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Pricing the generalized assignment problem

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  • Drexl, Andreas
  • Jørnsten, Kurt

Abstract

The generalized assignment problem (GAP) examines the maximum profit assignment of jobs to processors such that each job is assigned to precisely one processor subject to capacity restrictions on the processors. Due to the fact that the GAP is an NP-hard integer program dual prices are not readily available. In this paper we propose a family of linear programming models the optimal solution of which is integral "almost always". We provide a computational proof of this conjecture by an in-depth experimental study of 1500 instances generated according to the standard procedure adopted in literature. Summarizing this analysis we have linear prices for all but 17 of the whole bunch of instances and, hence, there exists a linear price function that supports the optimal assignment of jobs to processors.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:cauman:627
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    References listed on IDEAS

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    2. Martin Savelsbergh, 1997. "A Branch-and-Price Algorithm for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 45(6), pages 831-841, December.
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    4. 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.
    5. G. Terry Ross & Richard M. Soland, 1977. "Modeling Facility Location Problems as Generalized Assignment Problems," Management Science, INFORMS, vol. 24(3), pages 345-357, November.
    6. Marshall L. Fisher & R. Jaikumar & Luk N. Van Wassenhove, 1986. "A Multiplier Adjustment Method for the Generalized Assignment Problem," Management Science, INFORMS, vol. 32(9), pages 1095-1103, September.
    7. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    8. T. D. Klastorin, 1979. "Note--On the Maximal Covering Location Problem and the Generalized Assignment Problem," Management Science, INFORMS, vol. 25(1), pages 107-112, January.
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    Cited by:

    1. Briskorn, Dirk & Knust, Sigrid, 2008. "On Circular 2-Factorizations of the Complete Tripartite Graph," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 636, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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