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Exact and heuristic solution approaches for the mixed integer setup knapsack problem

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  • Altay, Nezih
  • Robinson Jr., Powell E.
  • Bretthauer, Kurt M.

Abstract

We consider a class of knapsack problems that include setup costs for families of items. An individual item can be loaded into the knapsack only if a setup cost is incurred for the family to which it belongs. A mixed integer programming formulation for the problem is provided along with exact and heuristic solution methods. The exact algorithm uses cross decomposition. The proposed heuristic gives fast and tight bounds. In addition, a Benders decomposition algorithm is presented to solve the continuous relaxation of the problem. This method for solving the continuous relaxation can be used to improve the performance of a branch and bound algorithm for solving the integer problem. Computational performance of the algorithms are reported and compared to CPLEX.

Suggested Citation

  • Altay, Nezih & Robinson Jr., Powell E. & Bretthauer, Kurt M., 2008. "Exact and heuristic solution approaches for the mixed integer setup knapsack problem," European Journal of Operational Research, Elsevier, vol. 190(3), pages 598-609, November.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:3:p:598-609
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    References listed on IDEAS

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    1. Akinc, Umit, 2006. "Approximate and exact algorithms for the fixed-charge knapsack problem," European Journal of Operational Research, Elsevier, vol. 170(2), pages 363-375, April.
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    5. VAN ROY, Tony J., 1983. "Cross decomposition for mixed integer programming," LIDAM Reprints CORE 496, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Ali, Agha Iqbal & O'Connor, Debra J., 2010. "The impact of distribution system characteristics on computational tractability," European Journal of Operational Research, Elsevier, vol. 200(2), pages 323-333, January.

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