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A note on robust 0-1 optimization with uncertain cost coefficients. (English) Zbl 1112.90050

Summary: Based on the recent approach of D. Bertsimas and M. Sim [Math. Program. 98, No. 1-3 (B), 49–71 (2003; Zbl 1082.90067), with D. Pachamanova, Oper. Res. Lett. 32, No. 6, 510–516 (2004; Zbl 1054.90046)] to robust optimization in the presence of data uncertainty, we prove an easily computable and simple bound on the probability that the robust solution gives an objective function value worse than the robust objective function value, under the assumption that only cost coefficients are subject to uncertainty. We exploit the binary nature of the optimization problem in proving our results. A discussion on the cost of ignoring uncertainty is also included.

MSC:

90C09 Boolean programming
90C15 Stochastic programming
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