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A PTAS for non-resumable open shop scheduling with an availability constraint

Author

Listed:
  • Yuan Yuan

    (Dalian University of Technology)

  • Yan Lan

    (Dalian Minzu University)

  • Ning Ding
  • Xin Han

    (Dalian University of Technology)

Abstract

Shop scheduling problem is one of the most classical problems in combinatorial optimization. In this paper, we study two-machine open shop scheduling problem, provided that one machine is subject to maintenance period which has to be performed in a fixed time interval. The target is to minimize the makespan. This paper considers non-resumable scenario, i.e., if a job which starts before the maintenance period cannot be completed before the maintenance period, then it must be restarted after the interval from scratch. We only discuss the case that the maintenance period is performed on the first machine, while the case of the maintenance period on the second machine is symmetric. We obtain a polynomial time approximation scheme, which is better than the best previous result $$\frac{4}{3}$$ 4 3 .

Suggested Citation

  • Yuan Yuan & Yan Lan & Ning Ding & Xin Han, 2022. "A PTAS for non-resumable open shop scheduling with an availability constraint," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 350-362, March.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:2:d:10.1007_s10878-021-00773-7
    DOI: 10.1007/s10878-021-00773-7
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    References listed on IDEAS

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    1. C.T. Ng & Mikhail Y. Kovalyov, 2004. "An FPTAS for scheduling a two‐machine flowshop with one unavailability interval," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 307-315, April.
    2. J. Breit & G. Schmidt & V. A. Strusevich, 2003. "Non-preemptive two-machine open shop scheduling with non-availability constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(2), pages 217-234, May.
    3. Shakhlevich, N. V. & Strusevich, V. A., 1993. "Two machine open shop scheduling problem to minimize an arbitrary machine usage regular penalty function," European Journal of Operational Research, Elsevier, vol. 70(3), pages 391-404, November.
    4. Mosheiov, Gur & Sarig, Assaf & Strusevich, Vitaly A & Mosheiff, Jonathan, 2018. "Two-machine flow shop and open shop scheduling problems with a single maintenance window," European Journal of Operational Research, Elsevier, vol. 271(2), pages 388-400.
    5. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    6. V.A. Strusevich, 1998. "A greedy open shop heuristic with job priorities," Annals of Operations Research, Springer, vol. 83(0), pages 253-270, October.
    7. Bo Chen & Vitaly A. Strusevich, 1993. "Approximation Algorithms for Three-Machine Open Shop Scheduling," INFORMS Journal on Computing, INFORMS, vol. 5(3), pages 321-326, August.
    8. Kubiak, Wieslaw & Blazewicz, Jacek & Formanowicz, Piotr & Breit, Joachim & Schmidt, Gunter, 2002. "Two-machine flow shops with limited machine availability," European Journal of Operational Research, Elsevier, vol. 136(3), pages 528-540, February.
    9. T Lorigeon & J-C Billaut & J-L Bouquard, 2002. "A dynamic programming algorithm for scheduling jobs in a two-machine open shop with an availability constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1239-1246, November.
    10. Lee, Chung-Yee, 1999. "Two-machine flowshop scheduling with availability constraints," European Journal of Operational Research, Elsevier, vol. 114(2), pages 420-429, April.
    11. M.A. Kubzin & V.A. Strusevich & J. Breit & G. Schmidt, 2006. "Polynomial‐time approximation schemes for two‐machine open shop scheduling with nonavailability constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 16-23, February.
    12. Lu Lu & Marc E. Posner, 1993. "An NP-Hard Open Shop Scheduling Problem with Polynomial Average Time Complexity," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 12-38, February.
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