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Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
xinchen{at}illinois.edu
yzhang30{at}illinois.edu

In this paper, we introduce the extended affinely adjustable robust counterpart to modeling and solving multistage uncertain linear programs with fixed recourse. Our approach first reparameterizes the primitive uncertainties and then applies the affinely adjustable robust counterpart proposed in the literature, in which recourse decisions are restricted to be linear in terms of the primitive uncertainties. We propose a special case of the extended affinely adjustable robust counterpart—the splitting-based extended affinely adjustable robust counterpart—and illustrate both theoretically and computationally that the potential of the affinely adjustable robust counterpart method is well beyond the one presented in the literature. Similar to the affinely adjustable robust counterpart, our approach ends up with deterministic optimization formulations that are tractable and scalable to multistage problems.

Subject classifications: programming; stochastic.
History: Received March 2007; revision received January 2008; accepted March 2008.

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