Multistage robust mixed-integer optimization under endogenous uncertainty

Wei Feng, Yiping Feng, Qi Zhang

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)460-475
Number of pages16
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - Oct 16 2021

Bibliographical note

Funding Information:
We gratefully acknowledge financial support from the National Key Research and Development Program of China (No. 2019YFB1705004 ), Science Fund for Creative Research Groups of NSFC (No. 61621002 ), and China Scholarship Council (CSC) (No. 201906320317 ).

Publisher Copyright:
© 2021 Elsevier B.V.


  • Decision rules
  • Endogenous uncertainty
  • Mixed-integer recourse
  • Multistage robust optimization


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