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On Robust Optimization of Two-Stage Systems

Samer Takriti (takriti***at***us.ibm.com)
Shabbir Ahmed (sahmed***at***isye.gatech.edu)

Abstract: Robust optimization extends stochastic programming models by incorporating measures of variability into the objective function. This paper explores robust optimization in the context of two-stage planning systems. First, we propose the use of a generalized Benders decomposition algorithm for solving robust models. Next, we argue that using an arbitrary measure for variability can lead to sub-optimal second-stage decisions. To overcome this drawback, we propose a sufficient condition on the variability measure to preserve second-stage optimality. Under this condition, a modification of the L-shaped decomposition method solves the robust formulation efficiently.

Keywords: Stochastic Programming, Robust Optimization, Decision making under Uncertainty

Category 1: Stochastic Programming

Category 2: Robust Optimization

Category 3: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: To appear in Mathematical Programming, 2003

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Entry Submitted: 02/21/2001
Entry Accepted: 02/21/2001
Entry Last Modified: 06/09/2003

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