Cover Inequalities for the Robust Knapsack Problem

  • Published : 2008.05.31

Abstract

Robust knapsack problem appears when dealing with data uncertainty on the knapsack constraint. This note presents a generalization of the cover inequality for the problem with its lifting procedure. Specifically, we show that the lifting can be done in a polynomial time as in the usual knapsack problem. The results can serve as a building block in devising an efficient branch-and-cut algorithm for the general robust (0, 1) IP problem.

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References

  1. E. Balas, Disjunctive Programming. Anal. Disc. Math. 5 (1979), 3-51 https://doi.org/10.1016/S0167-5060(08)70342-X
  2. D. Bertsimas and M. Sim, Robust Discrete Optimization and Network Flows, Mathematical Programming (Ser. B) 98 (2003) 49-71 https://doi.org/10.1007/s10107-003-0396-4
  3. D. Bertsimas and M. Sim, "The Price of Robustness," Operations Research 52, 1 (2004), 35-53 https://doi.org/10.1287/opre.1030.0065
  4. Nemhauser, G. L. and L. A. Wolsey, Integer and Combinatorial Optimization, John Wiley and Sons 1999