yeah.

Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.

Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.

Simon London: Right. Right.

Hugo Sarrazin: So it’s the same thing in problem solving.

Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.

Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?

Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.

Simon London: Would you agree with that?

Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.

You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.

Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?

Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.

Simon London: Step six. You’ve done your analysis.

Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”

Simon London: But, again, these final steps are about motivating people to action, right?

Charles Conn: Yeah.

Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.

Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.

Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.

Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.

Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?

Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.

You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.

Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.

Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”

Hugo Sarrazin: Every step of the process.

Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?

Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.

Simon London: Problem definition, but out in the world.

Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.

Simon London: So, Charles, are these complements or are these alternatives?

Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.

Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?

Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.

The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.

Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.

Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.

Hugo Sarrazin: Absolutely.

Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.

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Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.

Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.

Charles Conn: It was a pleasure to be here, Simon.

Hugo Sarrazin: It was a pleasure. Thank you.

Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.

Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.

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26 Good Examples of Problem Solving (Interview Answers)

By Biron Clark

Published: November 15, 2023

Employers like to hire people who can solve problems and work well under pressure. A job rarely goes 100% according to plan, so hiring managers will be more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical in your approach.

But how do they measure this?

They’re going to ask you interview questions about these problem solving skills, and they might also look for examples of problem solving on your resume and cover letter. So coming up, I’m going to share a list of examples of problem solving, whether you’re an experienced job seeker or recent graduate.

Then I’ll share sample interview answers to, “Give an example of a time you used logic to solve a problem?”

Problem-Solving Defined

It is the ability to identify the problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation. 

Problem-solving also involves critical thinking, communication, listening, creativity, research, data gathering, risk assessment, continuous learning, decision-making, and other soft and technical skills.

Solving problems not only prevent losses or damages but also boosts self-confidence and reputation when you successfully execute it. The spotlight shines on you when people see you handle issues with ease and savvy despite the challenges. Your ability and potential to be a future leader that can take on more significant roles and tackle bigger setbacks shine through. Problem-solving is a skill you can master by learning from others and acquiring wisdom from their and your own experiences. 

It takes a village to come up with solutions, but a good problem solver can steer the team towards the best choice and implement it to achieve the desired result.

Watch: 26 Good Examples of Problem Solving

Examples of problem solving scenarios in the workplace.

  • Correcting a mistake at work, whether it was made by you or someone else
  • Overcoming a delay at work through problem solving and communication
  • Resolving an issue with a difficult or upset customer
  • Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
  • Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
  • Troubleshooting and resolving technical issues
  • Handling and resolving a conflict with a coworker
  • Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
  • Taking initiative when another team member overlooked or missed something important
  • Taking initiative to meet with your superior to discuss a problem before it became potentially worse
  • Solving a safety issue at work or reporting the issue to those who could solve it
  • Using problem solving abilities to reduce/eliminate a company expense
  • Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
  • Changing how a process, team, or task is organized to make it more efficient
  • Using creative thinking to come up with a solution that the company hasn’t used before
  • Performing research to collect data and information to find a new solution to a problem
  • Boosting a company or team’s performance by improving some aspect of communication among employees
  • Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem Solving Examples for Recent Grads/Entry Level Job Seekers

  • Coordinating work between team members in a class project
  • Reassigning a missing team member’s work to other group members in a class project
  • Adjusting your workflow on a project to accommodate a tight deadline
  • Speaking to your professor to get help when you were struggling or unsure about a project
  • Asking classmates, peers, or professors for help in an area of struggle
  • Talking to your academic advisor to brainstorm solutions to a problem you were facing
  • Researching solutions to an academic problem online, via Google or other methods
  • Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

You can share all of the examples above when you’re asked questions about problem solving in your interview. As you can see, even if you have no professional work experience, it’s possible to think back to problems and unexpected challenges that you faced in your studies and discuss how you solved them.

Interview Answers to “Give an Example of an Occasion When You Used Logic to Solve a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” since you’re likely to hear this interview question in all sorts of industries.

Example Answer 1:

At my current job, I recently solved a problem where a client was upset about our software pricing. They had misunderstood the sales representative who explained pricing originally, and when their package renewed for its second month, they called to complain about the invoice. I apologized for the confusion and then spoke to our billing team to see what type of solution we could come up with. We decided that the best course of action was to offer a long-term pricing package that would provide a discount. This not only solved the problem but got the customer to agree to a longer-term contract, which means we’ll keep their business for at least one year now, and they’re happy with the pricing. I feel I got the best possible outcome and the way I chose to solve the problem was effective.

Example Answer 2:

In my last job, I had to do quite a bit of problem solving related to our shift scheduling. We had four people quit within a week and the department was severely understaffed. I coordinated a ramp-up of our hiring efforts, I got approval from the department head to offer bonuses for overtime work, and then I found eight employees who were willing to do overtime this month. I think the key problem solving skills here were taking initiative, communicating clearly, and reacting quickly to solve this problem before it became an even bigger issue.

Example Answer 3:

In my current marketing role, my manager asked me to come up with a solution to our declining social media engagement. I assessed our current strategy and recent results, analyzed what some of our top competitors were doing, and then came up with an exact blueprint we could follow this year to emulate our best competitors but also stand out and develop a unique voice as a brand. I feel this is a good example of using logic to solve a problem because it was based on analysis and observation of competitors, rather than guessing or quickly reacting to the situation without reliable data. I always use logic and data to solve problems when possible. The project turned out to be a success and we increased our social media engagement by an average of 82% by the end of the year.

Answering Questions About Problem Solving with the STAR Method

When you answer interview questions about problem solving scenarios, or if you decide to demonstrate your problem solving skills in a cover letter (which is a good idea any time the job description mention problem solving as a necessary skill), I recommend using the STAR method to tell your story.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them. So before jumping in and talking about the problem that needed solving, make sure to describe the general situation. What job/company were you working at? When was this? Then, you can describe the task at hand and the problem that needed solving. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact.

Finally, describe a positive result you got.

Whether you’re answering interview questions about problem solving or writing a cover letter, you should only choose examples where you got a positive result and successfully solved the issue.

Example answer:

Situation : We had an irate client who was a social media influencer and had impossible delivery time demands we could not meet. She spoke negatively about us in her vlog and asked her followers to boycott our products. (Task : To develop an official statement to explain our company’s side, clarify the issue, and prevent it from getting out of hand). Action : I drafted a statement that balanced empathy, understanding, and utmost customer service with facts, logic, and fairness. It was direct, simple, succinct, and phrased to highlight our brand values while addressing the issue in a logical yet sensitive way.   We also tapped our influencer partners to subtly and indirectly share their positive experiences with our brand so we could counter the negative content being shared online.  Result : We got the results we worked for through proper communication and a positive and strategic campaign. The irate client agreed to have a dialogue with us. She apologized to us, and we reaffirmed our commitment to delivering quality service to all. We assured her that she can reach out to us anytime regarding her purchases and that we’d gladly accommodate her requests whenever possible. She also retracted her negative statements in her vlog and urged her followers to keep supporting our brand.

What Are Good Outcomes of Problem Solving?

Whenever you answer interview questions about problem solving or share examples of problem solving in a cover letter, you want to be sure you’re sharing a positive outcome.

Below are good outcomes of problem solving:

  • Saving the company time or money
  • Making the company money
  • Pleasing/keeping a customer
  • Obtaining new customers
  • Solving a safety issue
  • Solving a staffing/scheduling issue
  • Solving a logistical issue
  • Solving a company hiring issue
  • Solving a technical/software issue
  • Making a process more efficient and faster for the company
  • Creating a new business process to make the company more profitable
  • Improving the company’s brand/image/reputation
  • Getting the company positive reviews from customers/clients

Every employer wants to make more money, save money, and save time. If you can assess your problem solving experience and think about how you’ve helped past employers in those three areas, then that’s a great start. That’s where I recommend you begin looking for stories of times you had to solve problems.

Tips to Improve Your Problem Solving Skills

Throughout your career, you’re going to get hired for better jobs and earn more money if you can show employers that you’re a problem solver. So to improve your problem solving skills, I recommend always analyzing a problem and situation before acting. When discussing problem solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Next, to get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t. Think about how you can get better at researching and analyzing a situation, but also how you can get better at communicating, deciding the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem solving ability.

If you practice the tips above, you’ll be ready to share detailed, impressive stories and problem solving examples that will make hiring managers want to offer you the job. Every employer appreciates a problem solver, whether solving problems is a requirement listed on the job description or not. And you never know which hiring manager or interviewer will ask you about a time you solved a problem, so you should always be ready to discuss this when applying for a job.

Related interview questions & answers:

  • How do you handle stress?
  • How do you handle conflict?
  • Tell me about a time when you failed

Biron Clark

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The Ultimate Problem Solving Model Guide For Crafting Perfect Solutions

Anthony Metivier | November 11, 2022 | Thinking

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Ideally, that model should be easy to remember and quick to implement. 

The problem is this:

Not all problems are the same. There’s no such thing as a problem solving chart or diagram that is going to apply to all situations. 

So instead of forcing every issue you’re facing into some bogus Six Steps of Problem Solving Formula, let’s get real.

Let’s look at a number of multi-step problem solving formulas. Once you have this list, you can pick the models most likely to work and enjoy much better results thanks to variety. 

The 9 Best Problem Solving Models And Formulas

As you go through this list, consider taking notes. As you do, jot down different times when these different approaches might help you.

Remember: not all problems are created the same, so the exact problem solving steps you follow need to be suited to the task at hand. Flexibility based on knowledge of what’s available is a key part of objective reasoning .

This point is important because there are some steps to follow before we even look at any models.

  • Recognize that a problem exists and give it a name
  • Represent the problem in the best possible medium (writing, graphics, video)
  • List your goals for solving the problem states
  • Generate and evaluate possible solutions
  • Select the best possible solution
  • Execution the best possible solution 
  • Analyze and determine if the solution you’ve chosen solves the problem

This process is sometimes confused with the standard problem solving model. But in actuality it is the meta-level understanding you need before using any particular model.

One: The Standard Problem Solving Model

As mentioned, many people consider the steps I just listed the standard model for solving problems. They may even simplify it into a problem solving chart like this:

simple problem solving chart

I would suggest making your initial approach much more robust. 

Two: The Dynamic Problem Solving Model

The Dynamic Problem solving model breaks the process into much more distinct phases. 

In phase one, we want to spend as much time as possible going deep into the problem. Look at it in as many ways as possible and from as many perspectives and contexts as you can.

  • Name and describe the problem, ideally in multiple media
  • Explore its contexts
  • Study similar examples
  • Research opportunities for interviewing people who have solved the problem before

dynamic problem solving model

Next, you want to bring in as many idea generation steps as you can. 

  • Brainstorming
  • Mind mapping
  • Gamification
  • Rating the solutions

Once you have visualized and gathered your ideas by brainstorming them onto paper or using a mind map, there are many ways you can gamify.

