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A Lagrangian Dual-Based Branch-and-Bound Algorithm for the Generalized Multi-Assignment Problem

Listed author(s):
  • June S. Park

    (Department of Management Sciences, 108 Pappajohn Business Adm. Bldg., The University of Iowa, Iowa City, Iowa 52242-1000)

  • Byung Ha Lim

    (US West Advanced Technologies, Applied Research, Suite 280, 4001 Discovery Drive, Boulder, Colorado 80303)

  • Youngho Lee

    (US West Advanced Technologies, Applied Research, Suite 280, 4001 Discovery Drive, Boulder, Colorado 80303)

Registered author(s):

    This paper develops a Lagrangian dual-based branch-and-bound algorithm for the generalized multi-assignment problem (GMAP) which includes the well-known generalized assignment problem (GAP) as a special case. In GMAP, an object may be required to be duplicated in multiple locations. We develop a Lagrangian dual ascent algorithm for GMAP. This dual ascent and the subgradient search each possess advantages that can be combined to develop a new Lagrangian dual search algorithm. The latter algorithm, when incorporated into a branch-and-bound algorithm as the lower bounding scheme, can accelerate the search process. Computational results demonstrate the efficiency and robustness of this branch-and-bound algorithm not only for GMAPs, but for GAPs that are more difficult than could be solved by previous algorithms.

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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 44 (1998)
    Issue (Month): 12-Part-2 (December)
    Pages: 271-282

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    Handle: RePEc:inm:ormnsc:v:44:y:1998:i:12-part-2:p:s271-s282
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    1. 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.
    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.
    3. 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.
    4. 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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