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Optimization-Based Scenario Reduction for Data-Driven Two-Stage Stochastic Optimization

Author

Listed:
  • Dimitris Bertsimas

    (Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

  • Nishanth Mundru

    (Benefits Science Technologies, Needham, Massachusetts 02494)

Abstract

We propose a novel, optimization-based method that takes into account the objective and problem structure for reducing the number of scenarios, m , needed for solving two-stage stochastic optimization problems. We develop a corresponding convex optimization-based algorithm and show that, as the number of scenarios increase, the proposed method recovers the SAA solution. We report computational results with both synthetic and real-world data sets that show that the proposed method has significantly better performance for m = 1 − 2 % of n in relation to other state of the art methods (importance sampling, Monte Carlo sampling, and Wasserstein scenario reduction with squared Euclidean norm). Additionally, we propose variants of classical scenario reduction algorithms (which rely on the Euclidean norm) and show that these variants consistently outperform their traditional versions.

Suggested Citation

  • Dimitris Bertsimas & Nishanth Mundru, 2023. "Optimization-Based Scenario Reduction for Data-Driven Two-Stage Stochastic Optimization," Operations Research, INFORMS, vol. 71(4), pages 1343-1361, July.
    • Handle: RePEc:inm:oropre:v:71:y:2023:i:4:p:1343-1361
    DOI: 10.1287/opre.2022.2265
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