Multistage robust mixed-integer optimization under endogenous uncertainty

A B S T R A C T Endogenous, i.e. decision-dependent, uncertainty has received increased interest in the stochastic programming community. In the robust optimization context, however, it has rarely been considered. This work addresses multistage robust mixed-integer optimization with decision-dependent uncertainty sets. The proposed framework allows us to consider both continuous and integer recourse, including recourse decisions that affect the uncertainty set. We derive a tractable reformulation of the problem by leveraging recent advances in the construction of nonlinear decision rules, and introduce discontinuous piecewise linear decision rules for continuous recourse. Computational experiments are performed to gain insights on the impact of endogenous uncertainty, the benefit of discrete recourse, and computational performance. Our results indicate that the level of conservatism in the solution can be significantly reduced if endogenous uncertainty and mixed-integer recourse are properly modeled. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study addresses multistage robust mixed-integer optimization with decision-dependent uncertainty sets, proposing a framework that allows consideration of both continuous and integer recourse. By leveraging recent advances in constructing nonlinear decision rules and introducing discontinuous piecewise linear decision rules for continuous recourse, the authors derive a tractable reformulation of the problem. Computational experiments show that properly modeling endogenous uncertainty and mixed-integer recourse can significantly reduce the conservatism in the solution.