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A Min-Max-Sum Resource Allocation Problem and Its Applications

Author

Listed:
  • Selcuk Karabati

    (College of Administrative Sciences and Economics, Koç University, Sariyer, Istanbul 80910, Turkey)

  • Panagiotis Kouvelis

    (Olin School of Business, Washington University, Campus Box 1133, St Louis, Missouri 63130-4899)

  • Gang Yu

    (Department of MSIS, McCombs School of Business, The University of Texas at Austin, Austin, Texas 78712)

Abstract

In this paper we consider a class of discrete resource-allocation problems with a min-max-sum objective function. We first provide several examples of practical applications of this problem. We then develop a branch-and-bound procedure for solving the general case of this computationally intractable problem. The proposed solution procedure employs a surrogate relaxation technique to obtain lower and upper bounds on the optimal objective function value of the problem. To obtain the multipliers of the surrogate relaxation, two alternative approaches are discussed. We also discuss a simple approximation algorithm with a tight bound. Our computational results support the effectiveness of the branch-and-bound procedure for fairly large-size problems.

Suggested Citation

  • Selcuk Karabati & Panagiotis Kouvelis & Gang Yu, 2001. "A Min-Max-Sum Resource Allocation Problem and Its Applications," Operations Research, INFORMS, vol. 49(6), pages 913-922, December.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:6:p:913-922
    DOI: 10.1287/opre.49.6.913.10023
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    References listed on IDEAS

    as
    1. Christopher S. Tang, 1988. "A Max-Min Allocation Problem: Its Solutions and Applications," Operations Research, INFORMS, vol. 36(2), pages 359-367, April.
    2. Selcuk Karabati & Panagiotis Kouvelis & Gang Yu, 1995. "The Discrete Resource Allocation Problem in Flow Lines," Management Science, INFORMS, vol. 41(9), pages 1417-1430, September.
    3. Muralidharan S. Kodialam & Hanan Luss, 1998. "Algorithms for Separable Nonlinear Resource Allocation Problems," Operations Research, INFORMS, vol. 46(2), pages 272-284, April.
    4. Fred Glover, 1975. "Surrogate Constraint Duality in Mathematical Programming," Operations Research, INFORMS, vol. 23(3), pages 434-451, June.
    5. Harvey J. Greenberg & William P. Pierskalla, 1970. "Surrogate Mathematical Programming," Operations Research, INFORMS, vol. 18(5), pages 924-939, October.
    6. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    7. Dan Trietsch & Kenneth R. Baker, 1993. "Basic Techniques for Lot Streaming," Operations Research, INFORMS, vol. 41(6), pages 1065-1076, December.
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    Cited by:

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    3. Min Yang & Qingxian An & Tao Ding & Pengzhen Yin & Liang Liang, 2019. "Carbon emission allocation in China based on gradually efficiency improvement and emission reduction planning principle," Annals of Operations Research, Springer, vol. 278(1), pages 123-139, July.

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