objectives of the assignment problem can include

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Assignment problem

The problem of optimally assigning $ m $ individuals to $ m $ jobs. It can be formulated as a linear programming problem that is a special case of the transport problem :

maximize $ \sum _ {i,j } c _ {ij } x _ {ij } $

$$ \sum _ { j } x _ {ij } = a _ {i} , i = 1 \dots m $$

(origins or supply),

$$ \sum _ { i } x _ {ij } = b _ {j} , j = 1 \dots n $$

(destinations or demand), where $ x _ {ij } \geq 0 $ and $ \sum a _ {i} = \sum b _ {j} $, which is called the balance condition. The assignment problem arises when $ m = n $ and all $ a _ {i} $ and $ b _ {j} $ are $ 1 $.

If all $ a _ {i} $ and $ b _ {j} $ in the transposed problem are integers, then there is an optimal solution for which all $ x _ {ij } $ are integers (Dantzig's theorem on integral solutions of the transport problem).

In the assignment problem, for such a solution $ x _ {ij } $ is either zero or one; $ x _ {ij } = 1 $ means that person $ i $ is assigned to job $ j $; the weight $ c _ {ij } $ is the utility of person $ i $ assigned to job $ j $.

The special structure of the transport problem and the assignment problem makes it possible to use algorithms that are more efficient than the simplex method . Some of these use the Hungarian method (see, e.g., [a5] , [a1] , Chapt. 7), which is based on the König–Egervary theorem (see König theorem ), the method of potentials (see [a1] , [a2] ), the out-of-kilter algorithm (see, e.g., [a3] ) or the transportation simplex method.

In turn, the transportation problem is a special case of the network optimization problem.

A totally different assignment problem is the pole assignment problem in control theory.

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How to Solve the Assignment Problem: A Complete Guide

Table of Contents

Assignment problem is a special type of linear programming problem that deals with assigning a number of resources to an equal number of tasks in the most efficient way. The goal is to minimize the total cost of assignments while ensuring that each task is assigned to only one resource and each resource is assigned to only one task. In this blog, we will discuss the solution of the assignment problem using the Hungarian method, which is a popular algorithm for solving the problem.

Understanding the Assignment Problem

Before we dive into the solution, it is important to understand the problem itself. In the assignment problem, we have a matrix of costs, where each row represents a resource and each column represents a task. The objective is to assign each resource to a task in such a way that the total cost of assignments is minimized. However, there are certain constraints that need to be satisfied – each resource can be assigned to only one task and each task can be assigned to only one resource.

Solving the Assignment Problem

There are various methods for solving the assignment problem, including the Hungarian method, the brute force method, and the auction algorithm. Here, we will focus on the steps involved in solving the assignment problem using the Hungarian method, which is the most commonly used and efficient method.

Step 1: Set up the cost matrix

The first step in solving the assignment problem is to set up the cost matrix, which represents the cost of assigning a task to an agent. The matrix should be square and have the same number of rows and columns as the number of tasks and agents, respectively.

Step 2: Subtract the smallest element from each row and column

To simplify the calculations, we need to reduce the size of the cost matrix by subtracting the smallest element from each row and column. This step is called matrix reduction.

Step 3: Cover all zeros with the minimum number of lines

The next step is to cover all zeros in the matrix with the minimum number of horizontal and vertical lines. This step is called matrix covering.

Step 4: Test for optimality and adjust the matrix

To test for optimality, we need to calculate the minimum number of lines required to cover all zeros in the matrix. If the number of lines equals the number of rows or columns, the solution is optimal. If not, we need to adjust the matrix and repeat steps 3 and 4 until we get an optimal solution.

Step 5: Assign the tasks to the agents

The final step is to assign the tasks to the agents based on the optimal solution obtained in step 4. This will give us the most cost-effective or profit-maximizing assignment.

