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Heuristics for the multi‐resource generalized assignment problem

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  • Joseph B. Mazzola
  • Steven P. Wilcox

Abstract

The well‐known generalized assignment problem (GAP) involves the identification of a minimum‐cost assignment of tasks to agents when each agent is constrained by a resource in limited supply. The multi‐resource generalized assignment problem (MRGAP) is the generalization of the GAP in which there are a number of different potentially constraining resources associated with each agent. This paper explores heuristic procedures for the MRGAP. We first define a three‐phase heuristic which seeks to construct a feasible solution to MRGAP and then systematically attempts to improve the solution. We then propose a modification of the heuristic for the MRGAP defined previously by Gavish and Pirkul. The third procedure is a hybrid heuristic that combines the first two heuristics, thus capturing their relative strengths. We discuss extensive computational experience with the heuristics. The hybrid procedure is seen to be extremely effective in solving MRGAPs, generating feasible solutions to more than 99% of the test problems and consistently producing near‐optimal solutions. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 468–483, 2001

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  • Joseph B. Mazzola & Steven P. Wilcox, 2001. "Heuristics for the multi‐resource generalized assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(6), pages 468-483, September.
    • Handle: RePEc:wly:navres:v:48:y:2001:i:6:p:468-483
    DOI: 10.1002/nav.1029
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    References listed on IDEAS

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    1. Joseph B. Mazzola & Alan W. Neebe, 1986. "Resource-Constrained Assignment Scheduling," Operations Research, INFORMS, vol. 34(4), pages 560-572, August.
    2. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    3. 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.
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    6. Gerard Cornuejols & Marshall L. Fisher & George L. Nemhauser, 1977. "Exceptional Paper--Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms," Management Science, INFORMS, vol. 23(8), pages 789-810, April.
    7. CORNUEJOLS, Gérard & FISHER, Marshall L. & NEMHAUSER, George L., 1977. "Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms," LIDAM Reprints CORE 292, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Pirkul, Hasan, 1986. "An integer programming model for the allocation of databases in a distributed computer system," European Journal of Operational Research, Elsevier, vol. 26(3), pages 401-411, September.
    9. 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.
    10. Michael A. Trick, 1992. "A linear relaxation heuristic for the generalized assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 137-151, March.
    11. Gavish, Bezalel & Pirkul, Hasan, 1985. "Zero-one integer programs with few constraints --Efficient branch and bound algorithms," European Journal of Operational Research, Elsevier, vol. 22(1), pages 35-43, October.
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    Cited by:

    1. Monnerat, Filipe & Dias, Joana & Alves, Maria João, 2019. "Fleet management: A vehicle and driver assignment model," European Journal of Operational Research, Elsevier, vol. 278(1), pages 64-75.

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