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The elastic generalized assignment problem

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  • R M Nauss

    (University of Missouri–St. Louis,)

Abstract

The generalized assignment problem (GAP) has been studied by numerous researchers over the past 30 years or so. Simply stated, one must find a minimum-cost assignment of tasks to agents such that each task is assigned to exactly one agent and such that each agent's resource capacity is honoured. The problem is known to be NP-hard. In this paper, we study the elastic generalized assignment problem (EGAP). The elastic version of GAP allows agent resource capacity to be violated at additional cost. Another version allows undertime costs to be assessed as well if an agent's resource capacity is not used to its full extent. The EGAP is also NP-hard. We describe a special-purpose branch-and-bound algorithm that utilizes linear programming cuts, feasible solution generators, Lagrangean relaxation and subgradient optimization. We present computational results on a large collection of randomly generated ‘hard’ problems with up to 4000 binary variables.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:12:d:10.1057_palgrave.jors.2601806
    DOI: 10.1057/palgrave.jors.2601806
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    4. Cattrysse, Dirk G. & Van Wassenhove, Luk N., 1992. "A survey of algorithms for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 60(3), pages 260-272, August.
    5. Cattrysse, Dirk & Degraeve, Zeger & Tistaert, Jurgen, 1998. "Solving the generalised assignment problem using polyhedral results," European Journal of Operational Research, Elsevier, vol. 108(3), pages 618-628, August.
    6. A. M. Geoffrion & R. E. Marsten, 1972. "Integer Programming Algorithms: A Framework and State-of-the-Art Survey," Management Science, INFORMS, vol. 18(9), pages 465-491, May.
    7. Robert M. Nauss, 1976. "An Efficient Algorithm for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 23(1), pages 27-31, September.
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    Cited by:

    1. Büther, Marcel & Briskorn, Dirk, 2007. "Reducing the 0-1 knapsack problem with a single continuous variable to the standard 0-1 knapsack problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 629, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. M Büther, 2010. "Reducing the elastic generalized assignment problem to the standard generalized assignment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1582-1595, November.
    3. Büther, Marcel, 2007. "Reducing the elastic generalized assignment problem to the standard generalized assignment problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 632, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Büther, Marcel, 2008. "Beam search for the elastic generalized assignment problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 634, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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