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Remarks on: "Some Extensions of the Discrete Lotsizing and Scheduling Problem"

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  • Wolfgang Bruggemann

    (Institut fur Logistik und Transport, Universitat Hamburg, 20146 Hamburg, Germany)

  • Hermann Jahnke

    (Wirtschaftswissenschaftliche Fakultat, Universitat Bielefeld, 33615 Bielefeld, Germany)

Abstract

Saloman et al. (Salomon, M., L. G. Kroon, R. Kuik, L. N. Van Wassenhove. 1991. Some extensions of the discrete lotsizing and scheduling problem. Management Sci. 37 801--812.) claim the NP-completeness of different variants of the discrete lot-sizing and scheduling problem (DLSP) which are differentiated by using a six-field notation. However, some of the given proofs are incorrect because the transformations employed map certain data values of the preimage problem to the number of data in the resulting instance and are hence not polynomial. As an example, we concentrate here on the 1/*/SI/G/A-optimization problem (Salomon et al. [Salomon, M., L. G. Kroon, R. Kuik, L. N. Van Wassenhove. 1991. Some extensions of the discrete lotsizing and scheduling problem. Management Sci. 37 801--812.], Theorem 3). Similar arguments pertain to the 1/*/A/G/SI-DLSP, too.

Suggested Citation

  • Wolfgang Bruggemann & Hermann Jahnke, 1997. "Remarks on: "Some Extensions of the Discrete Lotsizing and Scheduling Problem"," Management Science, INFORMS, vol. 43(1), pages 122-122, January.
    • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:1:p:122-122
    DOI: 10.1287/mnsc.43.1.122
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    Cited by:

    1. Bruggemann, Wolfgang & Jahnke, Hermann, 2000. "The discrete lot-sizing and scheduling problem: Complexity and modification for batch availability," European Journal of Operational Research, Elsevier, vol. 124(3), pages 511-528, August.
    2. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.

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