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

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Author Info

  • 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)

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.44.12.S271
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 44 (1998)
    Issue (Month): 12-Part-2 (December)
    Pages: S271-S282

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

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    Related research

    Keywords: Generalized Multi-Assignment Problem; Generalized Assignment Problem; Lagrangian Dual Ascent; Subgradient Search; Lagrangian Dual-Based Branch and Bound;

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