Solution of the Assignment Problem using the Hungarian Method

The Hungarian method is an algorithm that uses a step-by-step approach to find the optimal assignment. The algorithm consists of the following steps:

• Subtract the smallest entry in each row from all the entries of the row.
• Subtract the smallest entry in each column from all the entries of the column.
• Draw the minimum number of lines to cover all zeros in the matrix. If the number of lines drawn is equal to the number of rows, we have an optimal solution. If not, go to step 4.
• Determine the smallest entry not covered by any line. Subtract it from all uncovered entries and add it to all entries covered by two lines. Go to step 3.

The above steps are repeated until an optimal solution is obtained. The optimal solution will have all zeros covered by the minimum number of lines. The assignments can be made by selecting the rows and columns with a single zero in the final matrix.

Applications of the Assignment Problem

The assignment problem has various applications in different fields, including computer science, economics, logistics, and management. In this section, we will provide some examples of how the assignment problem is used in real-life situations.

Applications in Computer Science

The assignment problem can be used in computer science to allocate resources to different tasks, such as allocating memory to processes or assigning threads to processors.

Applications in Economics

The assignment problem can be used in economics to allocate resources to different agents, such as allocating workers to jobs or assigning projects to contractors.

Applications in Logistics

The assignment problem can be used in logistics to allocate resources to different activities, such as allocating vehicles to routes or assigning warehouses to customers.

Applications in Management

The assignment problem can be used in management to allocate resources to different projects, such as allocating employees to tasks or assigning budgets to departments.

Let’s consider the following scenario: a manager needs to assign three employees to three different tasks. Each employee has different skills, and each task requires specific skills. The manager wants to minimize the total time it takes to complete all the tasks. The skills and the time required for each task are given in the table below:

The assignment problem is to determine which employee should be assigned to which task to minimize the total time required. To solve this problem, we can use the Hungarian method, which we discussed in the previous blog.

Using the Hungarian method, we first subtract the smallest entry in each row from all the entries of the row:

Next, we subtract the smallest entry in each column from all the entries of the column:

We draw the minimum number of lines to cover all the zeros in the matrix, which in this case is three:

Since the number of lines is equal to the number of rows, we have an optimal solution. The assignments can be made by selecting the rows and columns with a single zero in the final matrix. In this case, the optimal assignments are:

• Emp 1 to Task 3
• Emp 2 to Task 2
• Emp 3 to Task 1

This assignment results in a total time of 9 units.

I hope this example helps you better understand the assignment problem and how to solve it using the Hungarian method.

Solving the assignment problem may seem daunting, but with the right approach, it can be a straightforward process. By following the steps outlined in this guide, you can confidently tackle any assignment problem that comes your way.

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Operations Research

1 Operations Research-An Overview

• History of O.R.
• Approach, Techniques and Tools
• Phases and Processes of O.R. Study
• Typical Applications of O.R
• Limitations of Operations Research
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2 Linear Programming: Formulation and Graphical Method

• General formulation of Linear Programming Problem
• Optimisation Models
• Basics of Graphic Method
• Important steps to draw graph
• Multiple, Unbounded Solution and Infeasible Problems
• Solving Linear Programming Graphically Using Computer
• Application of Linear Programming in Business and Industry

3 Linear Programming-Simplex Method

• Principle of Simplex Method
• Computational aspect of Simplex Method
• Simplex Method with several Decision Variables
• Two Phase and M-method
• Multiple Solution, Unbounded Solution and Infeasible Problem
• Sensitivity Analysis
• Dual Linear Programming Problem

4 Transportation Problem

• Basic Feasible Solution of a Transportation Problem
• Modified Distribution Method
• Stepping Stone Method
• Unbalanced Transportation Problem
• Degenerate Transportation Problem
• Transhipment Problem
• Maximisation in a Transportation Problem

5 Assignment Problem

• Solution of the Assignment Problem
• Unbalanced Assignment Problem
• Problem with some Infeasible Assignments
• Maximisation in an Assignment Problem
• Crew Assignment Problem

6 Application of Excel Solver to Solve LPP

• Building Excel model for solving LP: An Illustrative Example

7 Goal Programming

• Concepts of goal programming
• Goal programming model formulation
• Graphical method of goal programming
• The simplex method of goal programming
• Using Excel Solver to Solve Goal Programming Models
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8 Integer Programming

