Inequity-averse stochastic decision processes

Abstract

The paper extends two alternative approaches in inequity-averse optimization under uncertainty, the ex-ante approach and the ex-post approach, from a static to a dynamic decision making context. This is done by developing a stochastic multistage optimization framework evaluating payoffs by an equitable aggregation function. It is shown that global optimization of strategies leads to time-consistent policies only in the ex-post case. For the ex-ante case, a variant of a policy for which time consistency holds is proposed. To illustrate the concepts, a two-stage stochastic location–allocation problem from humanitarian logistics is investigated. For this application, the general algorithmic approaches can be cast into mathematical programming formulations, which yields a two-stage stochastic program and a bilevel program in the ex-post and in the ex-ante case, respectively. The resulting models are solved to optimality for a set of randomly generated instances, and a comparison of the outcomes for ex-post and ex-ante, also in terms of the “Price of Fairness”, is given.