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Planning Machine Maintenance in Two-Machine Shop Scheduling

Author

Listed:
  • M. A. Kubzin

    (Legion Limited, 22--26 Albert Embankment, London SE1 7TJ, United Kingdom)

  • V. A. Strusevich

    (School of Computing and Mathematical Sciences, University of Greenwich, London SE10 9LS, United Kingdom)

Abstract

We consider the two-machine open shop and two-machine flow shop scheduling problems in which each machine has to be maintained exactly once during the planning period, and the duration of each of these intervals depends on its start time. The objective is to minimize the maximum completion time of all activities to be scheduled. We resolve complexity and approximability issues of these problems. The open shop problem is shown to be polynomially solvable for quite general functions defining the length of the maintenance intervals. By contrast, the flow shop problem is proved binary NP-hard and pseudopolynomially solvable by dynamic programming. We also present a fully polynomial approximation scheme and a fast 3/2-approximation algorithm.

Suggested Citation

  • M. A. Kubzin & V. A. Strusevich, 2006. "Planning Machine Maintenance in Two-Machine Shop Scheduling," Operations Research, INFORMS, vol. 54(4), pages 789-800, August.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:4:p:789-800
    DOI: 10.1287/opre.1060.0301
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    References listed on IDEAS

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    1. 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.
    2. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    3. Amotz Bar-Noy & Randeep Bhatia & Joseph (Seffi) Naor & Baruch Schieber, 2002. "Minimizing Service and Operation Costs of Periodic Scheduling," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 518-544, August.
    4. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
    5. Grigoriev, Alexander & van de Klundert, Joris & Spieksma, Frits C.R., 2006. "Modeling and solving the periodic maintenance problem," European Journal of Operational Research, Elsevier, vol. 172(3), pages 783-797, August.
    6. Gregory H. Graves & Chung‐Yee Lee, 1999. "Scheduling maintenance and semiresumable jobs on a single machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(7), pages 845-863, October.
    7. X Qi & T Chen & F Tu, 1999. "Scheduling the maintenance on a single machine," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1071-1078, October.
    8. Allesandro Agnetis & Pitu B. Mirchandani & Dario Pacciarelli & Andrea Pacifici, 2004. "Scheduling Problems with Two Competing Agents," Operations Research, INFORMS, vol. 52(2), pages 229-242, April.
    9. Mohan Gopalakrishnan & Sanjay L. Ahire & David M. Miller, 1997. "Maximizing the Effectiveness of a Preventive Maintenance System: An Adaptive Modeling Approach," Management Science, INFORMS, vol. 43(6), pages 827-840, June.
    10. 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.
    11. S. Anily & C.A. Glass & R. Hassin, 1999. "Scheduling maintenance services to three machines," Annals of Operations Research, Springer, vol. 86(0), pages 375-391, January.
    12. Lee, Chung-Yee, 1999. "Two-machine flowshop scheduling with availability constraints," European Journal of Operational Research, Elsevier, vol. 114(2), pages 420-429, April.
    13. 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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