• Some Integer Programming Formulation Techniques
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• Unimodularity
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9 Dynamic Programming

• Dynamic Programming Methodology: An Example
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10 Non-Linear Programming

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• Convex and Concave Functions
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• Quadratic Programming
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• NLP Models with Solver

11 Introduction to game theory and its Applications

• Important terms in Game Theory
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• 2 x n games
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12 Monte Carlo Simulation

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13 Queueing Models

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Quantitative Techniques: Theory and Problems by P. C. Tulsian, Vishal Pandey

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WHAT IS ASSIGNMENT PROBLEM

Assignment Problem is a special type of linear programming problem where the objective is to minimise the cost or time of completing a number of jobs by a number of persons.

The assignment problem in the general form can be stated as follows:

“Given n facilities, n jobs and the effectiveness of each facility for each job, the problem is to assign each facility to one and only one job in such a way that the measure of effectiveness is optimised (Maximised or Minimised).”

Several problems of management has a structure identical with the assignment problem.

Example I A manager has four persons (i.e. facilities) available for four separate jobs (i.e. jobs) and the cost of assigning (i.e. effectiveness) each job to each ...

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Assignment Problem: Meaning, Methods and Variations | Operations Research

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

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Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

• O. Erhun Kundakcioglu 3 &
• Saed Alizamir 3  

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Article Outline

Introduction

  Multiple-Resource Generalized Assignment Problem

  Multilevel Generalized Assignment Problem

  Dynamic Generalized Assignment Problem

  Bottleneck Generalized Assignment Problem

  Generalized Assignment Problem with Special Ordered Set

  Stochastic Generalized Assignment Problem

  Bi-Objective Generalized Assignment Problem

  Generalized Multi-Assignment Problem

  Exact Algorithms

  Heuristics

Conclusions

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Albareda-Sambola M, van der Vlerk MH, Fernandez E (2006) Exact solutions to a class of stochastic generalized assignment problems. Eur J Oper Res 173:465–487

Article   MATH   Google Scholar  

Amini MM, Racer M (1994) A rigorous computational comparison of alternative solution methods for the generalized assignment problem. Manag Sci 40(7):868–890

Amini MM, Racer M (1995) A hybrid heuristic for the generalized assignment problem. Eur J Oper Res 87(2):343–348

Asahiro Y, Ishibashi M, Yamashita M (2003) Independent and cooperative parallel search methods for the generalized assignment problem. Optim Method Softw 18:129–141

Article   MathSciNet   MATH   Google Scholar  

Balachandran V (1976) An integer generalized transportation model for optimal job assignment in computer networks. Oper Res 24(4):742–759

Barnhart C, Johnson EL, Nemhauser GL, Savelsbergh MWP, Vance PH (1998) Branch-and-price: column generation for solving huge integer programs. Oper Res 46(3):316–329

Beasley JE (1993) Lagrangean heuristics for location problems. Eur J Oper Res 65:383–399

Cario MC, Clifford JJ, Hill RR, Yang J, Yang K, Reilly CH (2002) An investigation of the relationship between problem characteristics and algorithm performance: a case study of the gap. IIE Trans 34:297–313

Google Scholar  

Cattrysse DG, Salomon M, Van LN Wassenhove (1994) A set partitioning heuristic for the generalized assignment problem. Eur J Oper Res 72:167–174

Cattrysse DG, Van LN Wassenhove (1992) A survey of algorithms for the generalized assignment problem. Eur J Oper Res 60:260–272

Ceselli A, Righini G (2006) A branch-and-price algorithm for the multilevel generalized assignment problem. Oper Res 54:1172–1184

Chalmet L, Gelders L (1976) Lagrangean relaxation for a generalized assignment type problem. In: Advances in OR. EURO, North Holland, Amsterdam, pp 103–109

Chu EC, Beasley JE (1997) A genetic algorithm for the generalized assignment problem. Comput Oper Res 24:17–23

