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Communications to the Editor--A Stochastic Bottleneck Assignment Problem

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  • Uri Yechiali

    (Columbia University)

Abstract

Consider an n-job stochastic bottleneck assignment problem in which the production rates are independent random variables rather than constants. Assume that the production rate, R ij , (R ij \geqq 0; i, j - 1, 2, ..., n) of man i when assigned to job j is: (1) exponentially distributed with mean 1/\lambda ij or (2) Weibull distributed with scale parameter \lambda ij and shape parameter \beta. It is shown that in either case, the assignment that maximizes the expected rate of the entire line is found by solving the deterministic assignment problem with "cost" matrix [\lambda ij ].

Suggested Citation

  • Uri Yechiali, 1968. "Communications to the Editor--A Stochastic Bottleneck Assignment Problem," Management Science, INFORMS, vol. 14(11), pages 732-733, July.
    • Handle: RePEc:inm:ormnsc:v:14:y:1968:i:11:p:732-733
    DOI: 10.1287/mnsc.14.11.732
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    Cited by:

    1. Yelin Fu & Jianshan Sun & K. Lai & John Leung, 2015. "A robust optimization solution to bottleneck generalized assignment problem under uncertainty," Annals of Operations Research, Springer, vol. 233(1), pages 123-133, October.
    2. I. Stancu-Minasian & R. Caballero & E. Cerdá & M. Muñoz, 1999. "The stochastic bottleneck linear programming problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 123-143, June.
    3. 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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