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The open shop scheduling problem with a given sequence of jobs on one machine

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  • Y.M. Shafransky
  • V.A. Strusevich

Abstract

The paper considers the open shop scheduling problem to minimize the make‐span, provided that one of the machines has to process the jobs according to a given sequence. We show that in the preemptive case the problem is polynomially solvable for an arbitrary number of machines. If preemption is not allowed, the problem is NP‐hard in the strong sense if the number of machines is variable, and is NP‐hard in the ordinary sense in the case of two machines. For the latter case we give a heuristic algorithm that runs in linear time and produces a schedule with the makespan that is at most 5/4 times the optimal value. We also show that the two‐machine problem in the nonpreemptive case is solvable in pseudopolynomial time by a dynamic programming algorithm, and that the algorithm can be converted into a fully polynomial approximation scheme. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 705–731, 1998

Suggested Citation

  • Y.M. Shafransky & V.A. Strusevich, 1998. "The open shop scheduling problem with a given sequence of jobs on one machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(7), pages 705-731, October.
    • Handle: RePEc:wly:navres:v:45:y:1998:i:7:p:705-731
    DOI: 10.1002/(SICI)1520-6750(199810)45:73.0.CO;2-F
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    References listed on IDEAS

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    1. V.A. Strusevich, 1997. "Shop scheduling problems under precedence constraints," Annals of Operations Research, Springer, vol. 69(0), pages 351-377, January.
    2. Clyde L. Monma, 1980. "Sequencing to Minimize the Maximum Job Cost," Operations Research, INFORMS, vol. 28(4), pages 942-951, August.
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    Cited by:

    1. T.C.E. Cheng & Svetlana A. Kravchenko & Bertrand M. T. Lin, 2019. "Server scheduling on parallel dedicated machines with fixed job sequences," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 321-332, June.
    2. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    3. Ting-Chun Lo & Bertrand M. T. Lin, 2021. "Relocation Scheduling in a Two-Machine Flow Shop with Resource Recycling Operations," Mathematics, MDPI, vol. 9(13), pages 1-35, June.
    4. Man-Ting Chao & Bertrand M. T. Lin, 2023. "Scheduling of Software Test to Minimize the Total Completion Time," Mathematics, MDPI, vol. 11(22), pages 1-17, November.
    5. A.A. Gladky & Y.M. Shafransky & V.A. Strusevich, 2004. "Flow Shop Scheduling Problems Under Machine–Dependent Precedence Constraints," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 13-28, March.
    6. F. Hwang & M. Kovalyov & B. Lin, 2014. "Scheduling for fabrication and assembly in a two-machine flowshop with a fixed job sequence," Annals of Operations Research, Springer, vol. 217(1), pages 263-279, June.
    7. Enrique Gerstl & Gur Mosheiov, 2023. "A note: maximizing the weighted number of Just-in-Time jobs for a given job sequence," Journal of Scheduling, Springer, vol. 26(4), pages 403-409, August.
    8. B. M. T. Lin & T. C. E. Cheng, 2011. "Scheduling with centralized and decentralized batching policies in concurrent open shops," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(1), pages 17-27, February.

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