An SDP approach for multiperiod mixed 0-1 linear programming models with stochastic dominance constraints for risk management

In this paper we consider multiperiod mixed 0–1 linear programming models underuncertainty. We propose a risk averse strategy using stochastic dominance con-straints (SDC) induced by mixed-integer linear recourse as the risk measure. TheSDC strategy extends the existing literature to the multistage case and includesboth first-order and second-order constraints. We propose a stochastic dynamicprogramming (SDP) solution approach, where one has to overcome the negativeimpact the cross-scenario constraints, due to SDC, have on the decomposability ofthe model. In our computational experience we compare our SDP against a com-mercial optimization package, in terms of solution accuracy and elapsed time. Weuse supply chain planning instances, where procurement, production, inventory, anddistribution decisions need to be made under demand uncertainty. We confirm thehardness of the testbed, where the benchmark cannot find a feasible solution for halfof the test instances while we always find one, and show the appealing tradeoff ofSDP, in terms of solution accuracy and elapsed time, when solving medium-to-largeinstances.This research has been partially supported by the grants MTM2009-14087-C04-01 from the SpanishMinistry of Science and Innovation and Risk Management from Comunidad de Madrid, Spain.