Fenchel and Disjunctive Decomposition for Mean-Risk Stochastic Integer Programs

Mean-risk stochastic integer programs (SIPs) include both expectation and a dispersion statistic in the objective function and are difficult to solve. We derive an integrated Fenchel and disjunctive decomposition method for mean-risk SIPs with fixed recourse for the absolute semideviation mean-risk measure. In this methodology we use subgradient-based optimization to solve the LP-relaxation of the problem. We then generate Fenchel decomposition cuts based on a subset of scenarios and use disjunctive programming to lift and translate the cuts so that they are valid for the rest of the scenarios. Preliminary computational results based on realistic instances will be presented