For example, you can:

  • Ask “what if” questions
  • Ask what Isaksen et al . call “wouldn’t it be nice if” or “wouldn’t it be terrible if” questions
  • Hold a contest for the best solution (internally and externally to your organization)
  • Go for a walk and try not to think about the problem and solutions and then write about your experience in withholding

Rating can be performed in various ways. You can divide the solutions you can up with into grades such as A+, A, B, etc. Or you can give the solutions you’ve gathered ratings from 1-10 and have as many people participate in the process as possible. 

For the final stage:

  • First choose and accept the path and ensure all team members are on the same page
  • Design the actions you’re going to take
  • Schedule the time for implementation and review design
  • Schedule the time for review 

This 3-stage problem solving model is far more robust than the standard solution. 

a man is showing his muscles

Three: The Brief Problem Solving Model

Isaac Newton reportedly said that in order to solve a problem, you just need to think about it constantly. But sometimes you don’t have all the time in the world.

Famous scientist Richard Feynman reflected on the scarcity of time when he described the following model:

1 Write down the problem.

2 Think really hard.

3 Write down the answer.

Sometimes finding the best possible solution really is just this simple. 

To expand a little on how this model might work in practice, you can:

  • Describe the problem broadly and without granular details
  • Briefly describe the best possible outcome and ideas for achieving it that come to mind
  • List the benefits of having it solved to create inspiration and momentum

If you’re in a hurry, this problem solving example will often work very well.

Four: The W.R.A.P. Problem Solving Model

Of all the faster problem solving model examples I’ve seen, the W.R.A.P. formula presented by Chip and Dan Heath in their book Decisive is my favorite. Although not immediate, it’s quite fast. 

W.R.A.P. stands for:

  • Widen your options
  • Reality test
  • Attain distance
  • Prepare to fail

The final point is especially important because we often don’t take time to consider what we’ll do if the solutions we choose do not perform to expectation. 

a watch on a towel

Five: Analyze For Advantage

Sometimes you just want to find the most advantageous outcome.

To do so, follow this model:

  • List the advantages you want as a result of solving the problem
  • List the existing assets, resources and advantages you have right now
  • List your current limitations, including any fears
  • List how you can refine your existing assets to combat those fears
  • Plan for maximum advantage based on your newly optimized assets

Six: Examine Pros and Cons

Although simplistic, a great model to follow in a hurry is to simply list the pros and cons. 

All you need to do is write pros and cons at the top of a piece of paper and draw a line down the center. 

As you list the pros and cons, your mind will probably start branching out and coming up with solutions so that the cons cannot take over.

Seven: Find the Forces

Often when we try to solve problems, we’re not looking deeply enough to find the one root cause. Even if we are, we can fail to find solutions because we’re so focused on finding just one source of the problem. 

a woman is walking between tree roots

Often, there are multiple forces or factors at work in causing a problem. To get started finding them, you can follow this model:

  • List all the people involved
  • List all the technologies involved
  • List all the situations involved
  • Describe the ways in which these different “forces” act upon creating the problem
  • Write out various scenarios in which changes are made to the different elements
  • Try to predict and previsualize various outcomes based on changes you could make

Eight: Peer into the Unconscious

Synectics appeared in the 1950s and assumed that many people struggle to solve problems because the solutions remain outside their conscious awareness. However, their unconscious mind might know the solution and be “hiding” it from the mind for various reasons. 

Robert Langs proposed a similar thesis, and wondered if the unconscious mind wasn’t something like an antivirus system of the mind. 

This idea is not so far-fetched, even though it can be strange to think that the mind would hide the perfect solution from you if it truly knows it.

In Mindshift , Barbara Oakley discusses research showing how the insular cortex can cause a pain response when a person is faced with certain tasks.

This suggests literally what her book title proposes: a shift of mind. 

There are many ways you can do this, and books by her, Langs, and the people behind Synectics are a great place to start for examples of various problem solving models that deal with this level of your mind.

Nine: The Problem Solving Situations Model

Discover Projects offers a great way to ensure that you find the right model for solving your problems. It involves identifying the problem correctly in the first place.

discover projects problem solving model example

They suggest there are at least 6 types of problems:

  • Type I problems: Known by the person with the problem, but only one solution is known.
  • Type II problems: A problem that is known by the person presenting the problem and the person hired to solve it, but the method of solution and solution are known only by the presenter.
  • Type III problems: the problem is known by the presenter and the solver; more than one method may be used to arrive at the solution, which the presenter knows.
  • Type IV problems: the problem is known by the presenter and the solver; the problem may be solved in more than one way; the presenter knows the range of solutions.
  • Type V problems: these problems are clearly defined and the problem is known by the presenter and the solver; the method and solution are unknown by the presenter and the solver.
  • Type VI problems: these problems are not clearly defined or are undefined, have little if any structure, and are complex; the problem is unknown by both the presenter and the solver; the method and solution are unknown by both the presenter and the solver.

When you do this kind of problem identification analysis (where relevant), many more solutions will arise than you would otherwise perceive.

a woman is holding a light bubble

The greatest aspect of this model is that it helps you find out who might have the solution. 

Another way of thinking about this approach is basically what Dan Sullivan is getting at in his Who Not How problem solving model. If you’re able to figure out who can solve the problem, chances are that person also knows how to solve it. 

The Best Problem Solving Model Of Them All

Please don’t feel that what I’m about to say is a trick.

It isn’t. It’s the ultimate solution.

The best problem solving model of them all is the one you practice.

And practice means committing the model to memory, using it consistently and optimizing your approach along the way. 

For an easy and fun way to commit any model to mind quickly, I invite you to get my FREE Memory Improvement Kit:

Magnetic Memory Method Free Memory Improvement Course

It’s a model of a different kind that helps you remove the issue of forgetting from your life. 

Once you’ve done that, you can follow multiple paths to solving the vexations of everyday life quickly. 

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Article • 8 min read

The FOCUS Model

A simple, efficient problem-solving approach.

By the Mind Tools Content Team

example of problem solving model

Are your business processes perfect, or could you improve them?

In an ever-changing world, nothing stays perfect for long. To stay ahead of your competitors, you need to be able to refine your processes on an ongoing basis, so that your services remain efficient and your customers stay happy.

This article looks the FOCUS Model – a simple quality-improvement tool that helps you do this.

About the Model

The FOCUS Model, which was created by the Hospital Corporation of America (HCA), is a structured approach to Total Quality Management (TQM) , and it is widely used in the health care industry.

The model is helpful because it uses a team-based approach to problem solving and to business-process improvement, and this makes it particularly useful for solving cross-departmental process issues. Also, it encourages people to rely on objective data rather than on personal opinions, and this improves the quality of the outcome.

It has five steps:

  • F ind the problem.
  • O rganize a team.
  • C larify the problem.
  • U nderstand the problem.
  • S elect a solution.

Applying the FOCUS Model

Follow the steps below to apply the FOCUS Model in your organization.

Step 1: Find the Problem

The first step is to identify a process that needs to be improved. Process improvements often follow the Pareto Principle , where 80 percent of issues come from 20 percent of problems. This is why identifying and solving one real problem can significantly improve your business, if you find the right problem to solve.

According to a popular analogy, identifying problems is like harvesting apples. At first, this is easy – you can pick apples up from the ground and from the lower branches of the tree. But the more fruit you collect, the harder it becomes. Eventually, the remaining fruit is all out of reach, and you need to use a ladder to reach the topmost branches.

Start with a simple problem to get the team up to speed with the FOCUS method. Then, when confidence is high, turn your attention to more complex processes.

If the problem isn't obvious, use these questions to identify possible issues:

  • What would our customers want us to improve?
  • How can we improve quality ?
  • What processes don't work as efficiently as they could?
  • Where do we experience bottlenecks in our processes?
  • What do our competitors or comparators do that we could do?
  • What frustrates and irritates our team?
  • What might happen in the future that could become a problem for us?

If you have several problems that need attention, list them all and use Pareto Analysis , Decision Matrix Analysis , or Paired Comparison Analysis to decide which problem to address first. (If you try to address too much in one go, you'll overload team members and cause unnecessary stress.)

Step 2: Organize a Team

Your next step is to assemble a team to address the problem.

Where possible, bring together team members from a range of disciplines – this will give you a broad range of skills, perspectives, and experience to draw on.

Select team members who are familiar with the issue or process in hand, and who have a stake in its resolution. Enthusiasm for the project will be greatest if people volunteer for it, so emphasize how individuals will benefit from being involved.

If your first choice of team member isn't available, try to appoint someone close to them, or have another team member use tools like Perceptual Positioning and Rolestorming to see the issue from their point of view.

Keep in mind that a diverse team is more likely to find a creative solution than a group of people with the same outlook.

Step 3: Clarify the Problem

Before the team can begin to solve the problem, you need to define it clearly and concisely.

According to " Total Quality Management for Hospital Nutrition Services ," a key text on the FOCUS Model, an enthusiastic team may be keen to attack an "elephant-sized" problem, but the key to success is to break it down into "sushi-sized" pieces that can be analyzed and solved more easily.

Use the Drill Down technique to break big problems down into their component parts. You can also use the 5 Whys Technique , Cause and Effect Analysis , and Root Cause Analysis to get to the bottom of a problem.

Record the details in a problem statement, which will then serve as the focal point for the rest of the exercise ( CATWOE can help you do this effectively.) Focus on factual events and measurable conditions such as:

  • Who does the problem affect?
  • What has happened?
  • Where is it occurring?
  • When does it happen?

The problem statement must be objective, so avoid relying on personal opinions, gut feelings, and emotions. Also, be on guard against "factoids" – statements that appear to be facts, but that are really opinions that have come to be accepted as fact.

Step 4: Understand the Problem

Once the problem statement has been completed, members of the team gather data about the problem to understand it more fully.

Dedicate plenty of time to this stage, as this is where you will identify the fundamental steps in the process that, when changed, will bring about the biggest improvement.

Consider what you know about the problem. Has anyone else tried to fix a similar problem before? If so, what happened, and what can you learn from this?

Use a Flow Chart or Swim Lane Diagram to organize and visualize each step; this can help you discover the stage at which the problem is happening. And try to identify any bottlenecks or failures in the process that could be causing problems.

As you develop your understanding, potential solutions to the problem may become apparent. Beware of jumping to "obvious" conclusions – these could overlook important parts of the problem, and could create a whole new process that fails to solve the problem.

Generate as many possible solutions as you can through normal structured thinking, brainstorming , reverse brainstorming , and Provocation . Don't criticize ideas initially – just come up with lots of possible ideas to explore.

Step 5: Select a Solution

The final stage in the process is to select a solution.

Use appropriate decision-making techniques to select the most viable option. Decision Trees , Paired Comparison Analysis , and Decision Matrix Analysis are all useful tools for evaluating your options.

