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

Amir Ardestani-Jaafari () and Erick Delage ()
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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

INFORMS Journal on Computing, 2021, vol. 33, issue 3, 1138-1161

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.

Keywords: two-stage adjustable robust optimization; affinely adjustable robust counterpart; linear programming relaxation; bilinear programming (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:33:y:2021:i:3:p:1138-1161

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