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Cyclical Schedules for Capacitated Lot Sizing with Dynamic Demands

Author

Listed:
  • Gerard M. Campbell

    (School of Business Administration, University of Connecticut, Storrs, Connecticut 06268)

  • Vincent A. Mabert

    (Graduate School of Business, Indiana University, Bloomington, Indiana 47405)

Abstract

Cyclical scheduling, where the time between production periods for each item is constant, offers simplicity and ease of control compared with noncyclical scheduling, where production periods are irregularly spaced. However, when demands are dynamic, flexibility in the spacing of production periods permits noncyclical scheduling to result in lower total costs. This study investigates the additional cost of cyclical scheduling. We focus upon the capacitated lot sizing problem (CLSP), which deals with planning production on a single, capacitated machine serving multiple items with dynamic demands. To establish cyclical schedules, a mathematical programming model is developed along with a heuristic solution technique and a Lagrangian-based lower bounding procedure. For problems solved in this study, differences between solution costs and lower bounds average less than 1%. Experiments are performed to evaluate the heuristic technique and to compare cyclical schedules with noncyclical ones. For comparison purposes, a noncyclical heuristic and problem sets from the literature are used. New problems based upon operating data from Ford Motor Company are also generated and solved. In this study, cyclical schedules average 4.4% higher in cost than noncyclical ones. Coefficient of demand variation most seriously influences differences in costs. Other significant factors include capacity utilization, setup time, time between orders, and number of items.

Suggested Citation

  • Gerard M. Campbell & Vincent A. Mabert, 1991. "Cyclical Schedules for Capacitated Lot Sizing with Dynamic Demands," Management Science, INFORMS, vol. 37(4), pages 409-427, April.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:4:p:409-427
    DOI: 10.1287/mnsc.37.4.409
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    Citations

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    Cited by:

    1. Charles, Mehdi & Dauzère-Pérès, Stéphane & Kedad-Sidhoum, Safia & Mazhoud, Issam, 2022. "Motivations and analysis of the capacitated lot-sizing problem with setup times and minimum and maximum ending inventories," European Journal of Operational Research, Elsevier, vol. 302(1), pages 203-220.
    2. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Carstensen, Peter, 1997. "Das Economic Lot Scheduling Problem: Überblick und LP-basiertes Verfahren," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 465, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. 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.
    5. Drexl, Andreas & Haase, Knut, 1993. "Sequential-analysis-based randomized-regret-methods for lotsizing and scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 323, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    6. 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.
    7. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, June.
    8. Ian R. Webb & Bruce R. Buzby & Gerard M. Campbell, 1997. "Cyclical schedules for the joint replenishment problem with dynamic demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(6), pages 577-589, September.

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