Once you've selected an idea, use tools such as Risk Analysis , "What If" Analysis , and the Futures Wheel to think about the possible consequences of moving ahead, and make a well-considered go/no-go decision to decide whether or not you should run the project.

People commonly use the FOCUS Model in conjunction with the Plan-Do-Check-Act cycle. Use this approach to implement your solutions in a controlled way.

The FOCUS Model is a simple quality-improvement tool commonly used in the health care industry. You can use it to improve any process, but it is particularly useful for processes that span different departments.

The five steps in FOCUS are as follows:

People often use the FOCUS Model in conjunction with the Plan-Do-Check-Act cycle, which allows teams to implement their solution in a controlled way.

Bataldan, P. (1992). 'Building Knowledge for Improvement: an Introductory Guide to the Use of FOCUS-PDCA,' Nashville: TN Quality Resource Group, Hospital Corporation of America.

Schiller, M., Miller-Kovach, M., and Miller-Kovach, K. (1994). 'Total Quality Management for Hospital Nutrition Services,' Aspen Publishers Inc. Available here .

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Critical & Creative Thinking - OER & More Resources: IDEAL problem solving

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VM: I had to inter-library loan this item to read the original content.  This is highly cited throughout literature, so I wanted to have a good grasp on what it covered.  Here are my notes and commentary:

  •  Full text From TNtech.edu: "Ideal Problem Solver, 2 ed." (c) 1984, 1993 more... less... Thanks to Center for Assessment & Improvement of Learning - Reports & Publications"
  • Full text from ERIC: The IDEAL Workplace: Strategies for Improving Learning, Problem Solving, and Creativity
  • Show your support: The Ideal Problem Solver: A Guide to Improving Thinking, Learning, and Creativity Second Edition

The reason you should learn the IDEAL method is so you don't need to avoid problems.  The more know about and practice problem solving, the easier it gets.  It is learnable skill. It also prompts you to look for problems and solutions instead of just doing things the same old way.

Improvement of problem solving skills.  

Model for analyzing the processes that underlie effective problem solving.

IDEAL Model for improving problem solving (Verbatim copy of Fig 2.1; p.12)

I = Identifying the problem.

D = Define and represent the problem.

E = Explore possible strategies.

A = Act on the strategies.

L = Look back and evaluate the effects of your activities.

ELABORATION:

I = Identifying that there is a problem that, once described as a problem, may be solved or improved.

D = Define and represent the problem.  Draw it instead of trying to imagine it.

E = Explore possible strategies & alternative approaches or viewpoints. 

General strategies: Break problem down into small simple problems. Working a problem backwards. Build scale model Try simulation experiment, with smaller or simpler sets.

A = Act on the strategies. Try, then reflect or recall. Actively try learning strategy.

L = Look back and evaluate the effects of your activities. Look at results of learning strategy used: Does it work to allow full recall?

"Many students make the mistake of assuming that they have "learned" adequately if the information seems to make sense as they read it in a textbook or hear it in a lecture."    (p. 23" Must  use or practice, recall, or paraphrase - in order to evaluate effectiveness of learning.  

Math: Do example problems before looking at solution to practice concepts.  Look at solution to see where you went wrong (or not). 

Don't let the test be the first time you evaluate your understanding of material

Problem identification and definition.

Proof of concept - act/look/evaluate.

To find an answer to a problem, you can dig deeper, or dig somewhere else.  

Question assumptions about limits  The old - think outside the box- strategy.

When memorizing, know what you need to remember  Definitions?  Concepts? Graphs?  Dates?  each teacher has different priorities...ask them what to focus on

Ways to solve problem of learning new information.

Techniques for improving memory.

Short term meomory

Long term memory

Remembering people's names

Studying for an essay test.

Using cues to retrieve information.  For example, you can remember IDEAL first and that will help you reconstruct the idea of how to solve problems.

Some strategies for remembering information:

Make a story full of memorable images.  

Funny obnoxious "vivid images" or "mental pictures" are more memorabl e. (Ex: random words in a list, passwords, people's names. Banana vomit haunts me.)

Rehearse over and over - over learn.   (Ex: Memorizing a phone number 867-5309 )

Rehearse words in groups - chunking. (Ex: Memorizing a part in a play, poems, pledges, short stories.)

Organize words into conceptual categories - Look for unifying relationships. (Recall, order not important. Ex: Shopping list, points in an essay.)

Look for similarities and coincidences in the words themselves. (Ex: How many words have e's, or 2 syllables, or have pun-ishing homonyms)

The feet that use the manual transmission car pedals are, from left to right: ​ C ( L eft-foot) utch , the  B( R ight-foot) ake , and the  A ccelerato ( R ight-foot)

Does order mimic alphabetical order? The manual transmission car pedals are, from left to right, the C lutch, the B rake, and the A ccelerator )   

Use Acronyms I dentify D efine ​E xplore A ct ​L ook

Acronym- easily remembered word: FACE

example of problem solving model

Acrostic- easily remembered phrase:    E very G ood B oy D eserves F udge

  • Modified image source: Commons.wikimedia.org

Don't waste time studying what you already know

Image - Name Strategy:

What is unique about the person?  What is unique about their name?

Find a relationship between the two.

Other Pairing Strategies:

method of loci: arranging words to be remembered in association with familiar location or path .

Peg-word method: arranging words to be remembered in association with number order or alphabet letter order .

Strategies to comprehend new information.

more difficult than

Strategies to memorize new information.

Learning with understanding - comprehending new information.

Knowledge of CORE CONCEPTS in a field SIMPLIFIES problem solving. 

Ways to approach a problem of learning information that seems to be arbitrary:

Over-learn:  rehearse the facts until they are mastered.  2+2=4

Find relationships between images or words that are memorable: story telling, silmilarieties, vivid images, pegging, etc.

When a concept seems unclear, learn more about it.

Memory- can be of seemingly arbitrary words or numbers: ROTE (Ex. Facts and relationships) appearance

Comprehension - is understanding significance or relationships or function

Novices often forced to memorize information until they learn enough (related concepts and context) to understand it.

The mere memorization of information rarely provides useful conceptual tools that enable one to solve new problems later on. (p. 61,69)

Taking notes will not necessarily lead to effective recall prompts. How do you know when you understand material? Self-test by trying to explain material to another person.That will expose gaps in understanding.

Recall answers or solve problems out of order to be sure you know which concepts to apply and why.

Look at mistakes made as soon as possible, and learn where you went wrong.

Uses of information require more or less precision in understanding, depending on context. (A pilot must know more about an airplane than a passenger.)

Evaluation basics: evaluate factual claims look for flaws in logic question assumptions that form the basis of the argument

Correlation does not necessarily prove cause and effect.

Importance of being able to criticize ideas and generate alternatives.

Strategies for effective criticism.

Strategies for formulating creative solutions.

Finding/understanding implicit assumptions that hamper brainstorming.

Strategies for making implicit assumptions explicit.

"The uncreative mind can spot wrong answers, but it takes a creative mnd to spot wrong questions ." Emphasis added. - Anthony Jay, (p.93)

Making implicit assumptions explicit: look for inconsistencies question assumptions make predictions analyze worst case get feedback & criticism from others

Increase generation of novel ideas: break down problem into smaller parts analyze properties on a simpler level use analogies use brainstorming give it a rest, sleep on it don't be in a hurry, let ideas incubate: ​talk to others, read, keep the problem in the back of your mind try to communicate your ideas as clearly as possible, preferably in writing. attempting to write or teach an idea can function as a discovery technique

Strategies for Effective Communication

What we are trying to accomplish (goal)

Evaluating communication fro effectiveness:

Identify and Define: Have you given audience basis to understand different points of view about a topic? Different problem definitions can lead to different solutions. Did you Explore pros and cons of different strategies? Did you take Action and then Look at consequences? Did you organize your content into main points that are easy to identify and remeber?

Did you use analogies and background information to put facts into context?

Did you make sure your facts were accurate and did you avoid making assumptions?Always check for logical fallacies and inconsistencies.  Did you include information that is novel and useful, instead of just regurgitating what everyone already knows?

After you communicate, get feedback and evaluate your strategies.  Look for effects, and learn from your mistakes.  (p. 117)

Identify and Define what (problem) you want to communicate, with respect to your audience and your goals. Explore strategies for communicating your ideas.Act - based on your strategies. Look at effects.

Summaries of Useful  Attitudes and Strategies: Anybody can use the IDEAL system to improve their problem solving skills.

Related Resources:

  • Teaching The IDEAL Problem-Solving Method To Diverse Learners Written by: Amy Sippl
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Teaching the IDEAL Problem-Solving Method to Diverse Learners

Written by:

  Amy Sippl

Filed under: EF 101 Series , Executive Functioning , Problem Solving

Published:  January 21, 2021

Last Reviewed: April 10, 2023

READING TIME:  ~ minutes

We may assume that teens and young adults come equipped with a strong sense of approaching difficult or uncertain situations. For many of the individuals we work with, problem-solving needs to be practiced and developed in the same way as academic and social skills. The IDEAL Problem Solving Method is one option to teach problem-solving to diverse learners.

What is problem-solving?

Problem-solving is the capacity to identify and describe a problem and generate solutions to fix it .

Problem-solving involves other executive functioning behaviors as well, including attentional control, planning , and task initiation . Individuals might use time management , emotional control, or organization skills to solve problems as well. Over time, learners can observe their behavior, use working memory , and self-monitor behaviors to influence how we solve future issues.

Why are problem-solving strategies important?

Not all diverse learners develop adequate problem-solving. Learners with a history of behavioral and learning challenges may not always use good problem-solving skills to manage stressful situations. Some students use challenging behaviors like talking back, arguing, property destruction, and aggression when presented with challenging tasks. Others might shut down, check out, or struggle to follow directions when encountering new or unknown situations.

Without a step-by-step model for problem-solving , including identifying a problem and choosing a replacement behavior to solve it, many of our children and students use challenging behaviors instead. The IDEAL Problem-Solving Method is one option to teach diverse learners to better approach difficult situations.

IDEAL Problem-Solving Method

In 1984, Bransford and Stein published one of the most popular and well-regarded problem-solving methods. It’s used both in industry and in education to help various learners establish a problem, generate solutions, and move forward quickly and efficiently. By teaching your learner each step of the IDEAL model, you can provide them with a set of steps to approach a problem with confidence.

The IDEAL Problem-Solving Method includes:

Word Image 2 Teaching The Ideal Problem-Solving Method To Diverse Learners

I – Identify the problem.

There’s no real way to create a solution to a problem unless you first know the scope of the problem. Encourage your learner to identify the issue in their own words. Outline the facts and the unknowns. Foster an environment where your learner is praised and supported for identifying and taking on new problems.

Examples of identifying problems:

  • “I have a math quiz next week and don’t know how to do the problems.”
  • “I can’t access my distance learning course website.”
  • “The trash needs to be taken out, and I can’t find any trash bags.”

