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

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