IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v36y1988i1p50-56.html
   My bibliography  Save this article

A Dynamic Programming Solution to the Dynamic, Multi-Item, Single-Machine Scheduling Problem

Author

Listed:
  • André Gascon

    (Université Laval, Québec, Canada)

  • Robert C. Leachman

    (University of California, Berkeley, California)

Abstract

This article presents a dynamic programming algorithm for scheduling, on a single machine, production of multiple items with time-varying deterministic demands. We formulate the scheduling problem with the objective of minimizing the sum of changeover and inventory holding costs. The formulation is appealing in that it represents changeover costs directly instead of by the familiar approximate technique of including setup costs in the objective. Our algorithm, which we developed using an approach similar to C. R. Glassey's that minimizes the total number of changeovers, casts the optimal schedule as a shortest path through a network embedded in a state space. It generates optimal schedules under two assumptions. First, we assume that in each time period within the planning horizon, the machine must either be shut down or be producing some one item for the entire time period. Second, we assume that inventory holding costs are representable as a nondecreasing function of aggregate inventory. We provide a number of numerical examples that we solved using the algorithm.

Suggested Citation

  • André Gascon & Robert C. Leachman, 1988. "A Dynamic Programming Solution to the Dynamic, Multi-Item, Single-Machine Scheduling Problem," Operations Research, INFORMS, vol. 36(1), pages 50-56, February.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:1:p:50-56
    DOI: 10.1287/opre.36.1.50
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.36.1.50
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.36.1.50?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. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    2. Olivér Ősz & Balázs Ferenczi & Máté Hegyháti, 2020. "Scheduling a forge with due dates and die deterioration," Annals of Operations Research, Springer, vol. 285(1), pages 353-367, February.
    3. Drexl, Andreas & Haase, Knut, 1995. "Proportional lotsizing and scheduling," International Journal of Production Economics, Elsevier, vol. 40(1), pages 73-87, June.
    4. Deng, Qichen & Santos, Bruno F. & Curran, Richard, 2020. "A practical dynamic programming based methodology for aircraft maintenance check scheduling optimization," European Journal of Operational Research, Elsevier, vol. 281(2), pages 256-273.
    5. Drexl, Andreas & Haase, Knut, 1992. "A new type of model for multi-item capacitated dynamic lotsizing and scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 286, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    6. Milind Dawande & Srinagesh Gavirneni & Yinping Mu & Suresh Sethi & Chelliah Sriskandarajah, 2010. "On the Interaction Between Demand Substitution and Production Changeovers," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 682-691, September.
    7. Klamroth, Kathrin & Wiecek, Margaret M., 2001. "A time-dependent multiple criteria single-machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 135(1), pages 17-26, November.
    8. Kozlovskaya, Nadezhda & Pakhomova, Nadezhda & Richter, Knut, 2016. "A general production and recovery EOQ model with stationary demand and return rates," Discussion Papers 378, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
    9. Jordan, Carsten & Drexl, Andreas, 1994. "Lotsizing and scheduling by batch sequencing," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 343, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

    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:oropre:v:36:y:1988:i:1:p:50-56. 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.