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Linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management

Author

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  • Amir Ardestani-Jaafari

    (Faculty of Management, University of British Columbia, Kelowna, British Columbia V1V 1V7, Canada)

  • Erick Delage

    (Department of Decision Sciences, HEC Montréal, Montréal, Québec H3T 2A7, Canada; Group for Research in Decision Analysis (GERAD), Montreal, Quebec H3T 1J4, Canada)

Abstract

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method mainly relies on a linearization scheme employed in bilinear programming; therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

Suggested Citation

  • Amir Ardestani-Jaafari & Erick Delage, 2021. "Linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1138-1161, July.
    • Handle: RePEc:inm:orijoc:v:33:y:2021:i:3:p:1138-1161
    DOI: 10.1287/ijoc.2020.0959
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    References listed on IDEAS

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    Cited by:

    1. Jianzhe Zhen & Ahmadreza Marandi & Danique de Moor & Dick den Hertog & Lieven Vandenberghe, 2022. "Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2410-2427, September.

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