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The Machine Repair Problem with Heterogeneous Populations

Author

Listed:
  • Donald Gross

    (George Washington University, Washington, D.C.)

  • John F. Ince

    (Maritime Administration, Washington, D.C.)

Abstract

The classic machine repair with spares (finite source) queueing model assumes all calling units are identical in failure and repair characteristics. This paper develops, for a first-come first-served discipline, a procedure for treating nonhomogeneous populations, specifically, a population with two types of items, each with exponential failure and repair times but with different mean values. Exact solutions are obtained for small population sizes and compared to approximate procedures using the classical theory. The exact model is essentially a two-stage cyclic queue with two classes of customers. Extensions of the model to N stages and M customer classes, priority disciplines, and other disciplines, including blocking, are discussed.

Suggested Citation

  • Donald Gross & John F. Ince, 1981. "The Machine Repair Problem with Heterogeneous Populations," Operations Research, INFORMS, vol. 29(3), pages 532-549, June.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:3:p:532-549
    DOI: 10.1287/opre.29.3.532
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    Cited by:

    1. William Liang & Barış Balcıog̃lu & Robert Svaluto, 2013. "Scheduling policies for a repair shop problem," Annals of Operations Research, Springer, vol. 211(1), pages 273-288, December.
    2. Dong Li & Nishant Mishra & Serguei Netessine, 2023. "Contracting for Product Support Under Information Asymmetry," Management Science, INFORMS, vol. 69(8), pages 4627-4645, August.
    3. Yang, Taho & Lee, Rong-Shean & Chen, Mu-Chen & Chen, Pangwei, 2005. "Queueing network model for a single-operator machine interference problem with external operations," European Journal of Operational Research, Elsevier, vol. 167(1), pages 163-178, November.

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