Robust and Stochastically Weighted Multiobjective Optimization Models and Reformulations

We introduce and study a family of models for multi-expert multi-objective/criteria decision making. These models use a concept of weight robustness to generate a risk averse decision. In particular, the multi-expert multi-criteria robust weighted sum approach (McRow) introduced in this paper identifies a (robust) Pareto optimum 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. Compact reformulations of the models with polyhedral and conic descriptions of the weight regions. The McRow model is developed further for stochastic multi-expert multi-criteria decision making by allowing ambiguity or randomness in the weight region as well as the objective functions. The properties of the proposed approach is illustrated with a few examples. The usefulness of the stochastic (McRow) model is demonstrated using a disaster planning example and an agriculture revenue management example.