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Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine

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  • Stéphane Dauzère‐Pérès
  • Marc Sevaux

Abstract

This paper tackles the general single machine scheduling problem, where jobs have different release and due dates and the objective is to minimize the weighted number of late jobs. The notion of master sequence is first introduced, i.e., a sequence that contains at least an optimal sequence of jobs on time. This master sequence is used to derive an original mixed‐integer linear programming formulation. By relaxing some constraints, a Lagrangean relaxation algorithm is designed which gives both lower and upper bounds. The special case where jobs have equal weights is analyzed. Computational results are presented and, although the duality gap becomes larger with the number of jobs, it is possible to solve problems of more than 100 jobs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 50: 2003

Suggested Citation

  • Stéphane Dauzère‐Pérès & Marc Sevaux, 2003. "Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(3), pages 273-288, April.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:3:p:273-288
    DOI: 10.1002/nav.10056
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    References listed on IDEAS

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    1. C. N. Potts & L. N. Van Wassenhove, 1988. "Algorithms for Scheduling a Single Machine to Minimize the Weighted Number of Late Jobs," Management Science, INFORMS, vol. 34(7), pages 843-858, July.
    2. Crauwels, H. A. J. & Potts, C. N. & Van Wassenhove, L. N., 1996. "Local search heuristics for single-machine scheduling with batching to minimize the number of late jobs," European Journal of Operational Research, Elsevier, vol. 90(2), pages 200-213, April.
    3. Hiroshi Kise & Toshihide Ibaraki & Hisashi Mine, 1978. "A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times," Operations Research, INFORMS, vol. 26(1), pages 121-126, February.
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    Cited by:

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    2. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.

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