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A Max-Min Allocation Problem: Its Solutions and Applications

Author

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  • Christopher S. Tang

    (University of California, Los Angeles, California)

Abstract

This paper describes a max-min allocation problem that has M constraints and N nonnegative integer variables. By exploring the structure of the optimal solution to this max-min allocation problem, we develop a nonsimplex-based algorithm that finds an optimal solution within O ( MN 2 ) operations. In addition, we show that a space allocation problem for a flexible component insertion machine can be formulated as a special case of this max-min allocation problem with one constraint. Furthermore, we present some manufacturing and production problems that can he formulated as max-min allocation problems, and hence, can be solved efficiently.

Suggested Citation

  • Christopher S. Tang, 1988. "A Max-Min Allocation Problem: Its Solutions and Applications," Operations Research, INFORMS, vol. 36(2), pages 359-367, April.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:2:p:359-367
    DOI: 10.1287/opre.36.2.359
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    Cited by:

    1. Kasin Ransikarbum & Scott J. Mason, 2016. "Multiple-objective analysis of integrated relief supply and network restoration in humanitarian logistics operations," International Journal of Production Research, Taylor & Francis Journals, vol. 54(1), pages 49-68, January.
    2. Muralidharan S. Kodialam & Hanan Luss, 1998. "Algorithms for Separable Nonlinear Resource Allocation Problems," Operations Research, INFORMS, vol. 46(2), pages 272-284, April.
    3. Klein, Rachelle S. & Luss, Hanan & Rothblum, Uriel G., 1995. "Multiperiod allocation of substitutable resources," European Journal of Operational Research, Elsevier, vol. 85(3), pages 488-503, September.
    4. Mhand Hifi & Slim Sadfi, 2002. "The Knapsack Sharing Problem: An Exact Algorithm," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 35-54, March.
    5. Fujimoto, Masako & Yamada, Takeo, 2006. "An exact algorithm for the knapsack sharing problem with common items," European Journal of Operational Research, Elsevier, vol. 171(2), pages 693-707, June.
    6. 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.
    7. Christ, Quentin & Dauzère-Pérès, Stéphane & Lepelletier, Guillaume, 2019. "An Iterated Min–Max procedure for practical workload balancing on non-identical parallel machines in manufacturing systems," European Journal of Operational Research, Elsevier, vol. 279(2), pages 419-428.
    8. Yamada, Takeo & Futakawa, Mayumi & Kataoka, Seiji, 1998. "Some exact algorithms for the knapsack sharing problem," European Journal of Operational Research, Elsevier, vol. 106(1), pages 177-183, April.
    9. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    10. Thekra Al-douri & Mhand Hifi & Vassilis Zissimopoulos, 2021. "An iterative algorithm for the Max-Min knapsack problem with multiple scenarios," Operational Research, Springer, vol. 21(2), pages 1355-1392, June.
    11. Yuceer, Umit, 1997. "A multi-product loading problem: a model and solution method," European Journal of Operational Research, Elsevier, vol. 101(3), pages 519-531, September.

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