Abstract
We present the dynamic control system for the service rate in an M/M/1 queuing system, to optimize the inventory of critical repairable spare components for a fleet of mobile equipment in presence of an adjustable single server repair facility, namely, the repair rate can be expedited or slowed down. We consider the normal and expedited rates, when the faster repair rate implies higher repair costs. The repair rate selection depends on the number of units in operational condition; actual operating units plus stock on hand is generated at the moment of demand for a spare. The resulting optimal policy is to minimize the expected cost per unit time for the inventory system in the long run.
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References
G. D. Sccuder, “An evaluation of overtime policies for a repair shop,” J. Oper. Manag., No. 6 (1985).
A. Sleptchenko, M. C. van der Heijden, and A. van Harten, “Trade-off between inventory and repair capacity in spare parts networks,” J. Oper. Res. Soc., 54 (2003).
M. J. Carrillo, “Extensions of Palm’s theorem: a review,” Manag. Sci., 37 (1991).
A. K. S. Jardine and A. H. C. Tsang, Maintenance, Replacement and Reliability: Theory and Applications, CRC Press, Boca Raton (2006).
J. R. Bradley, “Optimal control of a dual service rate M/M/1 production-inventory model,” Eur. J. Oper. Res., 161 (2005).
J. M. George and J. M. Harrison, “Dynamic control of a queue with adjustable service rate,” Oper. Res., 49 (2001).
S. Stidham and R. R. Weber, “Monotonic and insensitive optimal policies for control queues with undiscounted costs,” Oper. Res., 37 (1989).
T. B. Crabill, “Optimal control of a maintenance system with variable service rates,” Oper. Res., 22 (1974).
R. A. Howard, Dynamic Programming and Markov Processes, M. I. T. Press, Cambridge (1960).
M. L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming, Wiley, New York (1994).
D. Louit, D. Banjevic, and A. K. S. Jardine, “Optimization models for critical spare parts inventories — a reliability approach,” submitted to Eur. J. Oper. Res., available upon request (2005).
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Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 4, pp. 41–49, July–August, 2010.
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Louit, D., Pascual, R. & Jardine, A. Dynamic Optimization Model for Mining Equipment Repair by Using the Spare-Parts Inventory. J Min Sci 46, 394–403 (2010). https://doi.org/10.1007/s10913-010-0049-y
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DOI: https://doi.org/10.1007/s10913-010-0049-y