D – Define an outcome

The second step in the IDEAL problem-solving process is to define an outcome or goal for problem-solving. Multiple people can agree that a problem exists but have very different ideas on goals or outcomes. By deciding on an outlined objective first, it can speed up the process of identifying solutions.

Defining outcomes and goals may be a difficult step for some diverse learners. The results don’t need to be complicated, but just clear for everyone involved.

Examples of defining outcomes:

  • “I want to do well on my math quiz.”
  • “I get access to the course website.”
  • “The trash gets taken out before the trash pickup day tomorrow.”

E – Explore possible strategies.

Once you have an outcome, encourage your learner to brainstorm possible strategies. All possible solutions should be on the table during this stage, so encourage learners to make lists, use sticky notes, or voice memos to record any ideas. If your learner struggles with creative idea generation, help them develop a plan of resources for who they might consult in the exploration stage.

Examples of possible strategies to solve a problem:

  • “I review the textbook; I ask for math help from a friend; I look up the problems online; I email my teacher.”
  • “I email my teacher for the course access; I ask for help from a classmate; I try to reset my password.”
  • “I use something else for a trash bag; I place an online order for bags; I take the trash out without a bag; I ask a neighbor for a bag; I go shopping for trash bags.”

A – Anticipate Outcomes & Act

Once we generate a list of strategies, the next step in the IDEAL problem-solving model recommends that you review the potential steps and decide which one is the best option to use first. Helping learners to evaluate the pros and cons of action steps can take practice. Ask questions like, “What might happen if you take this step?” or “Does that step make you feel good about moving forward or uncertain?”

After evaluating the outcomes, the next step is to take action. Encourage your learner to move forward even if they may not know the full result of taking action. Support doing something, even if it might not be the same strategy, you might take to solve a problem or the ‘best’ solution.

L – Look and Learn

The final step in the IDEAL problem-solving model is to look and learn from an attempt to solve a problem. Many parents and teachers forget this critical step in helping diverse learners to stop and reflect when problem-solving goes well and doesn’t go well. Helping our students and children learn from experience can make problem-solving more efficient and effective in the future. Ask questions like “How did that go?” and “What do you think you’ll do differently next time?”

Examples of Look and Learn statements:

  • “I didn’t learn the problems from looking at the textbook, but it did help to call a friend. I’ll start there next time.”
  • “When I didn’t have access to the course website, resetting my password worked.”
  • “I ran out of trash bags because I forgot to put them on the shopping list . I’ll buy an extra box of trash bags to have them on hand, so I don’t run out next time.”

Practice Problem-Solving

For ideas on common problems, download our deck of problem-solving practice cards. Set aside time to practice, role-play, give feedback, and rehearse again if needed.

How to teach the IDEAL problem-solving method

Top businesses and corporations spend thousands of dollars on training teams to implement problem-solving strategies like the IDEAL method. Employees practice and role-play common problems in the workplace . Coaches give supportive feedback until everyone feels confident in each of the steps.

Teachers and parents can use the same process to help students and children use the IDEAL problem-solving method. Set aside time to review common problems or social scenarios your learner might encounter. Practice using the IDEAL method when emotions and tensions aren’t running as high. Allow your learner to ask questions, work through problems, and receive feedback and praise for creating logical action plans.

Further Reading

  • Bransford, J., and Stein, B., “The Ideal Problem Solver” (1993). Centers for Teaching and Technology – Book Library . 46. https://digitalcommons.georgiasouthern.edu/ct2-library/4
  • Executive Functioning 101: Planning Skills
  • Executive Functioning: Task Initiation
  • Executive Functioning Skills by Age: What to Expect
  • Kern, L., George, M. P., & Weist, M. D. (2016). Supporting students with emotional and behavioral problems. Baltimore, MD: Paul H. Brookes.

About The Author

Amy Sippl is a Minnesota-based Board Certified Behavior Analyst (BCBA) and freelance content developer specializing in helping individuals with autism and their families reach their best possible outcomes. Amy earned her Master's Degree in Applied Behavior Analysis from St. Cloud State University and also holds undergraduate degrees in Psychology and Family Social Science from University of Minnesota – Twin Cities. Amy has worked with children with autism and related developmental disabilities for over a decade in both in-home and clinical settings. Her content focuses on parents, educators, and professionals in the world of autism—emphasizing simple strategies and tips to maximize success. To see more of her work visit amysippl.com .

Related Posts

Organization skills: long-term strategies and supports for diverse learners, alternatives to journaling for neurodivergent teens, impulse control: long term strategies & supports for diverse learners, how to make vacation planning executive function friendly, mind mapping: how to help your teen learn to plan ahead, understanding the adhd iceberg: a comprehensive guide for parents and educators.

Life Skills Advocate is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com. Some of the links in this post may be Amazon.com affiliate links, which means if you make a purchase, Life Skills Advocate will earn a commission. However, we only promote products we actually use or those which have been vetted by the greater community of families and professionals who support individuals with diverse learning needs.

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How to improve your problem-solving at work: skills, models and examples

How to improve problem solving skills

Highly valued by employers, problem-solving is needed in just about any line of work. We’ll show you how to step up your ability to take on workplace challenges below…

Whether you’re a seasoned manager or in a junior role, you’re bound to encounter challenges that need tackling head on during your week. And when it comes to overcoming them, fine-tuned, well-honed problem-solving skills are the way to do it.

If your problem-solving has been off in the past, then it can be difficult to take a step back before you act. Luckily, problem-solving is a skill to be learned like any other.

To help you get to grips with this valued skill, we’ll define problem-solving in detail, show you why it matters, and offer some pointers for improving your problem-solving skills.

What are problem-solving skills?

Problem-solving skills let us take on issues without resorting to hasty decisions and snap judgements. They’re what allow us to better understand the challenges before us so we can come up with solutions for dealing with them.

Depending on what the problem is, such skills may call on things like active listening , teamwork, creative thinking or mathematical analysis. Whatever you use to reach a solution, problem-solving is a valuable soft skill that most employers will look for in potential employees.

Why are problem-solving skills important?

Problem-solvers are equipped to take on what comes their way. When they have the right tools at their disposal, they’re in a better position to observe the issue, judge it accordingly, and act in the most effective way. And through experience, these skills become more refined and precise, allowing them to take on tougher problems.

So, why else are they important? Let’s look at what else problem-solving can add to an employee’s skillset…

Greater time management skills

When you know how to approach a problem, greater time management skills tend to come naturally. Because you can balance your time more efficiently, your ability to weigh up your options becomes more precise and considered, allowing you to make less hasty decisions that could make a problem worse.

More creative thinking

Those with strong problem-solving skills can always see the opportunity in a challenge. By tackling problems with innovative solutions, you might find that the result is stronger than you expect.

Improved performance under pressure

When deadlines loom or change is on the horizon, a lack of problem-solving skills could be what leads to poor or half-baked solutions. Because they’re naturally geared towards dealing with the unknown and the unexpected, problem-solvers are less inclined to feel pressure when it arises.

Greater addressing of risk

As well as the ability to deal with the issue itself, problem-solvers are well-equipped to address problems that could spring up later down the line based on trends, patterns and current events . This allows them to possess a degree of control over the future.

How to improve your problem-solving skills

So, how can you improve your ability to solve problems in the workplace? The following tips can help give you an edge whatever your position in a company may be.

Look for opportunities to solve problems

If you’re not used to taking them on, it can be easy to sit back and let someone else deal with problems. Instead of shying away from them, put yourself in situations where problems can arise.

We don’t mean deliberately making mistakes here, but taking on more duties in your current role, with another team or outside your organisation can help familiarise you with the kind of problems that can occur and ways to deal with them.

Observe how others solve problems

By shadowing your colleagues, you can learn problem-solving techniques and put them into practice yourself. Ask a colleague if you can observe their strategy, or schedule in a one-to-one to ask about how they take on problems.

Familiarise yourself with practice problems

There’s a wealth of resources in print and online that you can use to improve your problem-solving skills. These materials offer all sorts of scenarios to put your abilities to the test, unearthing skills you didn’t know you had.

An example problem-solving model

There are several problem-solving models out there, but typically, they follow the broad steps below.

1. Define the problem

Take a step back and analyse the situation. Are there multiple problems? What is causing them? How do these problems affect you and others involved?

Then, drill into the problem by doing the following:

• Separate facts from opinion

• Identify what has caused the problem

• Discuss with team members to gather more information

• Gather relevant data

At this stage, don’t be tempted to come up with a solution. You’re simply trying to find out what the problem is.

2. Identify potential solutions

While you may have only come up with one solution to a problem in the past, brainstorming several alternatives is a better approach. Ask colleagues for their input and get some insights from those with experience of similar problems.

In coming up with alternatives, consider the following:

• Weigh up what might slow down solving the problem

• Ensure your ideas align with goals and objectives

• Identify long and short-term solutions

• Write down the solutions you come up with

3. Evaluate your solutions

Once you have a list of solutions, you need to evaluate them further before acting. What are the positive and negative consequences of each? What resources will you need to carry them out? How much time and, if necessary, who else will you need to put the solution in place?

4. Choose a solution

Your evaluation should clarify which solution best suits the problem. Now it’s time to put that solution into practice.

Before you do, consider:

• Does it solve the problem without creating another?

• Have you reached a group consensus over the solution?

• Is implementing it practical and straightforward?

• Does it fit within company policies and procedures?

5. Put the solution into action

Once you’ve decided on the right solution, it needs to be implemented. Your action plan should include measurable objectives that allow you to monitor its success, as well as timelines and feedback channels your team can use during implementation.

Making sure this plan is communicated to everyone involved will also be key to its success.

6. Assess how effective the solution is

Your work isn’t done just yet! You’ll need to measure how things are progressing to ensure the solution is working as intended. Doing so means you can course-correct should further surprises arise, or else go back to alternative solutions.

How to show problem-solving skills on your CV and at interviews

As we said up top, problem-solving is highly valued by employers, so you’ll want to highlight such abilities on your CV, cover letter and in interviews.

Think back to previous roles for examples of when you used problem-solving skills. It’s not enough to say you’re good at problem-solving; employers will be looking for concrete examples, so be sure to mention them in your cover letter and use bullet points on your CV with specifics.

In interviews, you might be called on to describe times when you encountered problems in previous roles. Here, you should mention the processes you followed to address these issues, the skills you used, and the outcomes achieved.

Likewise, you may be asked hypothetical questions to show how you would solve problems. Base your answers on the steps above, and use the STARR method in conjunction with previous instances of problem-solving to give a detailed yet concise response.

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What Is Problem-Solving Therapy?

