Simultaneous incorporation of flexibility and economic risk in operational planning under uncertainty

Abstract

In this paper, an integrated metric is introduced with which future plan feasibility together with the potential economic risk is assessed for two-period linear planning models. It is based on the concepts of flexibility, the ability of handling uncertainty while meeting production requirements, and maximum regret, the maximum potential economic loss involved in the implementation of a plan in the face of uncertainty. An algorithmic procedure is proposed for the estimation of such a combined metric. It involves the solution of two multiparametric linear programming subproblems for the evaluation of maximum regret, with which analytical expressions of the regret as a function of the uncertain parameters and the plan are obtained. These expressions are then incorporated in a mixed-integer index programming formulation for the evaluation of a combined flexibility-regret index. In this way, trade-offs between plan flexibility and economics are established. The incorporation of these analytical tools into an overall planning framework is also shown and illustrated with example problems.