On robust optimization of two-stage systems

Robust-optimization models belong to a special class of stochastic programs, where the traditional expected cost minimization objective is replaced by one that explicitly addresses cost variability. This paper explores robust optimization in the context of two-stage planning systems. We show that, u...

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Bibliographic Details
Published in:Mathematical programming 2004, Vol.99 (1), p.109-126
Main Authors: TAKRITI, Samer, AHMED, Shabbir
Format: Article
Language:English
Subjects:
Applied sciences
Costs
Decision making
Decision theory. Utility theory
Decomposition
Exact sciences and technology
Operational research and scientific management
Operational research. Management science
Optimization
Process planning
Random variables
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Summary:Robust-optimization models belong to a special class of stochastic programs, where the traditional expected cost minimization objective is replaced by one that explicitly addresses cost variability. This paper explores robust optimization in the context of two-stage planning systems. We show that, under arbitrary measures for variability, the robust optimization approach might lead to suboptimal solutions to the second-stage planning problem. As a result, the variability of the second-stage costs may be underestimated, thereby defeating the intended purpose of the model. We propose sufficient conditions on the variability measure to remedy this problem. Under the proposed conditions, a robust optimization model can be efficiently solved using a variant of the L-shaped decomposition algorithm for traditional stochastic linear programs. We apply the proposed framework to standard stochastic-programming test problems and to an application that arises in auctioning excess electric power.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-003-0373-y