Applying the minimax criterion in stochastic recourse programs

Abstract

We consider an optimization problem in which some uncertain parmeters are replaced by random variables. The minimax approach to stochastic programming concerns the problem of minimizing the worst expected value of the objective function with respect to the set of probability measures that are consistent with the available information on random data. Only very few practicable solution procedures have been proposed for this problem and the existing ones rely on simplifying assumptions. In this paper, we establish a number of stability results for the minimax stochastic program, justifying in particular the approach of restricting attention to probability measures with support in some unknown finite set. Following this approach, we elaborate solution procedures for the minimax problem in the setting of two-stage stochastic recourse models, considering the linear recourse case as well as the integer recourse case. Since the solution procedures are modifications of well-known algorithms, their efficacy is immediate from the computational testing of these procedures and we do not report results of any computational experiments.