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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
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    Citations

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    Cited by:

    1. 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.
    2. Drexl, Andreas & Haase, Knut, 1995. "Proportional lotsizing and scheduling," International Journal of Production Economics, Elsevier, vol. 40(1), pages 73-87, June.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

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