Arlin Cuncic, MA, is the author of "Therapy in Focus: What to Expect from CBT for Social Anxiety Disorder" and "7 Weeks to Reduce Anxiety." She has a Master's degree in psychology.

example of problem solving model

Daniel B. Block, MD, is an award-winning, board-certified psychiatrist who operates a private practice in Pennsylvania.

example of problem solving model

Verywell / Madelyn Goodnight

Problem-Solving Therapy Techniques

How effective is problem-solving therapy, things to consider, how to get started.

Problem-solving therapy is a brief intervention that provides people with the tools they need to identify and solve problems that arise from big and small life stressors. It aims to improve your overall quality of life and reduce the negative impact of psychological and physical illness.

Problem-solving therapy can be used to treat depression , among other conditions. It can be administered by a doctor or mental health professional and may be combined with other treatment approaches.

At a Glance

Problem-solving therapy is a short-term treatment used to help people who are experiencing depression, stress, PTSD, self-harm, suicidal ideation, and other mental health problems develop the tools they need to deal with challenges. This approach teaches people to identify problems, generate solutions, and implement those solutions. Let's take a closer look at how problem-solving therapy can help people be more resilient and adaptive in the face of stress.

Problem-solving therapy is based on a model that takes into account the importance of real-life problem-solving. In other words, the key to managing the impact of stressful life events is to know how to address issues as they arise. Problem-solving therapy is very practical in its approach and is only concerned with the present, rather than delving into your past.

This form of therapy can take place one-on-one or in a group format and may be offered in person or online via telehealth . Sessions can be anywhere from 30 minutes to two hours long. 

Key Components

There are two major components that make up the problem-solving therapy framework:

  • Applying a positive problem-solving orientation to your life
  • Using problem-solving skills

A positive problem-solving orientation means viewing things in an optimistic light, embracing self-efficacy , and accepting the idea that problems are a normal part of life. Problem-solving skills are behaviors that you can rely on to help you navigate conflict, even during times of stress. This includes skills like:

  • Knowing how to identify a problem
  • Defining the problem in a helpful way
  • Trying to understand the problem more deeply
  • Setting goals related to the problem
  • Generating alternative, creative solutions to the problem
  • Choosing the best course of action
  • Implementing the choice you have made
  • Evaluating the outcome to determine next steps

Problem-solving therapy is all about training you to become adaptive in your life so that you will start to see problems as challenges to be solved instead of insurmountable obstacles. It also means that you will recognize the action that is required to engage in effective problem-solving techniques.

Planful Problem-Solving

One problem-solving technique, called planful problem-solving, involves following a series of steps to fix issues in a healthy, constructive way:

  • Problem definition and formulation : This step involves identifying the real-life problem that needs to be solved and formulating it in a way that allows you to generate potential solutions.
  • Generation of alternative solutions : This stage involves coming up with various potential solutions to the problem at hand. The goal in this step is to brainstorm options to creatively address the life stressor in ways that you may not have previously considered.
  • Decision-making strategies : This stage involves discussing different strategies for making decisions as well as identifying obstacles that may get in the way of solving the problem at hand.
  • Solution implementation and verification : This stage involves implementing a chosen solution and then verifying whether it was effective in addressing the problem.

Other Techniques

Other techniques your therapist may go over include:

  • Problem-solving multitasking , which helps you learn to think clearly and solve problems effectively even during times of stress
  • Stop, slow down, think, and act (SSTA) , which is meant to encourage you to become more emotionally mindful when faced with conflict
  • Healthy thinking and imagery , which teaches you how to embrace more positive self-talk while problem-solving

What Problem-Solving Therapy Can Help With

Problem-solving therapy addresses life stress issues and focuses on helping you find solutions to concrete issues. This approach can be applied to problems associated with various psychological and physiological symptoms.

Mental Health Issues

Problem-solving therapy may help address mental health issues, like:

  • Chronic stress due to accumulating minor issues
  • Complications associated with traumatic brain injury (TBI)
  • Emotional distress
  • Post-traumatic stress disorder (PTSD)
  • Problems associated with a chronic disease like cancer, heart disease, or diabetes
  • Self-harm and feelings of hopelessness
  • Substance use
  • Suicidal ideation

Specific Life Challenges

This form of therapy is also helpful for dealing with specific life problems, such as:

  • Death of a loved one
  • Dissatisfaction at work
  • Everyday life stressors
  • Family problems
  • Financial difficulties
  • Relationship conflicts

Your doctor or mental healthcare professional will be able to advise whether problem-solving therapy could be helpful for your particular issue. In general, if you are struggling with specific, concrete problems that you are having trouble finding solutions for, problem-solving therapy could be helpful for you.

Benefits of Problem-Solving Therapy

The skills learned in problem-solving therapy can be helpful for managing all areas of your life. These can include:

  • Being able to identify which stressors trigger your negative emotions (e.g., sadness, anger)
  • Confidence that you can handle problems that you face
  • Having a systematic approach on how to deal with life's problems
  • Having a toolbox of strategies to solve the issues you face
  • Increased confidence to find creative solutions
  • Knowing how to identify which barriers will impede your progress
  • Knowing how to manage emotions when they arise
  • Reduced avoidance and increased action-taking
  • The ability to accept life problems that can't be solved
  • The ability to make effective decisions
  • The development of patience (realizing that not all problems have a "quick fix")

Problem-solving therapy can help people feel more empowered to deal with the problems they face in their lives. Rather than feeling overwhelmed when stressors begin to take a toll, this therapy introduces new coping skills that can boost self-efficacy and resilience .

Other Types of Therapy

Other similar types of therapy include cognitive-behavioral therapy (CBT) and solution-focused brief therapy (SFBT) . While these therapies work to change thinking and behaviors, they work a bit differently. Both CBT and SFBT are less structured than problem-solving therapy and may focus on broader issues. CBT focuses on identifying and changing maladaptive thoughts, and SFBT works to help people look for solutions and build self-efficacy based on strengths.

This form of therapy was initially developed to help people combat stress through effective problem-solving, and it was later adapted to address clinical depression specifically. Today, much of the research on problem-solving therapy deals with its effectiveness in treating depression.

Problem-solving therapy has been shown to help depression in: 

  • Older adults
  • People coping with serious illnesses like cancer

Problem-solving therapy also appears to be effective as a brief treatment for depression, offering benefits in as little as six to eight sessions with a therapist or another healthcare professional. This may make it a good option for someone unable to commit to a lengthier treatment for depression.

Problem-solving therapy is not a good fit for everyone. It may not be effective at addressing issues that don't have clear solutions, like seeking meaning or purpose in life. Problem-solving therapy is also intended to treat specific problems, not general habits or thought patterns .

In general, it's also important to remember that problem-solving therapy is not a primary treatment for mental disorders. If you are living with the symptoms of a serious mental illness such as bipolar disorder or schizophrenia , you may need additional treatment with evidence-based approaches for your particular concern.

Problem-solving therapy is best aimed at someone who has a mental or physical issue that is being treated separately, but who also has life issues that go along with that problem that has yet to be addressed.

For example, it could help if you can't clean your house or pay your bills because of your depression, or if a cancer diagnosis is interfering with your quality of life.

Your doctor may be able to recommend therapists in your area who utilize this approach, or they may offer it themselves as part of their practice. You can also search for a problem-solving therapist with help from the American Psychological Association’s (APA) Society of Clinical Psychology .

If receiving problem-solving therapy from a doctor or mental healthcare professional is not an option for you, you could also consider implementing it as a self-help strategy using a workbook designed to help you learn problem-solving skills on your own.

During your first session, your therapist may spend some time explaining their process and approach. They may ask you to identify the problem you’re currently facing, and they’ll likely discuss your goals for therapy .

Keep In Mind

Problem-solving therapy may be a short-term intervention that's focused on solving a specific issue in your life. If you need further help with something more pervasive, it can also become a longer-term treatment option.

Get Help Now

We've tried, tested, and written unbiased reviews of the best online therapy programs including Talkspace, BetterHelp, and ReGain. Find out which option is the best for you.

Shang P, Cao X, You S, Feng X, Li N, Jia Y. Problem-solving therapy for major depressive disorders in older adults: an updated systematic review and meta-analysis of randomized controlled trials .  Aging Clin Exp Res . 2021;33(6):1465-1475. doi:10.1007/s40520-020-01672-3

Cuijpers P, Wit L de, Kleiboer A, Karyotaki E, Ebert DD. Problem-solving therapy for adult depression: An updated meta-analysis . Eur Psychiatry . 2018;48(1):27-37. doi:10.1016/j.eurpsy.2017.11.006

Nezu AM, Nezu CM, D'Zurilla TJ. Problem-Solving Therapy: A Treatment Manual . New York; 2013. doi:10.1891/9780826109415.0001

Owens D, Wright-Hughes A, Graham L, et al. Problem-solving therapy rather than treatment as usual for adults after self-harm: a pragmatic, feasibility, randomised controlled trial (the MIDSHIPS trial) .  Pilot Feasibility Stud . 2020;6:119. doi:10.1186/s40814-020-00668-0

Sorsdahl K, Stein DJ, Corrigall J, et al. The efficacy of a blended motivational interviewing and problem solving therapy intervention to reduce substance use among patients presenting for emergency services in South Africa: A randomized controlled trial . Subst Abuse Treat Prev Policy . 2015;10(1):46. doi:doi.org/10.1186/s13011-015-0042-1

Margolis SA, Osborne P, Gonzalez JS. Problem solving . In: Gellman MD, ed. Encyclopedia of Behavioral Medicine . Springer International Publishing; 2020:1745-1747. doi:10.1007/978-3-030-39903-0_208

Kirkham JG, Choi N, Seitz DP. Meta-analysis of problem solving therapy for the treatment of major depressive disorder in older adults . Int J Geriatr Psychiatry . 2016;31(5):526-535. doi:10.1002/gps.4358

Garand L, Rinaldo DE, Alberth MM, et al. Effects of problem solving therapy on mental health outcomes in family caregivers of persons with a new diagnosis of mild cognitive impairment or early dementia: A randomized controlled trial . Am J Geriatr Psychiatry . 2014;22(8):771-781. doi:10.1016/j.jagp.2013.07.007

Noyes K, Zapf AL, Depner RM, et al. Problem-solving skills training in adult cancer survivors: Bright IDEAS-AC pilot study .  Cancer Treat Res Commun . 2022;31:100552. doi:10.1016/j.ctarc.2022.100552

Albert SM, King J, Anderson S, et al. Depression agency-based collaborative: effect of problem-solving therapy on risk of common mental disorders in older adults with home care needs . The American Journal of Geriatric Psychiatry . 2019;27(6):619-624. doi:10.1016/j.jagp.2019.01.002

By Arlin Cuncic, MA Arlin Cuncic, MA, is the author of "Therapy in Focus: What to Expect from CBT for Social Anxiety Disorder" and "7 Weeks to Reduce Anxiety." She has a Master's degree in psychology.

example of problem solving model

  • What is Problem-Oriented Policing?
  • History of Problem-Oriented Policing
  • Key Elements of POP

The SARA Model

  • The Problem Analysis Triangle
  • Situational Crime Prevention
  • 25 Techniques
  • Links to Other POP Friendly Sites
  • About POP en Español

A commonly used problem-solving method is the SARA model (Scanning, Analysis, Response and Assessment). The SARA model contains the following elements:

  • Identifying recurring problems of concern to the public and the police.
  • Identifying the consequences of the problem for the community and the police.
  • Prioritizing those problems.
  • Developing broad goals.
  • Confirming that the problems exist.
  • Determining how frequently the problem occurs and how long it has been taking place.
  • Selecting problems for closer examination.
  • Identifying and understanding the events and conditions that precede and accompany the problem.
  • Identifying relevant data to be collected.
  • Researching what is known about the problem type.
  • Taking inventory of how the problem is currently addressed and the strengths and limitations of the current response.
  • Narrowing the scope of the problem as specifically as possible.
  • Identifying a variety of resources that may be of assistance in developing a deeper understanding of the problem.
  • Developing a working hypothesis about why the problem is occurring.
  • Brainstorming for new interventions.
  • Searching for what other communities with similar problems have done.
  • Choosing among the alternative interventions.
  • Outlining a response plan and identifying responsible parties.
  • Stating the specific objectives for the response plan.
  • Carrying out the planned activities.

