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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. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    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. 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.
    13. 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.

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