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

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  • 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)

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:12-part-2:p:s271-s282
    DOI: 10.1287/mnsc.44.12.S271
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Adriano De Maio & Claudio Roveda, 1971. "An all Zero-One Algorithm for a Certain Class of Transportation Problems," Operations Research, INFORMS, vol. 19(6), pages 1406-1418, October.
    4. 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.
    5. 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.
    6. 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:

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