Assessment:

  • Determining whether the plan was implemented (a process evaluation).
  • Collecting pre and postresponse qualitative and quantitative data.
  • Determining whether broad goals and specific objectives were attained.
  • Identifying any new strategies needed to augment the original plan.
  • Conducting ongoing assessment to ensure continued effectiveness.

Physics informed neural networks for an inverse problem in peridynamic models

  • Original Article
  • Open access
  • Published: 21 March 2024

Cite this article

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  • Fabio V. Difonzo 1 ,
  • Luciano Lopez 2 &
  • Sabrina F. Pellegrino 3  

Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we propose to apply radial basis functions (RBFs) as activation functions in suitably designed Physics Informed Neural Networks (PINNs) to solve the inverse problem of computing the perydinamic kernel in the nonlocal formulation of classical wave equation, resulting in what we call RBF-iPINN. We show that the selection of an RBF is necessary to achieve meaningful solutions, that agree with the physical expectations carried by the data. We support our results with numerical examples and experiments, comparing the solution obtained with the proposed RBF-iPINN to the exact solutions.

Avoid common mistakes on your manuscript.

1 Introduction to the peridynamic inverse problem

We consider the following PDE in peridynamic formulation:

where \(C:\mathbb {R}\rightarrow \mathbb {R}\) , representing the so-called kernel function, is a nonnegative even function.

In the one-dimensional case, the model describes the dynamic response of an infinite bar composed of a linear microelastic material.

The main important aspect of such constitutive model is that it takes into account long-range interactions and their effects. The equation of motion ( 1.1 ) was proposed by Silling in 2000 in [ 29 ] in the framework of continuum mechanics theory with the name of linear peridynamics. This is an integral-type nonlocal model involving only the displacement field and not its gradient. This leads to a theory able to incorporate cracks, fractures and other kind of singularities.

The general initial-value problem associated with ( 1.1 ) is well-posed (see [ 13 ]) and due to the presence of long-range forces, the solution shows a dispersive behavior. The length-scale of the long-range interactions is parameterized by a positive scalar value \(\delta >0\) called horizon, which represents the maximum interaction distance between two material particles. In the more general setting, this parameter is intrinsically incorporated into the kernel function C , that is meant to weigh the nonlocal interactions.

If the kernel function C , also known as micromodulus function, is a suitable generalized function, in the limit of short-range forces, or equivalently taking the limit as \(\delta \rightarrow 0\) , the linear peridynamic model ( 1.1 ) reduces to the wave equation \(\partial _{tt}\theta (x,t)-\partial _{xx}\theta (x,t)=0\) , (see [ 25 ] and references therein). As a consequence, the length-scale parameter \(\delta\) can be viewed as a measure of the degree of nonlocality of the model.

In order to maintain the consistency with Newton’s third law, the micromodulus function must be even:

Moreover, due to the dispersive effects C must be such that

for every wave number \(k\ne 0\) .

Additionally, since the interaction between two material particles should become negligible as the distance between particles become very large, we can assume that

If a material is characterized by a finite horizon, so that no interactions happen within particles that have relative distance greater than \(\delta\) , then we can assume that the support of the kernel function is given by \([-\delta ,\delta ]\) and the model ( 1.1 ) writes as

Of course, such condition is less restrictive than ( 1.4 ).

It is clear that a different microelastic material corresponds to a different kernel function and, as a consequence, the kernel function involved in the model provides different constitutive models.

In literature there are several kernel functions satisfying conditions ( 1.2 ), ( 1.3 ), and ( 1.4 ). In particular, according to [ 36 ], we will focus on a Gauss-type kernel in the form

Moreover, we aim to validate the choice of a distributed kernel function with shape

proposed in [ 7 ] in nonlocal unsaturated soil model contexts.

In this paper, we aim to solve the inverse problem described in ( 1.1 ) for learning the shape of the kernel function C , by implementing a Physics Informed Neural Network (PINN). More specifically, we show that this inverse problem requires a careful selection of activation functions in all the layers and a correct interaction with kernel initializers. It can be seen, in fact, that a naive choice on these functions would result in unreliable predictions and possibly unfeasible solutions. More precisely, we see that, if the neural network structure is not chosen accordingly to appropriate geometric knowledge relative to the data, then PINN output returns different, still acceptable, results, showing a lack of uniqueness. Therefore we will show that, as long as the peridynamic operator is bounded on a compact support \([-\delta ,\delta ]\) and the PINN architecture is build accordingly, as a consequence of the well posedness conditions of the peridynamic formulation, the learned kernel fulfills all the requirements expected, provided that PINN structure is accurate enough.

2 Introduction to PINNs

Physics-Informed Neural Networks (PINNs) have emerged as a transformative approach to tackle both direct and inverse problems associated with PDEs. These innovative neural network architectures seamlessly integrate the principles of physics into the machine learning framework. By doing so, PINNs offer a promising solution to efficiently and accurately model, simulate, and optimize complex systems governed by PDEs. More specifically, they can be employed to solve both direct and inverse problems; in the latter case, such PINNs are commonly referred to as inverse PINNs.

Direct problems involve finding solutions to PDEs that describe the evolution of physical systems under specified initial and boundary conditions. Traditional numerical methods, such as finite element analysis (see [ 18 , 39 ]), finite difference methods with composite quadrature formulas (see [ 21 ]) and applied to spectral fractional models (see [ 12 ]), model order reduction methods (see [ 27 ]), meshfree methods (see [ 28 , 30 ]), adaptive refinement techniques (see [ 2 , 9 ]) and collocation and Galerkin methods (see [ 1 ]) have been widely used for solving direct problems. Moreover, more recently spectral methods with volume penalization techniques (see for instance [ 17 , 20 ]) and Chebyshev spectral methods (see [ 22 , 35 ]) have been developed in order to increase the order of convergence, to improve the accuracy of the results and to maintain the consistency of the method even in presence of singularities.

However, these approaches often require substantial computational resources and may struggle with high-dimensional or non-linear problems. Additionally, such methods need to know the constitutive parameters of the model such as the analytic expression of the kernel function, the size of the horizon and the Young’s modulus to predict fractures in the material under consideration and, in suitable configurations, they fail to impose boundary conditions. In order to provide some hint in this direction, a data-driven approach can be developed. In [ 31 ] the authors propose a geometry-aware method in physics informed neural network to exactly imposing boundary conditions over complex domains. In [ 40 ] the authors investigate both a forward and an inverse problems of high-dimensional nonlinear wave equations via a deep neural networks with the activation function, while in [ 34 ] a combination of an orthogonal decomposition with a neural network is applied to build a reduced order model. In [ 23 ], the authors present an unsupervised convolutional neural network architecture with nonlocal interactions for solving PDEs using Peridynamic Differential Operator as a convolutional filter. Indeed, this approach results to be very efficient when the model is governed by an integral operator (see for instance [ 37 ]).

Inverse problems, on the other hand, are concerned with determining unknown parameters, boundary conditions, or the PDE itself, given limited or noisy observations of the system behavior. These problems frequently arise in real-world applications, including medical imaging [ 38 ], geophysics [ 4 , 6 ], material characterization [ 10 ], and industrial process optimization [ 24 ]. Inverse problems are inherently ill-posed, as multiple solutions or no solutions may exist, making their resolution challenging. In fact, several issues could arise in solving inverse problems, especially related to irregular geometries [ 15 ], or also small data regimes, incomplete data or incomplete models [ 26 ].

In the context of nonlocal elasticity theory, in [ 33 ] the authors propose a methodology based on a constrained least squares optimization to solve inverse problems in heterogeneous media using state-based peridynamics in order to derive parameter values characterizing several material properties and to establish conditions for fracture patterns in geological setting.

Thus, Physics-Informed Neural Networks represent a paradigm shift in the way to approach direct and inverse problems associated with PDEs. Their ability to combine data-driven learning with physical principles opens up new frontiers in scientific research, engineering design, and problem-solving across a wide spectrum of domains.

2.1 PINN paradigm

In this paper, we will consider a Feed-Forward fully connected Neural Network (FF-DNN), also called Multi-Layer Perceptron (MLP) (see [ 5 ] and references therein).

In a PINN the solution space is approximated through a combination of activation functions, acting on all the hidden layers, with the independent variable used as the network inputs. Letting \(x\in \mathbb {R}^n\) , in a Feed-Forward network each layer feeds the next one through nested transformation, so that a it can be seen, letting L be the number of layers, as

where, for each layer \(l=1,\ldots ,L\) , \(\sigma _l:\mathbb {R}^n\rightarrow \mathbb {R}^m\) is the activation function, which operates componentwise, \(W_l\) is the weight matrix and \(b_l\) is the bias vector. Thus, the output \(z_L\in \mathbb {R}^m\) of a FF-NN can be expressed as a single function of the input vector x , defined as the composition of all the layers above in the following way:

The aim of a PINN is to minimize, through a Stochastic Gradient Descent method, a suitable objective function called loss function , that would take into account the physics of the problem, with respect to all the components, called trainable parameters, of \(W_l,b_l\) , for \(l=1,\ldots ,L\) .

More specifically, given a general PDE of the form \(\mathcal {P}(f)=0\) , where \(\mathcal {P}\) represents the differential operator acting on f , the loss function used by a PINN is usually given by

where \(f^*\) is the training dataset (of points inside the domain or on the boundary), and \(0^*\) is the expected (true) value for the differential operation \(\mathcal {P}(f)\) at any given training or sampling point; the chosen norm \(\Vert \cdot \Vert\) (it may be different for each term in the loss function) depends on the functional space and the specific problem. Selecting a correct norm (so to avoid overfitting) for the loss function evaluation is an important problem in PINN, and recently in [ 32 ] authors have proposed spectral techniques based on Fourier residual method to overcome computational and accuracy issues. The first term in the right-hand side of ( 2.2 ) is referred to as data fitting loss, while the second term is referred to as residual loss, which is responsible to make a NN be informed by physics. We address the construction of the loss function in Sect.  3.3 .