Cohen R, Katzir L, Raz D (2006) An efficient approximation for the generalized assignment problem. Inf Process Lett 100:162–166

de Farias Jr, Johnson EL, Nemhauser GL (2000) A generalized assignment problem with special ordered sets: a polyhedral approach. Math Program, Ser A 89:187–203

de Farias Jr, Nemhauser GL (2001) A family of inequalities for the generalized assignment polytope. Oper Res Lett 29:49–55

DeMaio A, Roveda C (1971) An all zero-one algorithm for a class of transportation problems. Oper Res 19:1406–1418

Diaz JA, Fernandez E (2001) A tabu search heuristic for the generalized assignment problem. Eur J Oper Res 132:22–38

Drexl A (1991) Scheduling of project networks by job assignment. Manag Sci 37:1590–1602

Dyer M, Frieze A (1992) Probabilistic analysis of the generalised assignment problem. Math Program 55:169–181

Article   MathSciNet   Google Scholar  

Feltl H, Raidl GR (2004) An improved hybrid genetic algorithm for the generalized assignment problem. In: SAC '04; Proceedings of the 2004 ACM symposium on Applied computing. ACM Press, New York, pp 990–995

Chapter   Google Scholar  

Fisher ML, Jaikumar R (1981) A generalized assignment heuristic for vehicle routing. Netw 11:109–124

Fisher ML, Jaikumar R, van Wassenhove LN (1986) A multiplier adjustment method for the generalized assignment problem. Manag Sci 32:1095–1103

Fleischer L, Goemans MX, Mirrokni VS, Sviridenko M (2006) Tight approximation algorithms for maximum general assignment problems. In SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm. ACM Press, New York, pp 611–620

Book   Google Scholar  

Freling R, Romeijn HE, Morales DR, Wagelmans APM (2003) A branch-and-price algorithm for the multiperiod single-sourcing problem. Oper Res 51(6):922–939

French AP, Wilson JM (2002) Heuristic solution methods for the multilevel generalized assignment problem. J Heuristics 8:143–153

French AP, Wilson JM (2007) An lp-based heuristic procedure for the generalized assignment problem with special ordered sets. Comput Oper Res 34:2359–2369

Garey MR, Johnson DS (1990) Computers and Intractability; A Guide to the Theory of NP-Completeness. Freeman, New York

Gavish B, Pirkul H (1991) Algorithms for the multi-resource generalized assignment problem. Manag Sci 37:695–713

Geoffrion AM, Graves GW (1974) Multicommodity distribution system design by benders decomposition. Manag Sci 20(5):822–844

Glover F, Hultz J, Klingman D (1979) Improved computer based planning techniques, part ii. Interfaces 4:17–24

Gottlieb ES, Rao MR (1990) \( (1,k) \) -configuration facets for the generalized assignment problem. Math Program 46(1):53–60

Gottlieb ES, Rao MR (1990) The generalized assignment problem: Valid inequalities and facets. Math Stat 46:31–52

MathSciNet   MATH   Google Scholar  

Guignard M, Rosenwein MB (1989) An improved dual based algorithm for the generalized assignment problem. Oper Res 37(4):658–663

Haddadi S (1999) Lagrangian decomposition based heuristic for the generalized assignment problem. Inf Syst Oper Res 37:392–402

Haddadi S, Ouzia H (2004) Effective algorithm and heuristic for the generalized assignment problem. Eur J Oper Res 153:184–190

Hajri-Gabouj S (2003) A fuzzy genetic multiobjective optimization algorithm for a multilevel generalized assignment problem. IEEE Trans Syst 33:214–224

Janak SL, Taylor MS, Floudas CA, Burka M, Mountziaris TJ (2006) Novel and effective integer optimization approach for the nsf panel-assignment problem: a multiresource and preference-constrained generalized assignment problem. Ind Eng Chem Res 45:258–265

Article   Google Scholar  

Jörnsten K, Nasberg M (1986) A new lagrangian relaxation approach to the generalized assignment problem. Eur J Oper Res 27:313–323

