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Coordinating Aggregate and Detailed Scheduling Decisions in the One-Machine Job Shop: Part I. Theory

Author

Listed:
  • L. Gelders

    (Catholic University of Louvain, Louvain, Belgium)

  • P. R. Kleindorfer

    (International Institute of Management, Berlin, Germany)

Abstract

This paper presents a formal model of the one-machine job-shop scheduling problem with variable capacity. Its primary interest focuses on the trade-off between overtime and detailed scheduling costs. The scheduling problem considered is minimizing the sum of weighted tardiness and weighted flow-time costs for a given capacity plan (i.e., a given overtime plan). The paper generalizes sequence-theory results to this case where possible, analyzes various lower-bounding structures for the problem, outlines a preliminary branch-and-bound algorithm, and illustrates several interesting features of the algorithm and bounding structures by an example. Extensions of the results to more complex environments are discussed.

Suggested Citation

  • L. Gelders & P. R. Kleindorfer, 1974. "Coordinating Aggregate and Detailed Scheduling Decisions in the One-Machine Job Shop: Part I. Theory," Operations Research, INFORMS, vol. 22(1), pages 46-60, February.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:1:p:46-60
    DOI: 10.1287/opre.22.1.46
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    Citations

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    Cited by:

    1. J. J. Kanet, 2007. "New Precedence Theorems for One-Machine Weighted Tardiness," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 579-588, August.
    2. V. Balachandran, 1977. "A Survey of the Applications of the Operator Theory of Parametric Programming for the Transportation and Generalized Transportation Problems," Discussion Papers 300, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    4. Alexandre Mazier & Jean-Charles Billaut & Jean-François Tournamille, 2010. "Scheduling preparation of doses for a chemotherapy service," Annals of Operations Research, Springer, vol. 178(1), pages 145-154, July.
    5. V. Jorge Leon & S. David Wu, 1992. "On scheduling with ready‐times, due‐dates and vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(1), pages 53-65, February.

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