2020/08/26 by Wei Feng, Feng, Wei, Yiping Feng +3 · 1 citation
Decision Sciences · Engineering · Mathematics · #FOS: Mathematics #Fuzzy Systems and Optimization #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2008.11633
openalex publication_date 2020/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.