Jörnsten KO, Varbrand P (1990) Relaxation techniques and valid inequalities applied to the generalized assignment problem. Asia-P J Oper Res 7(2):172–189

Klastorin TD (1979) An effective subgradient algorithm for the generalized assignment problem. Comp Oper Res 6:155–164

Klastorin TD (1979) On the maximal covering location problem and the generalized assignment problem. Manag Sci 25(1):107–112

Kogan K, Khmelnitsky E, Ibaraki T (2005) Dynamic generalized assignment problems with stochastic demands and multiple agent task relationships. J Glob Optim 31:17–43

Kogan K, Shtub A, Levit VE (1997) Dgap – the dynamic generalized assignment problem. Ann Oper Res 69:227–239

Kuhn H (1995) A heuristic algorithm for the loading problem in flexible manufacturing systems. Int J Flex Manuf Syst 7:229–254

Laguna M, Kelly JP, Gonzfilez-Velarde JL, Glover F (1995) Tabu search for the multilevel generalized assignment problem. Eur J Oper Res 82:176–189

Lawler E (1976) Combinatorial Optimization: Networks and Matroids. Holt, Rinehart, Winston, New York

MATH   Google Scholar  

Lin BMT, Huang YS, Yu HK (2001) On the variable-depth-search heuristic for the linear-cost generalized assignment problem. Int J Comput Math 77:535–544

Lorena LAN, Narciso MG (1996) Relaxation heuristics for a generalized assignment problem. Eur J Oper Res 91:600–610

Lorena LAN, Narciso MG, Beasley JE (2003) A constructive genetic algorithm for the generalized assignment problem. J Evol Optim

Lourenço HR, Serra D (1998) Adaptive approach heuristics for the generalized assignment problem. Technical Report 288, Department of Economics and Business, Universitat Pompeu Fabra, Barcelona

Lourenço HR, Serra D (2002) Adaptive search heuristics for the generalized assignment problem. Mathw Soft Comput 9(2–3):209–234

Martello S, Toth P (1981) An algorithm for the generalized assignment problem. In: Brans JP (ed) Operational Research '81, 9th IFORS Conference, North-Holland, Amsterdam, pp 589–603

Martello S, Toth P (1990) Knapsack Problems: Algorithms and Computer Implementations. Wiley, New York

Martello S, Toth P (1992) Generalized assignment problems. Lect Notes Comput Sci 650:351–369

MathSciNet   Google Scholar  

Martello S, Toth P (1995) The bottleneck generalized assignment problem. Eur J Oper Res 83:621–638

Mazzola JB, Neebe AW (1988) Bottleneck generalized assignment problems. Eng Costs Prod Econ 14(1):61–65

Mazzola JB, Wilcox SP (2001) Heuristics for the multi-resource generalized assignment problem. Nav Res Logist 48(6):468–483

Monfared MAS, Etemadi M (2006) The impact of energy function structure on solving generalized assignment problem using hopfield neural network. Eur J Oper Res 168:645–654

Morales DR, Romeijn HE (2005) Handbook of Combinatorial Optimization, supplement vol B. In: Du D-Z, Pardalos PM (eds) The Generalized Assignment Problem and extensions. Springer, New York, pp 259–311

Narciso MG, Lorena LAN (1999) Lagrangean/surrogate relaxation for generalized assignment problems. Eur J Oper Res 114:165–177

Nauss RM (2003) Solving the generalized assignment problem: an optimizing and heuristic approach. INFORMS J Comput 15(3):249–266

Nauss RM (2005) The elastic generalized assignment problem. J Oper Res Soc 55:1333–1341

Nowakovski J, Schwarzler W, Triesch E (1999) Using the generalized assignment problem in scheduling the rosat space telescope. Eur J Oper Res 112:531–541

Nutov Z, Beniaminy I, Yuster R (2006) A  \( (1-1/e) \) ‐approximation algorithm for the generalized assignment problem. Oper Res Lett 34:283–288

Park JS, Lim BH, Lee Y (1998) A lagrangian dual-based branch-and-bound algorithm for the generalized multi-assignment problem. Manag Sci 44(12S):271–275

