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Technical Note—An Improved Dual Based Algorithm for the Generalized Assignment Problem

Author

Listed:
  • Monique Guignard

    (University of Pennsylvania, Philadelphia, Pennsylvania)

  • Moshe B. Rosenwein

    (AT&T Bell Laboratories, Holmdel, New Jersey)

Abstract

The generalized assignment problem (GAP) determines the minimum cost assignment of n jobs to m agents such that each job is assigned to exactly one agent, subject to an agent's capacity. Existing solution algorithms have not solved problems with more than 100 decision variables. This paper designs an optimization algorithm for the GAP that effectively solves problems with up to 500 variables. Compared with existing procedures, this algorithm requires fewer enumeration nodes and shorter running times. Improved performance stems from: an enhanced Lagrangian dual ascent procedure that solves a Lagrangian dual at each enumeration node; adding a surrogate constraint to the Lagrangian relaxed model: and an elaborate branch-and-bound scheme. An empirical investigation of various problem structures, not considered in existing literature, is also presented.

Suggested Citation

  • Monique Guignard & Moshe B. Rosenwein, 1989. "Technical Note—An Improved Dual Based Algorithm for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 37(4), pages 658-663, August.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:4:p:658-663
    DOI: 10.1287/opre.37.4.658
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    Citations

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    Cited by:

    1. Cattrysse, D. G. & van Wassenhove, L. N., 1990. "A Survey Of Algorithms For The Generalized Assignment Problem," Econometric Institute Archives 272389, Erasmus University Rotterdam.
    2. Hill, Raymond R. & Reilly, Charles H., 2000. "Multivariate composite distributions for coefficients in synthetic optimization problems," European Journal of Operational Research, Elsevier, vol. 121(1), pages 64-77, February.
    3. Narciso, Marcelo G. & Lorena, Luiz Antonio N., 1999. "Lagrangean/surrogate relaxation for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 114(1), pages 165-177, April.
    4. Atan, Tankut S. & Pandit, Ram, 1996. "Auxiliary tool allocation in flexible manufacturing systems," European Journal of Operational Research, Elsevier, vol. 89(3), pages 642-659, March.
    5. Pessoa, Artur Alves & Hahn, Peter M. & Guignard, Monique & Zhu, Yi-Rong, 2010. "Algorithms for the generalized quadratic assignment problem combining Lagrangean decomposition and the Reformulation-Linearization Technique," European Journal of Operational Research, Elsevier, vol. 206(1), pages 54-63, October.
    6. Robert M. Nauss, 2003. "Solving the Generalized Assignment Problem: An Optimizing and Heuristic Approach," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 249-266, August.
    7. Haddadi, Salim & Ouzia, Hacene, 2004. "Effective algorithm and heuristic for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 153(1), pages 184-190, February.
    8. Amini, Mohammad M. & Racer, Michael & Ghandforoush, Parviz, 1998. "Heuristic sensitivity analysis in a combinatoric environment: An exposition and case study," European Journal of Operational Research, Elsevier, vol. 108(3), pages 604-617, August.
    9. Raymond R. Hill & Charles H. Reilly, 2000. "The Effects of Coefficient Correlation Structure in Two-Dimensional Knapsack Problems on Solution Procedure Performance," Management Science, INFORMS, vol. 46(2), pages 302-317, February.
    10. June S. Park & Byung Ha Lim & Youngho Lee, 1998. "A Lagrangian Dual-Based Branch-and-Bound Algorithm for the Generalized Multi-Assignment Problem," Management Science, INFORMS, vol. 44(12-Part-2), pages 271-282, December.
    11. R M Nauss, 2004. "The elastic generalized assignment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1333-1341, December.
    12. P N Ram Kumar & T T Narendran, 2011. "On the usage of Lagrangean Relaxation for the convoy movement problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 722-728, April.
    13. Laguna, Manuel & Kelly, James P. & Gonzalez-Velarde, JoseLuis & Glover, Fred, 1995. "Tabu search for the multilevel generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 82(1), pages 176-189, April.
    14. H. Edwin Romeijn & Dolores Romero Morales, 2001. "Generating Experimental Data for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 49(6), pages 866-878, December.
    15. Lorena, Luiz Antonio N. & Narciso, Marcelo G., 1996. "Relaxation heuristics for a generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 91(3), pages 600-610, June.
    16. Joseph B. Mazzola & Steven P. Wilcox, 2001. "Heuristics for the multi‐resource generalized assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(6), pages 468-483, September.
    17. Klose, Andreas & Drexl, Andreas, 2001. "Combinatorial optimisation problems of the assignment type and a partitioning approach," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 545, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    18. Martello, Silvano & Toth, Paolo, 1995. "The bottleneck generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 83(3), pages 621-638, June.
    19. Charles H. Reilly, 2009. "Synthetic Optimization Problem Generation: Show Us the Correlations!," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 458-467, August.
    20. Diaz, Juan A. & Fernandez, Elena, 2001. "A Tabu search heuristic for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 132(1), pages 22-38, July.
    21. Drexl, Andreas & Jørnsten, Kurt, 2007. "Pricing the generalized assignment problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 627, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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