Multistage adaptive stochastic mixed integer optimization through piecewise decision rule approximation

Abstract

This work studies the multistage adaptive stochastic mixed integer optimization problem, where the aim is to find adaptive continuous and integer decision policies that optimize the expected objective. While searching for the exact optimal policy is challenging, piecewise decision rule-based solution framework is studied and two types of strategies are compared: uncertainty set partitioning and uncertainty lifting. Adaptive binary and continuous decisions are approximated through piecewise constant and affine decision rule, respectively. The original optimization problem is solved through robust counterpart optimization technique. The proposed methods are applied to an inventory control problem and a chemical process capacity planning problem. Results show that the two methods provide flexible options with the trade-off between solution quality and computational efficiency. The uncertainty set partitioning based method leads to better solution quality and is appropriate to small-scale problems. On the other hand, the lifting method provides significant computational efficiency especially for large problems.