Robust solutions of uncertain linear programs

Authors:
A. Ben-Tal;A. Nemirovski
Affiliations:
Technion-Israel Institute of Technology, Faculty of Industrial Engineering and Management, Technion City, 32000 Haifa, Israel;Technion-Israel Institute of Technology, Faculty of Industrial Engineering and Management, Technion City, 32000 Haifa, Israel
Venue:
Operations Research Letters
Year:
1999

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Abstract

We treat in this paper linear programming (LP) problems with uncertain data. The focus is on uncertainty associated with hard constraints: those which must be satisfied, whatever is the actual realization of the data (within a prescribed uncertainty set). We suggest a modeling methodology whereas an uncertain LP is replaced by its robust counterpart (RC). We then develop the analytical and computational optimization tools to obtain robust solutions of an uncertain LP problem via solving the corresponding explicitly stated convex RC program. In particular, it is shown that the RC of an LP with ellipsoidal uncertainty set is computationally tractable, since it leads to a conic quadratic program, which can be solved in polynomial time.