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Minimum weighted number of tardy jobs on an m-machine flow-shop with a critical machine

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  • Mosheiov, Gur
  • Sarig, Assaf

Abstract

We study a flow-shop problem, where each of the jobs is limited to no more than two operations. One of these operations is common for all the jobs, and is performed on the same ("critical") machine. Reflecting many applications, jobs are assumed to be processed in blocks on the critical machine. All the jobs share a common due-date, and the objective is minimum weighted number of tardy jobs. We prove that the problem is NP-hard. Then we formulate the problem as an integer program, and introduce a pseudo-polynomial dynamic programming algorithm, proving that the problem is NP-hard in the ordinary sense. We also propose an efficient heuristic, which is shown numerically to produce very close-to-optimal schedules. Finally, we show that the special case of identical weights is polynomially solvable.

Suggested Citation

  • Mosheiov, Gur & Sarig, Assaf, 2010. "Minimum weighted number of tardy jobs on an m-machine flow-shop with a critical machine," European Journal of Operational Research, Elsevier, vol. 201(2), pages 404-408, March.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:2:p:404-408
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    References listed on IDEAS

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    1. Drobouchevitch, I. G. & Strusevich, V. A., 2000. "Heuristics for the two-stage job shop scheduling problem with a bottleneck machine," European Journal of Operational Research, Elsevier, vol. 123(2), pages 229-240, June.
    2. Kyparisis, George J. & Koulamas, Christos, 2000. "Flow shop and open shop scheduling with a critical machine and two operations per job," European Journal of Operational Research, Elsevier, vol. 127(1), pages 120-125, November.
    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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