Skip to main content
SpringerLink
Log in

Generalized Assignment Problem

  • Reference work entry
Encyclopedia of Optimization

Article Outline

Introduction

Extensions

  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

Methods

  Exact Algorithms

  Heuristics

Conclusions

References

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. 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 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. 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 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. 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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  8. 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 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. 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 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  24. 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 

  25. 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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  27. 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

    Article  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  38. 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 

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

    Article  MATH  Google Scholar 

  40. 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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  43. 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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  46. 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

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  48. 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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

  51. 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

    Google Scholar 

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

    Google Scholar 

  53. 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

    Google Scholar 

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

    MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  59. 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

    Article  MathSciNet  MATH  Google Scholar 

  60. 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

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  64. 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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  66. 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

    Article  Google Scholar 

  67. 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,

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  80. 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

    Article  MathSciNet  MATH  Google Scholar 

  81. 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

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  88. 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

    Article  MathSciNet  MATH  Google Scholar 

  89. 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

    Article  MathSciNet  MATH  Google Scholar 

  90. 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

    Google Scholar 

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

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

    O. Erhun Kundakcioglu & Saed Alizamir

Authors
  1. O. Erhun Kundakcioglu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saed Alizamir
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

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

Download citation

Publish with us

Policies and ethics

Search

Navigation