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Scheduling maintenance services to three machines

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  • S. Anily
  • C.A. Glass
  • R. Hassin

Abstract

We study a discrete problem of scheduling activities of three types under the constraintthat at most a single activity can be scheduled to any one period. Applications of such amodel are the scheduling of maintenance service to machines and multi‐item replenishmentof stock. We assume that the cost associated with any given type of activity increases linearlywith the number of periods since the last execution of this type. The problem is to specifyat which periods to execute each of the activity types in order to minimize the long‐runaverage cost per period. We analyze various forms of optimal solution which may occur,relating them to the combination of the three machine cost constants. Some cases remainunsolved by this method and for these we develop a heuristic whose worst case performanceis no more than 3.33% from the optimal. Copyright Kluwer Academic Publishers 1999

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  • 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.
    • Handle: RePEc:spr:annopr:v:86:y:1999:i:0:p:375-391:10.1023/a:1018971222185
    DOI: 10.1023/A:1018971222185
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Bollapragada, Srinivas & Gupta, Aparna & Lawsirirat, Chaipat, 2007. "Managing a portfolio of long term service agreements," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1399-1411, November.

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