Robust and Stochastically Weighted Multiobjective Optimization Models and Reformulations

We introduce and study a family of models for multiexpert multiobjective/criteria decision making. These models use a concept of weight robustness to generate a risk-averse decision. In particular, the multiexpert multicriteria robust weighted sum approach (McRow) introduced in this paper identifies a (robust) Pareto decision that minimizes the worst-case weighted sum of objectives over a given weight region. The corresponding objective value, called the robust value of a decision, is shown to be increasing and concave in the weight set. We study compact reformulations of the McRow model with polyhedral and conic descriptions of the weight regions. The McRow model is developed further for stochastic multiexpert multicriteria decision making by allowing ambiguity or randomness in the weight region as well as the objective functions. The properties of the proposed approach are illustrated with a few textbook examples. The usefulness of the stochastic McRow model is demonstrated using a disaster planning example and an agriculture revenue management example.