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A Fully Polynomial Approximation Scheme for Single-Product Scheduling in a Finite Capacity Facility

Author

Listed:
  • Bezalel Gavish

    (Vanderbilt University, Nashville, Tennessee)

  • Robert E. Johnson

    (Pennsylvania State University, University Park, Pennsylvania)

Abstract

This paper considers a version of the economic lot sizing problem for a single product produced in a facility of finite capacity over a finite time horizon with specifiable start and end conditions. A set of algorithms is presented that will approximate the optimal production schedule to a given allowable error (ε). Algorithms with computation time bounds of O (1/ε 2 ) are presented which allow for setups of finite length, setups with or without direct cash flow, quite general cost and demand functions, and a wide variety of production policy constraints. The procedures make no a priori assumptions about the form of the optimal solution. Numerical results are included.

Suggested Citation

  • Bezalel Gavish & Robert E. Johnson, 1990. "A Fully Polynomial Approximation Scheme for Single-Product Scheduling in a Finite Capacity Facility," Operations Research, INFORMS, vol. 38(1), pages 70-83, February.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:1:p:70-83
    DOI: 10.1287/opre.38.1.70
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Sarker, Bhaba R. & Diponegoro, Ahmad, 2009. "Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers," European Journal of Operational Research, Elsevier, vol. 194(3), pages 753-773, May.
    4. 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.
    5. Awi Federgruen & Joern Meissner & Michal Tzur, 2007. "Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 55(3), pages 490-502, June.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
    10. 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).
    11. Süral, Haldun & Denizel, Meltem & Van Wassenhove, Luk N., 2009. "Lagrangean relaxation based heuristics for lot sizing with setup times," European Journal of Operational Research, Elsevier, vol. 194(1), pages 51-63, April.
    12. Brahimi, Nadjib & Dauzere-Peres, Stephane & Najid, Najib M. & Nordli, Atle, 2006. "Single item lot sizing problems," European Journal of Operational Research, Elsevier, vol. 168(1), pages 1-16, January.

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