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Reducing the 0-1 Knapsack Problem with a Single Continuous Variable to the Standard 0-1 Knapsack Problem

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  • Marcel Büther

    (Christian-Albrechts-Universität zu Kiel, Germany)

  • Dirk Briskorn

    (Universität zu Köln, Germany)

Abstract

The 0-1 knapsack problem with a single continuous variable (KPC) is a natural extension of the binary knapsack problem (KP), where the capacity is not any longer fixed but can be extended which is expressed by a continuous variable. This variable might be unbounded or restricted by a lower or upper bound, respectively. This paper concerns techniques in order to reduce several variants of KPC to KP which enables the authors to employ approaches for KP. The authors propose both, an equivalent reformulation and a heuristic one bringing along less computational effort. The authors show that the heuristic reformulation can be customized in order to provide solutions having an objective value arbitrarily close to the one of the original problem.

Suggested Citation

  • Marcel Büther & Dirk Briskorn, 2012. "Reducing the 0-1 Knapsack Problem with a Single Continuous Variable to the Standard 0-1 Knapsack Problem," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 3(1), pages 1-12, January.
    • Handle: RePEc:igg:joris0:v:3:y:2012:i:1:p:1-12
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    Cited by:

    1. Jiyoung Choi & Chungmok Lee & Sungsoo Park, 2018. "Dantzig–Wolfe decomposition approach to the vehicle assignment problem with demand uncertainty in a hybrid hub-and-spoke network," Annals of Operations Research, Springer, vol. 264(1), pages 57-87, May.
    2. Jimyung Kang & Jee-Hyong Lee, 2017. "Data-Driven Optimization of Incentive-based Demand Response System with Uncertain Responses of Customers," Energies, MDPI, vol. 10(10), pages 1-17, October.

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