Stage-t scenario dominance for risk-averse multi-stage stochastic mixed-integer programs

Abstract This paper presents a new and general approach, named “Stage- t Scenario Dominance,” to solve the risk-averse multi-stage stochastic mixed-integer programs (M-SMIPs). Given monotonic objective function, our method derives partial ordering of scenarios by pairwise comparing realization uncertain parameters at each time stage under scenario. Specifically, we derive bounds implications from Dominance” using solving subset individual scenario sub-problems up . Using these inferences, generate cutting planes tackle computational difficulty M-SMIPs. We also results on minimum number scenario-dominance relations generated. demonstrate use this methodology version mean-conditional value-at-risk (CVaR) dynamic knapsack problem. Our experiments address those instances that have uncertainty, which correspond objective, left-hand side, right-hand side parameters. Computational show “scenario dominance"-based can reduce solution for mean-risk, stochastic, multi-stage, multi-dimensional problems with both integer continuous variables, whose structure is similar mean-risk M-SMIPs, varying risk characteristics one-to-two orders magnitude numbers random variables in stage. strong dominance cuts perform well ten stage, ninety total. The proposed framework be applied wide range risk-neutral M-SMIP problems.