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On the Optimal Operating Policy for the Machine Repair Problem When Failure and Repair Times Have Erlang Distribution

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  • Lola Coleman Goheen

    (Stanford Research Institute, Menlo Park, California)

Abstract

In the machine repair problem we are given m + n identical machines, m operating and n spares. All machines are independent of one another. When an operating machine fails, it is immediately sent to one of K repair facilities and immediately replaced by a spare machine, if one is available. Repair facility i has s j independent and identical repairmen, 1 ≦ i ≦ k . Repairmen work on machines on a one-to-one basis. The cost of repairing a failed machine is a constant depending upon the facility performing the repair. Moreover, if the number of operating machines falls below m , a penalty is accrued at a rate depending on the shortage.This paper treats the following decision problem: to assign (at the time of each failure) the failed machine to a repair facility so as to minimize the long-run average cost when K ≧ 2 and failure and repair times have Erlang distribution. We show that determining a stationary policy to minimize long-run average cost and long-run average expected cost is equivalent to solving a certain nonlinear program. The nonlinear program has a simple structure and an optimal solution.

Suggested Citation

  • Lola Coleman Goheen, 1977. "On the Optimal Operating Policy for the Machine Repair Problem When Failure and Repair Times Have Erlang Distribution," Operations Research, INFORMS, vol. 25(3), pages 484-492, June.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:3:p:484-492
    DOI: 10.1287/opre.25.3.484
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    Cited by:

    1. Haque, Lani & Armstrong, Michael J., 2007. "A survey of the machine interference problem," European Journal of Operational Research, Elsevier, vol. 179(2), pages 469-482, June.
    2. Delasay, Mohammad & Kolfal, Bora & Ingolfsson, Armann, 2012. "Maximizing throughput in finite-source parallel queue systems," European Journal of Operational Research, Elsevier, vol. 217(3), pages 554-559.

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