IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v34y1988i3p420-426.html
   My bibliography  Save this article

An O(T 2 ) Algorithm for the NI/G/NI/ND Capacitated Lot Size Problem

Author

Listed:
  • Chia-Shin Chung

    (Department of Quantitative Business Analysis, Cleveland State University, Cleveland, Ohio 44115)

  • Chien-Hua Mike Lin

    (Department of Computer and Information Science, Cleveland State University, Cleveland, Ohio 44115)

Abstract

In this paper, we study a class of the capacitated dynamic lot size problem, where, over time, the setup costs are nonincreasing, the unit holding costs have arbitrary pattern, the unit production costs are nonincreasing and the capacities are nondecreasing. We investigate the properties of the optimal solution for the problem and develop the concept of candidate subplan. It is proven that only the candidate subplans need to be examined in searching for an optimal solution. A dynamic programming algorithm, incorporating the concept of candidate subplan, is then devised which has run time complexity of O(T 2 ).

Suggested Citation

  • Chia-Shin Chung & Chien-Hua Mike Lin, 1988. "An O(T 2 ) Algorithm for the NI/G/NI/ND Capacitated Lot Size Problem," Management Science, INFORMS, vol. 34(3), pages 420-426, March.
  • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:3:p:420-426
    DOI: 10.1287/mnsc.34.3.420
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.34.3.420
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.34.3.420?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Jinwen Ou, 2012. "Economic lot sizing with constant capacities and concave inventory costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(7), pages 497-501, October.
    3. 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.
    4. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2005. "Integrated Lot Sizing in Serial Supply Chains with Production Capacities," Management Science, INFORMS, vol. 51(11), pages 1706-1719, November.
    5. Okhrin, Irena & Richter, Knut, 2011. "An O(T3) algorithm for the capacitated lot sizing problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 211(3), pages 507-514, June.
    6. Berk, Emre & Toy, Ayhan Ozgur & Hazir, Oncu, 2008. "Single item lot-sizing problem for a warm/cold process with immediate lost sales," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1251-1267, June.
    7. 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).
    8. van Hoesel, C.P.M. & Romeijn, H.E. & Romero Morales, M.D. & Wagelmans, A., 2002. "Polynomial time algorithms for some multi-level lot-sizing problems with production capacities," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Hark-Chin Hwang & Wilco van den Heuvel & Albert P. M. Wagelmans, 2023. "Multilevel Lot-Sizing with Inventory Bounds," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1470-1490, November.
    10. Shaw, D.X. & Wagelmans, A.P.M., 1995. "An Algorithm for Single-item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs," Econometric Institute Research Papers EI 9526-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Hwang, Hark-Chin & Kang, Jangha, 2020. "The two-level lot-sizing problem with outbound shipment," Omega, Elsevier, vol. 90(C).

    More about this item

    Keywords

    lot sizing; dynamic programming;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:34:y:1988:i:3:p:420-426. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.