Communications to the Editor—A Stochastic Bottleneck Assignment Problem

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 ≧ 0; i , j = 1, 2, …, n ) of man i when assigned to job j is: (1) exponentially distributed with mean 1/ λ ij or (2) Weibull distributed with scale parameter λ ij and shape parameter β . 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 [ λ ij ].