The minimax approach to stochastic programming and an illustrative application

Abstract

The minimax approach to stochastic programming with recourse deals with the case of incomplete knowledge of the distribution F of the random coefficients. It leads to the deterministic program [ILM0001] where x is a given set of admissible solutions, φis a recourse function and f is a given set of distributions. To express the objective function of (*) in a form suitable for further computation, general results on the moment problem can be used.In section 1, the main ideas are briefly surveyed. Subsequently, the method is applied to (*) in section 2. It is shown how the results can be used both to draw conclusions on robustness of the optimal value of the given stochastic program with respect to the set of distributions considered, and to study sensitivity of the optimal solution with respect to a specified distribution. In section 3, an application to a stochastic model of a water resource system with incomplete knowledge about the distribution of the random demand is suggested