IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v54y2006i4p789-800.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1060.0301
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1060.0301?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Seyed Habib A. Rahmati & Abbas Ahmadi & Kannan Govindan, 2018. "A novel integrated condition-based maintenance and stochastic flexible job shop scheduling problem: simulation-based optimization approach," Annals of Operations Research, Springer, vol. 269(1), pages 583-621, October.
    2. Detienne, Boris, 2014. "A mixed integer linear programming approach to minimize the number of late jobs with and without machine availability constraints," European Journal of Operational Research, Elsevier, vol. 235(3), pages 540-552.
    3. 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.
    4. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    5. Allaoui, H. & Lamouri, S. & Artiba, A. & Aghezzaf, E., 2008. "Simultaneously scheduling n jobs and the preventive maintenance on the two-machine flow shop to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 112(1), pages 161-167, March.
    6. Maquirriain, Javier & García-Villoria, Alberto & Pastor, Rafael, 2024. "Matheuristics for scheduling of maintenance service with linear operation cost and step function maintenance cost," European Journal of Operational Research, Elsevier, vol. 315(1), pages 73-87.
    7. Kerem Bülbül & Safia Kedad-Sidhoum & Halil Şen, 2019. "Single-machine common due date total earliness/tardiness scheduling with machine unavailability," Journal of Scheduling, Springer, vol. 22(5), pages 543-565, October.
    8. Chen, Wen-Jinn, 2009. "Minimizing number of tardy jobs on a single machine subject to periodic maintenance," Omega, Elsevier, vol. 37(3), pages 591-599, June.
    9. Ali Salmasnia & Danial Mirabadi-Dastjerd, 2017. "Joint production and preventive maintenance scheduling for a single degraded machine by considering machine failures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 544-578, October.
    10. Asaf Levin & Gur Mosheiov & Assaf Sarig, 2009. "Scheduling a maintenance activity on parallel identical machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(1), pages 33-41, February.
    11. Gizem Keysan & George L. Nemhauser & Martin W. P. Savelsbergh, 2010. "Tactical and Operational Planning of Scheduled Maintenance for Per-Seat, On-Demand Air Transportation," Transportation Science, INFORMS, vol. 44(3), pages 291-306, August.
    12. Aggoune, Riad & Portmann, Marie-Claude, 2006. "Flow shop scheduling problem with limited machine availability: A heuristic approach," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 4-15, February.
    13. J-J Wang & J-B Wang & F Liu, 2011. "Parallel machines scheduling with a deteriorating maintenance activity," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1898-1902, October.
    14. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    15. 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.
    16. A. Beynaghi & F. Moztarzadeh & A. Shahmardan & R. Alizadeh & J. Salimi & M. Mozafari, 2019. "Makespan minimization for batching work and rework process on a single facility with an aging effect: a hybrid meta-heuristic algorithm for sustainable production management," Journal of Intelligent Manufacturing, Springer, vol. 30(1), pages 33-45, January.
    17. Rustogi, Kabir & Strusevich, Vitaly A., 2012. "Single machine scheduling with general positional deterioration and rate-modifying maintenance," Omega, Elsevier, vol. 40(6), pages 791-804.
    18. Aggoune, Riad, 2004. "Minimizing the makespan for the flow shop scheduling problem with availability constraints," European Journal of Operational Research, Elsevier, vol. 153(3), pages 534-543, March.
    19. Wen-Hung Wu & Yunqiang Yin & T C E Cheng & Win-Chin Lin & Juei-Chao Chen & Shin-Yi Luo & Chin-Chia Wu, 2017. "A combined approach for two-agent scheduling with sum-of-processing-times-based learning effect," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(2), pages 111-120, February.
    20. Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:54:y:2006:i:4:p:789-800. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.