The operator \(\mathcal {P}\) is usually performed using autodiff (Automatic Differentiation algorithm). In the context of peridynamic theory, in [ 16 ] authors propose, for the first time, a nonlocal alternative to autodiff by replacing the evaluation of f and its partial derivatives through the action of a Peridynamic Differential Operator (PDDO) on f .

A recent review on PINNs and related theory can be found in [ 11 ].

3 RBF-iPINN for the kernel function

In case one wants to solve an inverse problem, there will be more trainable parameters than only those coming from weight matrices and bias vectors. Hence, such further parameters have to be considered in the minimization iterations and their respective gradients must be computed as well.

However, in our case, the inverse problem does not involve the mere computation of scalar quantities, but rather a whole function, specifically the kernel function C in ( 1.1 ), which has also analytical and geometrical properties to be accounted for, such as nonnegativity and symmetry. In the PINN architecture proposed, these features reflect in the implementation of a NN model with two separated sets of layers, one for C and the other for \(\theta\) , and whose output would be both the solution to ( 1.1 ) and the unknown function C ; moreover, the loss function ( 2.2 ) has been accordingly endowed with further terms necessary to enforce the requirements on C .

From the point of view of the architecture, while nonnegatitivity of C has been simply enforced by requiring all trainable parameters in ( 2.1 ) to be nonnegative, symmetry has required a more specific treatment, both in terms of activation functions and in the way we have defined the loss function. Our idea has been to wisely select different activation functions for the two different sets of layers, inspired by the properties coming along with C and the data on \(\theta\) . In the following section we will introduce and discuss the technical approaches to deal with activation and loss functions.

3.1 Radial Basis Function Layer

As activation function for the first layer, whose input is x , a Radial Basis Function (RBF) is selected. By definition, a Radial Basis Function (RBF) is a real-valued function whose output depends only on the distance from a fixed center or prototype point. An RBF can be defined as

where \(\phi\) is the RBF function, x is the input to the RBF, c is the center or prototype point, \(\Vert x - c\Vert\) represents the distance between x and c .

RBFs are commonly used in various fields and, when used as activation functions in neural networks, they give rise to Radial Basis Function Neural Networks (RBFNNs) (see [ 14 ]).

We have considered two families of RBFs ( 3.1 ), sketched in Fig.  1 , given by

called inverse quadratic and multiquadric RBFs respectively, where all the parameters above could be taken to be trainable. This approach has recently been proposed in [ 3 ] in the context of direct problem for nonlinear PDEs, but used in the middle layer. However, we have extensively noticed that such a choice is not efficient to learn the kernel function C in ( 1.1 ), resulting in nonphysical results and excessively large computational time and cost. In fact, this has led us to introduce an RBF inverse PINN, that we called RBF-iPINN, where we select a Radial Basis Function as the activation function for the first layer, that has significantly sped up performance while providing the expected result if compared to the exact solution.

figure 1

Qualitative shapes of Radial Basis Functions defined in ( 3.2a ) and ( 3.2b ), respectively

3.2 RBF-iPINN Structure

Since the kernel function C depends on the sole spatial variable x , while the solution to ( 1.1 ) \(\theta\) depends on both space and time, then x ,  t need to be handled separately. To this purpose, the proposed RBF-iPINN is implemented in a serialized fashion, suitably connecting, as we are going to explain in details below, two different Neural Networks, which we may call spatial NN and temporal NN . In the spatial NN, the spatial variable x is the sole input of a hidden layer of 20 neurons, activated by an RBF as in ( 3.2 ), followed by 8 layers with 20 neurons each, activated by ReLu function. The output of this sequence of layers is then concatenated with t , providing the input for the temporal Neural Network. More specifically, this second part is made up by 8 layers, each containing 20 neurons and activated by a sigmoid function. Finally, the overall output of the RBF-iPINN is returned as an array that lists two tensors, the first carrying the kernel C , and the other carrying the dependent variable \(\theta\) ; the structure of the RBF-iPINN is sketched in Fig.  2 .

Let us notice that selecting the ReLU activation function for all the layers of the architecture could result in a loss of compatibility potential of the PINN, as reported in [ 19 ]. This consideration, also supported by several experiments, justifies the choice of the sigmoid activation function in the temporal NN. We witness that, however, other selections than sigmoid function do not perform satisfactorily enough as in the cases reported in Sect.  4 .

Moreover, the spatial NN is endowed with a kernel initializer of type glorot_normal , to better keep the variance of the weights consistent across layers, thus helping with training stability, while the temporal NN is endowed with a random_uniform kernel initializer; also, a nonnegative kernel constraint and a kernel regularizer of type l1_l2 , with weights \(l_1=l_2=0.01\) is applied to the spatial NN, which yields the computed kernel function. The nonnegativity constraint is expected to take care of that the kernel function is nonnegative, and is also coherent with the nonnegativity of the RBF activating the first layer of the spatial NN, which is in turn fed into the successive layers; the l1 parameter is meant to avoid overfitting, to encourage sparsity and to effectively perform feature selection; through the l2 parameter, on the other hand, we enforce the spatial NN to be more robust to outliers.

3.3 Loss Function

Given the constraints on C , we have to accordingly construct a loss function as in ( 2.2 ) with as many components as there are constraints to be enforced in the RBF-PINN. More specifically, we consider the following components to be part of \(\mathcal {L}\) :

In the selection of norms above, we have been guided by the features we want our PINN to take into account. More specifically, since we are interested in fitting data and in satisfying our model as much as possible, we selected the 2-norm for these contributions; however, since symmetry is to be expected from the PINN architecture and, in particular, from the first RBF layer, we measure its loss via the 1-norm, which is more sensible to small errors. Finally, we consider a weighted sum of the contributions given above as

where, for our simulations in Sect.  4 , we have set

These values have been suitably tuned, and turned out to perform well in all the experiments we carried out below.

3.4 Learning rate

The learning rate \(\alpha\) has been selected to be decreasing with the epoch in a quadratic way. More precisely, we implemented the following scheduler:

where N is the number of epochs chosen for the training. Thus, starting with a learning rate of \(\alpha _0\) at epoch 0, it progressively gets reduced according to ( 3.5 ) over the epochs, until it reaches the value \(\alpha _1\) at epoch N .

figure 2

RBF-iPINN structure. In our simulations, we set the number of ReLU and sigmoid activated hidden layers to 8, and the number of neurons per each layer, including the RBF layer, to 20

4 Numerical Simulations

In this section, we show results with our RBF-iPINN. All the experiments have been run using 1000 epochs with a learning rate defined in ( 3.5 ) and employed the ADAM optimizer. The machine used for the experiments is an Intel Core i7-8850 H CPU at 2.60GHz and 64 GB of RAM. Moreover, the PINNs, providing results in the examples below, have been developed in Python 3.10, using the library TensorFlow 2.15.0 within the interface Keras 3.0.1.

Moreover, real data, which are used in our simulations to compute the loss function ( 3.3b ), are synthetically built using appropriate spectral methods from [ 20 ] to solve ( 1.1 ).

A main feature of the numerical computation is the evaluation of the integral on the right-hand side of ( 1.1 ). In fact, in order to exploit the power of Keras on computing convolution products, we notice that

where the second term in the right-hand side above is the convolution product between the kernel C and the unknown function \(\theta\) . It has to be noticed here that the kernel function C is compactly supported, with support \([-\delta ,\delta ]\) . Now, in order to numerically compute such convolution product, let [0,  X ] be the space interval and let \(0<x_1<x_2<\ldots<x_{N-1}<x_N=X\) be the uniform spatial discretization of the interval [0,  X ] with stepsize \(h>0\) . the convolution product above can be numerically treated by determining the exact number of components in the vector \([C(x_i)]_{i=1}^n\) so that only points \(x_i\) such that

come into play when computing \(C(\Vert x\Vert )*\theta (x,t)\) . Since \(x_i=i\cdot h\) , then we deduce that the only indices involved in the convolution product are \(i,j=1,\ldots ,N\) such that

Since the peridynamic integral-operator in ( 1.5 ) is linear, we can derive in terms of the Green’s function a solution to the initial-value problem using continuous Fourier Transform. Such solution can be used to provide a dataset for the next simulations.

In the next two experiments, we exemplify on datasets derived from V-shaped kernel functions. This choice of kernel is justified by the fact that it is implemented in some nonlocal formulations of Richards’ equation as it is able to easily incorporate Dirichlet boundary conditions in the model (see [ 7 ]).

Thus, we select as activation function for the first layer of the spatial NN an RBF of type ( 3.2b ). Further, we tried both to keep all the three parameters \(\gamma ,\rho ,\mu\) trainable, and to fix \(\gamma\) while letting \(\rho ,\mu\) be trainable. According to our experience and for the following two cases, fixing \(\gamma\) improves convergence performance and result quality.

Example 4.1

Here we consider a dataset with \(t\in [0,20],\; x\in [-10,10]\) with spatial stepsize \(h=2\cdot 10^{-1}\) and \(\delta =10\) , and for which the analytical expression of the kernel is

We set \(\gamma =0.09\) , obtaining the results showed in Fig.  3 a, where we compare the true kernel function in ( 4.1 ) to the output of the proposed inverse RBF-iPINN. Setting \(\gamma =0.05\) in ( 3.2b ) provides qualitatively comparable results, as can be observed in Fig.  3 b.

figure 3

Learned kernel functions relative to Example 4.1 for different values of \(\gamma\) in ( 3.2b )

Example 4.2

Here we consider a dataset with \(t\in [0,20], x\in [-10,10]\) with spatial stepsize \(h=2\cdot 10^{-1}\) and \(\delta =1\) , and for which the analytical expression of the kernel is

We set \(\gamma =0.09\) , obtaining the results showed in Fig.  4 a, where we compare the true kernel function in ( 4.2 ) to the output of the proposed inverse RBF-iPINN. Setting \(\gamma =0.05\) provides results in Fig.  4 b.

figure 4

Learned kernel functions for different values of \(\gamma\) in ( 3.2b ) relative to Example 4.2

In the next example, we consider a bell-shaped kernel function to test the proposed RBF-iPINN. Accordingly, an RBF of type ( 3.2a ) is chosen to activate the first layer of the spatial NN.

Example 4.3

For this example, first we tuned hyperparameters, setting the kernel regularizers l1_l2 with weights 0.01 and 0.1 respectively, in order to try and catch, as better as possible, the correct qualitative behavior of the kernel in the interior of its compact support; moreover, on the account of the knowledge of the kernel shape, we decided to activate the first layer of the RBF-iPINN through ( 3.2a ), where we set the hyperparameter \(\gamma =1\) ; finally, for a better data fitting, we also selected the sup-norm in ( 3.3b ).

