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Approximation Formulations for the Single-Product Capacitated Lot Size Problem

Author

Listed:
  • Gabriel R. Bitran

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Hirofumi Matsuo

    (University of Texas, Austin, Texas)

Abstract

We consider two approximation formulations for the single-product capacitated lot size problem. One formulation restricts the number of production policies and the other rounds demands up to multiples of a constant. After briefly reviewing the literature within a new framework, we discuss the relations between these approximation formulations. Next, we provide relative error bounds and algorithms for solving the approximation problems. We demonstrate that these approximation formulations require a significantly smaller number of calculations than the original formulation, and that the relative error bounds are satisfactory for practical purposes.

Suggested Citation

  • Gabriel R. Bitran & Hirofumi Matsuo, 1986. "Approximation Formulations for the Single-Product Capacitated Lot Size Problem," Operations Research, INFORMS, vol. 34(1), pages 63-74, February.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:1:p:63-74
    DOI: 10.1287/opre.34.1.63
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    Citations

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    Cited by:

    1. Drexl, Andreas & Kimms, Alf, 1996. "Lot sizing and scheduling: Survey and extensions," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 421, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Hoesel C.P.M. van & Wagelmans A.P.M., 1997. "Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Chubanov, Sergei & Kovalyov, Mikhail Y. & Pesch, Erwin, 2008. "A single-item economic lot-sizing problem with a non-uniform resource: Approximation," European Journal of Operational Research, Elsevier, vol. 189(3), pages 877-889, September.
    4. Ng, C.T. & Kovalyov, Mikhail Y. & Cheng, T.C.E., 2010. "A simple FPTAS for a single-item capacitated economic lot-sizing problem with a monotone cost structure," European Journal of Operational Research, Elsevier, vol. 200(2), pages 621-624, January.
    5. van Hoesel, C.P.M. & Wagelmans, A.P.M., 1997. "Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems," Econometric Institute Research Papers EI 9735/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Rita Vachani, 1992. "Performance of heuristics for the uncapacitated lot‐size problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(6), pages 801-813, October.
    7. Kimms, Alf, 1996. "Improved lower bounds for the proportional lot sizing and scheduling problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 414, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    8. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    9. van Hoesel, C.P.M. & Wagelmans, A., 1997. "Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems," Research Memorandum 029, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Kimms, Alf, 1998. "Short-term management of lot production," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 480, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    11. C. P. M. van Hoesel & A. P. M. Wagelmans, 2001. "Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 339-357, May.
    12. Jian Yang & Boaz Golany & Gang Yu, 2005. "A concave‐cost production planning problem with remanufacturing options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 443-458, August.
    13. Chung-Lun Li & Vernon Ning Hsu & Wen-Qiang Xiao, 2004. "Dynamic Lot Sizing with Batch Ordering and Truckload Discounts," Operations Research, INFORMS, vol. 52(4), pages 639-654, August.

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