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Sensitivity analysis of the knapsack problem: Tighter lower and upper bound limits

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An Erratum to this article was published on 17 December 2008

Abstract

In this paper, we study the sensitivity of the optimum of the knapsack problem to the perturbation of the profit of a subset of items. We propose a polynomial heuristic in order to establish both lower and upper bound limits of the sensitivity interval. The aim is to stabilize any given optimal solution obtained by applying any exact algorithm. We then evaluate the effectiveness of the proposed solution procedure on an example and a set of randomly generated problem instances.

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References

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Author information

Authors and Affiliations

  1. CES-CNRS UMR 8174, Equipe CERMSEM, Université Paris 1 Panthon-Sorbonne, 106-112, Boulevard de l’Hôpital, 75647, Paris cedex 13, France

    Tarik Belgacem

  2. MIS, Axis: Discrete Optimization and Re-optimization, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039, Amiens cedex 01, France

    Mhand Hifi

Authors
  1. Tarik Belgacem
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  2. Mhand Hifi
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Corresponding author

Correspondence to Mhand Hifi.

Additional information

The original version was presented on ICSSSM’06. The authors are listed in alphabetical order.

Mhand Hifi is Professor of Computer Science and Operations Research in the University of Picardie Jules Verne, Amiens, France. He got his B.S. in Computer Engineering and Operations Research from USTHB, Algiers, Algeria. He got his M.S. in Modelling and Mathematical Methods in Economics from the University of Paris 1 Pantheon-Sorbonne. He got his Ph.D. in Computer Science from the University of Paris 1 and his HDR thesis from the University of Versailles St Quentin en Yvelines. His research interest is NP Hard combinatorial optimization (sequential and parallel approaches) applied to cutting, packing, knapsacking and other OR problems.

Tarik Belgacem got his PhD in Computer Science from the University of Paris 1 Pantheon-Sorbonne. He received his B.S. in Mathematics at the University of Mostaganem, Algeria. He got his M.S. in Discrete Mathematics and Computer Science from the University of Paris 1 Panteon-Sorbonne. His research interest is Combinatorial Optimization.

An erratum to this article can be found online at http://dx.doi.org/10.1007/s11518-008-5089-3.

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Belgacem, T., Hifi, M. Sensitivity analysis of the knapsack problem: Tighter lower and upper bound limits. J. Syst. Sci. Syst. Eng. 17, 156–170 (2008). https://doi.org/10.1007/s11518-008-5073-y

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  • DOI: https://doi.org/10.1007/s11518-008-5073-y

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