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K-Adaptability in Two-Stage Robust Binary Programming

Grani A. Hanasusanto¹; Daniel Kuhn²; Wolfram Wiesemann³

¹ Department of Computing, Imperial College London, London SW7 2AZ, United Kingdom · ² Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland · ³ Imperial College Business School, Imperial College London, London SW7 2AZ, United Kingdom

Over the last two decades, robust optimization has emerged as a computationally attractive approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multistage problems with continuous recourse. This paper takes a step toward extending the robust optimization methodology to problems with integer recourse, which have largely resisted solution so far. To this end, we approximate two-stage robust binary programs by their corresponding K-adaptability problems, in which the decision maker precommits to K second-stage policies, here -and-now, and implements the best of these policies once the uncertain parameters are observed. We study the approximation quality and the computational complexity of the K-adaptability problem, and we propose two mixed-integer linear programming reformulations that can be solved with off-the-shelf software. We demonstrate the effectiveness of our reformulations for stylized instances of supply chain design, route planning, and capital budgeting problems.

DOI

10.1287/opre.2015.1392

Volume

63 (4)

Pages

877-891

Language

en

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Sources

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