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A Rigorous Computational Comparison of Alternative Solution Methods for the Generalized Assignment Problem

Author

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  • Mohammad M. Amini

    (Department of Management Information Systems and Decision Sciences, The Fogelman College of Business and Economics, The University of Memphis, Memphis, Tennessee 38152)

  • Michael Racer

    (Department of Civil Engineering, The Herff College of Engineering, The University of Memphis, Memphis, Tennessee 38152)

Abstract

Statistical experimental design and analysis is a cornerstone for scientific inquiry that is rarely applied in reporting computational testing. This approach is employed to study the relative performance characteristics of the four leading algorithmic and heuristic alternatives to solve the Linear Cost Generalized Assignment Problem (LCGAP) against a newly developed heuristic, Variable-Depth Search Heuristic (VDSH). In assessing the relative effectiveness of the prominent solution methodologies and VDSH under the effects of various problem characteristics, we devise a carefully designed experimentation of state-of-the-art implementations; through a rigorous statistical analysis we identify the most efficient method(s) for commonly studied LCGAPs, and determine the effect on solution time and quality of problem class and size.

Suggested Citation

  • Mohammad M. Amini & Michael Racer, 1994. "A Rigorous Computational Comparison of Alternative Solution Methods for the Generalized Assignment Problem," Management Science, INFORMS, vol. 40(7), pages 868-890, July.
    • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:7:p:868-890
    DOI: 10.1287/mnsc.40.7.868
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Schmitt, Lawrence J. & Amini, Mohammad M., 1998. "Performance characteristics of alternative genetic algorithmic approaches to the traveling salesman problem using path representation: An empirical study," European Journal of Operational Research, Elsevier, vol. 108(3), pages 551-570, August.
    4. Woodcock, Andrew J. & Wilson, John M., 2010. "A hybrid tabu search/branch & bound approach to solving the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 207(2), pages 566-578, December.
    5. Jeet, V. & Kutanoglu, E., 2007. "Lagrangian relaxation guided problem space search heuristics for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1039-1056, November.
    6. Jafar Rezaei & Negin Salimi, 2015. "Optimal ABC inventory classification using interval programming," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 1944-1952, August.
    7. 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.
    8. Helena Ramalhinho-Lourenço & Daniel Serra, 1998. "Adaptive approach heuristics for the generalized assignment problem," Economics Working Papers 288, Department of Economics and Business, Universitat Pompeu Fabra.
    9. Marie Coffin & Matthew J. Saltzman, 2000. "Statistical Analysis of Computational Tests of Algorithms and Heuristics," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 24-44, February.
    10. 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.
    11. 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.
    12. 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.
    13. Reilly, Charles H. & Sapkota, Nabin, 2015. "A family of composite discrete bivariate distributions with uniform marginals for simulating realistic and challenging optimization-problem instances," European Journal of Operational Research, Elsevier, vol. 241(3), pages 642-652.
    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. Barbas, Javier & Marin, Angel, 2004. "Maximal covering code multiplexing access telecommunication networks," European Journal of Operational Research, Elsevier, vol. 159(1), pages 219-238, November.
    16. P J Densham & G Rushton, 1996. "Providing Spatial Decision Support for Rural Public Service Facilities That Require a Minimum Workload," Environment and Planning B, , vol. 23(5), pages 553-574, October.
    17. Charles H. Reilly, 2009. "Synthetic Optimization Problem Generation: Show Us the Correlations!," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 458-467, August.
    18. 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.
    19. Belarmino Adenso-Díaz & Manuel Laguna, 2006. "Fine-Tuning of Algorithms Using Fractional Experimental Designs and Local Search," Operations Research, INFORMS, vol. 54(1), pages 99-114, February.

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