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On the solution of a stochastic bottleneck assignment problem and its variations

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  • Prabuddha De
  • Jay B. Ghosh
  • Charles E. Wells

Abstract

In this article, we study the stochastic version of the so‐called bottleneck assignment problem. Our primary objective is to maximize the probability that the bottleneck value satisfies a specified target. Under general stochastic assumptions, we show that the solution in this case is easily obtained by solving a linear assignment problem. We next examine the situation where the target is to be minimized, given that the probability of satisfying the target exceeds a specified threshold. Finally, we address extensions to the original problem where a second objective is also considered.

Suggested Citation

  • Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1992. "On the solution of a stochastic bottleneck assignment problem and its variations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 389-397, April.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:3:p:389-397
    DOI: 10.1002/1520-6750(199204)39:33.0.CO;2-6
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    1. R. S. Garfinkel & M. R. Rao, 1971. "The bottleneck transportation problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 18(4), pages 465-472, December.
    2. Robert S. Garfinkel, 1971. "Technical Note—An Improved Algorithm for the Bottleneck Assignment Problem," Operations Research, INFORMS, vol. 19(7), pages 1747-1751, December.
    3. Joseph B. Mazzola & Alan W. Neebe, 1986. "Resource-Constrained Assignment Scheduling," Operations Research, INFORMS, vol. 34(4), pages 560-572, August.
    4. Wlodzimierz Szwarc, 1971. "Some remarks on the time transportation problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 18(4), pages 473-485, December.
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    Cited by:

    1. Ching-Chung Kuo, 2011. "Optimal assignment of resources to strengthen the weakest link in an uncertain environment," Annals of Operations Research, Springer, vol. 186(1), pages 159-173, June.

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