Communications to the Editor—A Stochastic Bottleneck Assignment Problem

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].