An approximation framework for two-stage ambiguous stochastic integer programs under mean-MAD information

Abstract

We consider two-stage recourse models in which only limited information is available on the probability distributions of the random parameters in the model. If all decision variables are continuous, then we are able to derive the worst-case and best-case probability distributions under the assumption that only the means and mean absolute deviations of the random parameters are known. Contrary to most existing results in the literature, these probability distributions are the same for every first-stage decision. The ambiguity set that we use in this paper also turns out to be particularly suitable for ambiguous recourse models involving integer decisions variables. For such problems, we develop a general approximation framework and derive error bounds for using these approximatons. We apply this approximation framework to mixed-ambiguous mixed-integer recourse models in which some of the probability distributions of the random parameters are known and others are ambiguous. To illustrate these results we carry out numerical experiments on a surgery block allocation problem.