Determinism Versus Uncertainty: Examining the Worst-Case Expected Performance of Data-Driven Policies

Xuecheng Tian, Shuaian Wang, Gilbert Laporte, Ying Yang

Research output: Contribution to journalArticlepeer-review

Abstract

This paper explores binary decision making, a critical domain in areas such as finance and supply chain management, where decision makers must often choose between a deterministic-cost option and an uncertain-cost option. Given the limited historical data on the uncertain cost and its unknown probability distribution, this research aims to ascertain how decision makers can optimize their decisions. To this end, we evaluate the worst-case expected performance of all possible data-driven policies, including the sample average approximation policy, across four scenarios differentiated by the extent of knowledge regarding the lower and upper bounds of the first moment of the uncertain cost distribution. Our analysis, using worst-case expected absolute regret and worst-case expected relative regret metrics, consistently shows that no data-driven policy outperforms the straightforward strategy of choosing either a deterministic-cost or uncertain-cost option in these scenarios. Notably, the optimal choice between these two options depends on the specific lower and upper bounds of the first moment. Our research contributes to the literature by revealing the minimal worst-case expected performance of all possible data-driven policies for binary decision-making problems.

Original languageEnglish
JournalEuropean Journal of Operational Research
Early online date27 Apr 2024
DOIs
Publication statusE-pub ahead of print - 27 Apr 2024

Acknowledgements

Thanks are due to the editor and the referees for their valuable comments.

Keywords

  • Data-driven optimization
  • Decision analysis
  • Sample average approximation
  • Worst-case expected performance

ASJC Scopus subject areas

  • Information Systems and Management
  • General Computer Science
  • Modelling and Simulation
  • Management Science and Operations Research

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