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Mathematical Programming manuscript No. (will be inserted by the editor)

Summary: Mathematical Programming manuscript No.
(will be inserted by the editor)
Samer Takriti Shabbir Ahmed
On Robust Optimization of Two-Stage Systems
Received: date / Revised version: date
Abstract. 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 ap-
proach 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 lin-
ear programs. We apply the proposed framework to standard stochastic-programming test
problems and to an application that arises in auctioning excess electric power.
Key words. Stochastic Programming, Robust Optimization, Decomposition
Methods, Risk Modeling, Utility Theory
Samer Takriti: Corresponding Author. Mathematical Sciences Department, IBM T.J. Wat-
son Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA, e-mail:


Source: Ahmed, Shabbir - School of Industrial and Systems Engineering, Georgia Institute of Technology


Collections: Engineering