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A Robust Optimization Perspective on Stochastic Programming

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
NUS Business School, National University of Singapore and Singapore MIT Alliance (SMA), Singapore
Fuqua School of Business, Duke University, Durham, North Carolina 27708
xinchen{at}uiuc.edu
dscsimm{at}nus.edu.sg
psun{at}duke.edu

In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. Using a linear decision rule, we also propose a tractable approximation approach for solving a class of multistage chance-constrained stochastic linear optimization problems. An attractive feature of the framework is that we convert the original model into a second-order cone program, which is computationally tractable both in theory and in practice. We demonstrate the framework through an application of a project management problem with uncertain activity completion time.

Subject classifications: programming; stochastic.
History: Received December 2004; revision received May 2006; accepted December 2006.