Pigatti A, de Aragao MP, Uchoa E (2005) Stabilized branch-and-cut-and-price for the generalized assignment problem. In: Electronic Notes in Discrete Mathematics, vol 19 of 2nd Brazilian Symposium on Graphs, Algorithms and Combinatorics, pp 385–395,

Osman IH (1995) Heuristics for the generalized assignment problem: simulated annealing and tabu search approaches. OR-Spektrum 17:211–225

Racer M, Amini MM (1994) A robust heuristic for the generalized assignment problem. Ann Oper Res 50(1):487–503

Romeijn HE, Morales DR (2000) A class of greedy algorithms for the generalized assignment problem. Discret Appl Math 103:209–235

Romeijn HE, Morales DR (2001) Generating experimental data for the generalized assignment problem. Oper Res 49(6):866–878

Romeijn HE, Piersma N (2000) A probabilistic feasibility and value analysis of the generalized assignment problem. J Comb Optim 4:325–355

Ronen D (1992) Allocation of trips to trucks operating from a single terminal. Comput Oper Res 19(5):445–451

Ross GT, Soland RM (1975) A branch and bound algorithm for the generalized assignment problem. Math Program 8:91–103

Ross GT, Soland RM (1977) Modeling facility location problems as generalized assignment problems. Manag Sci 24:345–357

Ross GT, Zoltners AA (1979) Weighted assignment models and their application. Manag Sci 25(7):683–696

Savelsbergh M (1997) A branch-and-price algorithm for the generalized assignment problem. Oper Res 45:831–841

Shmoys DB, Tardos E (1993) An approximation algorithm for the generalized assignment problem. Math Program 62:461–474

Shtub A (1989) Modelling group technology cell formation as a generalized assignment problem. Int J Prod Res 27:775–782

Srinivasan V, Thompson GL (1973) An algorithm for assigning uses to sources in a special class of transportation problems. Oper Res 21(1):284–295

Stützle T, Hoos H (1999) The Max-Min Ant System and Local Search for Combinatorial Optimization Problems. In: Voss S, Martello S, Osman IH, Roucairol C (eds) Meta-heuristics; Advances and trends in local search paradigms for optimization. Kluwer, Boston, pp 313–329

Toktas B, Yen JW, Zabinsky ZB (2006) Addressing capacity uncertainty in resource-constrained assignment problems. Comput Oper Res 33:724–745

Trick M (1992) A linear relaxation heuristic for the generalized assignment problem. Nav Res Logist 39:137–151

Trick MA (1994) Scheduling multiple variable-speed machines. Oper Res 42(2):234–248

Wilson JM (1997) A genetic algorithm for the generalised assignment problem. J Oper Res Soc 48:804–809

Wilson JM (2005) An algorithm for the generalized assignment problem with special ordered sets. J Heuristics 11:337–350

Yagiura M, Ibaraki T, Glover F (2004) An ejection chain approach for the generalized assignment problem. INFORMS J Comput 16:133–151

Yagiura M, Ibaraki T, Glover F (2006) A path relinking approach with ejection chains for the generalized assignment problem. Eur J Oper Res 169:548–569

Yagiura M, Yamaguchi T, Ibaraki T (1998) A variable depth search algorithm with branching search for the generalized assignment problem. Optim Method Softw 10:419–441

Yagiura M, Yamaguchi T, Ibaraki T (1999) A variable depth search algorithm for the generalized assignment problem. In: Voss S, Martello S, Osman IH, Roucairol C (eds) Meta-heuristics; Advances and Trends in Local Search paradigms for Optimization, Kluwer, Boston, pp 459–471

Zhang CW, Ong HL (2007) An efficient solution to biobjective generalized assignment problem. Adv Eng Softw 38:50–58

Zimokha VA, Rubinshtein MI (1988) R & d planning and the generalized assignment problem. Autom Remote Control 49:484–492

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O. Erhun Kundakcioglu & Saed Alizamir

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Kundakcioglu, O.E., Alizamir, S. (2008). Generalized Assignment Problem . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_200

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