An exact solution approach for risk-averse mixed-integer multi-stage stochastic programming problems

Abstract

Risk-averse mixed-integer multi-stage stochastic programming problems are challenging, large scale and non-convex optimization problems. In this study, we propose an exact solution algorithm for a type of these problems with an objective of dynamic mean-CVaR risk measure and binary first stage decision variables. The proposed algorithm is based on an evaluate-and-cut procedure and uses lower bounds obtained from a scenario tree decomposition method called as group subproblem approach. We also show that, under the assumption that the first stage integer variables are bounded, our algorithm solves problems with mixed-integer variables in all stages. Computational experiments on risk-averse multi-stage stochastic server location and generation expansion problems reveal that the proposed algorithm is able to solve problem instances with more than one million binary variables within a reasonable time under a modest computational setting.