In this case, the neural network shows a discrete ability to catch shape and support of the bell-shaped kernel, but fails in a good approximation of the characteristic parameters, as shown in Fig.  5 . In fact, in this case the true kernel is given by

figure 5

Learned kernel function compared to the true one from Example 4.3

Therefore, we have performed a further analysis by implementing a standard inverse PINN to learn parameters \(\gamma ^*\) and \(\sigma ^*\) in

Starting with initial guesses for \(\gamma ^*=3\) and for \(\sigma ^*=0.5\) , we run a PINN whose structure is the same as the second portion relative to \(\theta\) of the RBF-iPINN described above (see the architecture in Fig.  2 ). The training phase has been performed over 1000 epochs and with the same learning rate scheduler described in Sect.  3.4 , but with a faster descent obtained by setting \(\alpha _0=10^{-3}\) . Results are depicted in Fig.  6 . It can be deduced that the inverse PINN has been able to correctly detect the learned values which, at convergence, are given by \(\gamma ^*=2.3302033\) and \(\sigma ^*=1.0218402\) , being \(\frac{4}{\sqrt{\pi }}\approx 2.2567583\) .

figure 6

Gaussian kernel function learned from ( 4.4 ), compared to the true one from Example 4.3

We stress that a prior geometrical knowledge about the kernel function to learn is necessary to correctly set up the spatial NN of the RBF-iPINN. In fact, we report that, activating the spatial NN with an RBF of type ( 3.2a ) in Example 4.1 and Example 4.2 results in poor and nonphysical predictions; similar negative results show up if RBFs of type ( 3.2b ) are used in Example 4.3 .

5 Conclusions

In this work we have analyzed a peridynamic formulation of a classical wave equation, trying to compute the kernel function responsible for the nonlocal behavior of the model considered. We have proposed to utilize a Radial Basis Function (RBF) as activation function for the first layer of a suitably designed Physics Informed Neural Network (PINN) to solve the inverse problem. Specifically, our inverse PINN architecture has two neural networks working in series: the first set of layers, called spatial NN and whose first layer activated by some Radial Basis Function, takes the spatial data as input and yields the first output for recovering the kernel function; then, this first output is concatenated to the temporal data, thus providing a new tensor serving as input to the second set of layers, that is called temporal NN and that produces the output describing \(\theta\) , solution to the peridynamic wave equation. We called the proposed model RBF-iPINN. We have shown that, with a wise scheduler for the learning rate and necessary initializations of the spatial NN responsible for the kernel function computation, for standard selections of the activation RBF, the RBF-iPINN can provide reliable prediction of the kernel function, in case it has a V-shape behavior. We also tackle the case of Gaussian kernel function: here, RBF-iPINN is able to adequately detect the shape, but a further analysis is necessary to learn the expected parameters of a bell-shaped function. We did so by implementing a standard inverse PINN, practically tuning the very same second set of layer of the RBF-iPINN.

Such models turn out to be promising tools for investigating optimal controls problems in dimension 2 or higher (see, e.g., [ 8 ]), where an inverse PINN approach seems to provide robust and scalable results. Such considerations pave the way to further investigations about how to deal with more complicated peridynamic models via PINNs and Radial Basis Functions, that seem to be a powerful approach to this kind of problems, due to their inherently symmetric nature.

Availability of data and materials

No datasets were generated or analysed during the current study.

Alebrahim R (2023) Modified wave dispersion properties in 1D and 2D state-based peridynamic media. Comput Math Appl 151:21–35

Article   MathSciNet   Google Scholar  

Alebrahim R, Marfia S (2023) Adaptive PD-FEM coupling method for modeling pseudo-static crack growth in orthotropic media. Eng Fract Mech 294:109710

Article   Google Scholar  

Bai Jinshuai, Liu Gui-Rong, Gupta Ashish, Alzubaidi Laith, Feng Xi-Qiao, YuanTong Gu (2023) Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear partial differential equations. Computer Methods in Applied Mechanics and Engineering 415:116290

Bandai T, Ghezzehei TA (2022) Forward and inverse modeling of water flow in unsaturated soils with discontinuous hydraulic conductivities using physics-informed neural networks with domain decomposition. Hydrol Earth Syst Sci 26(16):4469–4495

Bengio Y, Ducharme R, Vincent P, Janvin C (2003) A neural probabilistic language model. J Mach Learn Res 3:1137–1155

Google Scholar  

Berardi M, Girardi G (2024) Modeling plant water deficit by a non-local root water uptake term in the unsaturated flow equation. Commun Nonlinear Sci Numer Simul 128:107583

Berardi M, Difonzo FV, Pellegrino SF (2023) A numerical method for a nonlocal form of Richards’ Equation based on Peridynamic theory. Comput Math Appl 143:23–32

Berardi M, Difonzo FV, Guglielmi R (2023) A preliminary model for optimal control of moisture content in unsaturated soils. Comput Geosci 27(6):1133–1144

Bobaru F, Yang M, Alves S, Silling F, Askari E, Xu J (2009) Convergence, adaptive refinement, and slaning in 1D peridynamics. Int J Numer Mech Eng 77:852–877

Chen X, Cao BT, Yuan Y, Meschke G (2023) Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios. Comput Methods Appl Mech Eng 405:115852

Cuomo S, Cola VSD, Giampaolo F, Rozza G, Raissi M, Piccialli F (2022) Scientific machine learning through physics-informed neural networks: where we are and what’s next. J Sci Comput 92(3):88

Difonzo FV, Garrappa R (2023) A numerical procedure for fractional-time-space differential equations with the spectral fractional laplacian. In: Angelamaria C, Marco D, Fabio D, Roberto G, Mariarosa M, Marina P (eds) Fractional Differential Equations, pages 29–51, Springer Nature Singapore, Singapore

Emmrich E, Puhst D (2015) Survey of existence results in nonlinear peridynamics in comparison with local elastodynamics. Comput. Methods Appl. Math. 15(4):483–496

Fasshauer GE (2007) Meshfree approximation methods with Matlab (With Cd-rom). World Scientific Publishing Company, Interdisciplinary Mathematical Sciences

Gao H, Zahr MJ, Wang J-X (2022) Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse problems. Comput Methods Appl Mech Eng 390:114502

Haghighat E, Bekar AC, Madenci E, Juanes R (2021) A nonlocal physics-informed deep learning framework using the peridynamic differential operator. Comput Methods Appl Mech Eng 385:114012

Jafarzadeh S, Larios A, Bobaru F (2020) Efficient solutions for nonlocal diffusion problems via boundary-adapted spectral methods. J Peridyn Nonlocal Model 2:85–110

Kilic B, Madenci E (2010) Coupling of peridynamic theory and the finite element method. J Mech Mater Struct 5(5):703–733

Kuangdai L, Jeyan T (2023) On the compatibility between neural networks and partial differential equations for physics-informed learning

Lopez L, Pellegrino SF (2021) A spectral method with volume penalization for a nonlinear peridynamic model. Int J Numer Methods Eng 122(3):707–725

Lopez L, Pellegrino SF (2022) A space-time discretization of a nonlinear peridynamic model on a 2D lamina. Comput Math Appl 116:161–175

Luciano Lopez and Sabrina Francesca Pellegrino (2023) Computation of eigenvalues for nonlocal models by spectral methods. J Peridyn Nonlocal Model 5(2):133–154

Mavi A, Bekar AC, Haghighat E, Madenci E (2023) An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator. Comput Methods Appl Mech Eng 407

Meng Z, Qian Q, Mengqiang X, Bo Y, Yildiz AR, Mirjalili Seyedali (2023) PINN-FORM: a new physics-informed neural network for reliability analysis with partial differential equation. Comput Methods Appl Mech Eng 414:116172

Oterkus S, Madenci E, Agwai A (2014) Peridynamic thermal diffusion. J Comput Phys 265:71–96

Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378:686–707

Regazzoni F, Dedè L, Quarteroni A (2019) Machine learning for fast and reliable solution of time-dependent differential equations. J. Comput. Phys. 397:108852

Shojaei A, Mudric T, Zaccariotto M, Galvanetto U (2016) A coupled meshless finite point/Peridynamic method for 2D dynamic fracture analysis. Int J Mech Sci 119:419–431

Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–209

Silling S, Askari E (2005) A meshfree based on the peridynamic model of solid mechanics. Comput Struct 83(17–18):1526–1535

Sukumar N, Srivastava A (2022) Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. Comput Methods Appl Mech Eng 389:114333

Taylor JM, Pardo D, Muga I (2023) A deep fourier residual method for solving PDEs using neural networks. Comput Methods Appl Mech Eng 405:115850

Turner DZ, van Bloemen Waanders BG, Parks ML (2015) Inverse problems in heterogeneous and fractured media using peridynamics. J Mech Materi Struct 10(5)

Vitullo P, Colombo A, Franco NR, Manzoni A, Zunino P (2024) Nonlinear model order reduction for problems with microstructure using mesh informed neural networks. Finite Elements Anal Design 229:104068

Wang L, Jafarzadeh S, Mousavi F, and Bobaru F (2023) PeriFast/Corrosion: A 3D Pseudospectral Peridynamic MATLAB Code for Corrosion. J Peridynamics Nonlocal Model:1–25

Weckner O, Abeyaratne R (2005) The effect of long-range forces on the dynamics of a bar. J Mech Phys Solids 53(3):705–728

Yuan L, Ni YQ, Deng XY, Hao S (2022) A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations. J Comput Phys 462

Yuyao Chen LL, Karniadakis GE, Dal Negro L (2020) Physics-informed neural networks for inverse problems in nano-optics and metamaterials. Opt Express 28(8):11618–11633

Zaccariotto M, Mudric T, Tomasi D, Shojaei A, Galvanetto U (2018) Coupling of FEM meshes with Peridynamic grids. Comput Methods Appl Mech Eng 330:471–497

Zhou Z, Wang L, Yan Z (2023) Deep neural networks learning forward and inverse problems of two-dimensional nonlinear wave equations with rational solitons. Comput Math Appl 151:164–171

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Acknowledgements

SFP has been supported by REFIN Project, grant number D1AB726C funded by Regione Puglia, and by PNRR MUR - M4C2 project, grant number N00000013 - CUP D93C22000430001. The three authors gratefully acknowledge the support of INdAM-GNCS 2023 Project, grant number CUP \(\_\) E53C22001930001, and INdAM-GNCS 2024 project, grant number CUP_E53C23001670001. They are also part of the INdAM research group GNCS.

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Difonzo, F.V., Lopez, L. & Pellegrino, S.F. Physics informed neural networks for an inverse problem in peridynamic models. Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-01957-5

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