Multistage robust mixed-integer optimization under endogenous uncertainty

•Adjustable robust optimization with decision-dependent polyhedral uncertainty sets.•Two-stage and multistage settings with both continuous and binary recourse.•Uncertainty set may be affected by binary recourse decisions in every stage.•Tractable approximations derived using a nonlinear decision ru...

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Veröffentlicht in:European journal of operational research Jg. 294; H. 2; S. 460 - 475
Hauptverfasser: Feng, Wei, Feng, Yiping, Zhang, Qi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 16.10.2021
Schlagworte:
Decision rules
Endogenous uncertainty
Mixed-integer recourse
Multistage robust optimization
Decision rules
Multistage robust optimization
Endogenous uncertainty
Mixed-integer recourse
ISSN:0377-2217, 1872-6860
Online-Zugang:Volltext
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Zusammenfassung:•Adjustable robust optimization with decision-dependent polyhedral uncertainty sets.•Two-stage and multistage settings with both continuous and binary recourse.•Uncertainty set may be affected by binary recourse decisions in every stage.•Tractable approximations derived using a nonlinear decision rule approach.•Results highlight benefit from endogenous uncertainty and mixed-integer recourse. 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2021.01.048