On highly robust efficient solutions to uncertain multiobjective linear programs

摘要

Decision making in the presence of uncertainty and multiple conflicting objectives is a real-life issue in many areas of human activity. To address this type of problem, we study highly robust (weakly) efficient solutions to uncertain multiobjective linear programs (UMOLPs) with objective-wise uncertainty in the objective function coefficients. We develop properties of the highly robust efficient set, characterize highly robust (weakly) efficient solutions using the cone of improving directions associated with the UMOLP, derive several upper and lower bound sets on the highly robust (weakly) efficient set, and present a robust counterpart for a class of UMOLPs. As various results rely on the acuteness of the cone of improving directions, we also propose methods to verify this property. (C) 2018 Elsevier B.V. All rights reserved.