Machine Repair Problem in Production Systems with Spares and Server Vacations

Jau-Chuan Ke; Ssu-Lang Lee; Cheng-Hwai Liou

RAIRO - Operations Research (2009)

  • Volume: 43, Issue: 1, page 35-54
  • ISSN: 0399-0559

Abstract

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This paper studies the machine repair problem consisting of M operating machines with S spare machines, and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return to the repair facility and operate one of three vacation policies: single vacation, multiple vacation, and hybrid single/multiple vacation. The Markov process and the matrix-geometric approach are used to develop the steady-state probabilities of the number of failed machines in the system as well as the performance measures. A cost model is developed to obtain the optimal values of the number of spares and the number of servers while maintaining a minimum specified level of system availability. Some numerical experiments are performed and some conclusions are drawn.

How to cite

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Ke, Jau-Chuan, Lee, Ssu-Lang, and Liou, Cheng-Hwai. "Machine Repair Problem in Production Systems with Spares and Server Vacations." RAIRO - Operations Research 43.1 (2009): 35-54. <http://eudml.org/doc/250656>.

@article{Ke2009,
abstract = { This paper studies the machine repair problem consisting of M operating machines with S spare machines, and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return to the repair facility and operate one of three vacation policies: single vacation, multiple vacation, and hybrid single/multiple vacation. The Markov process and the matrix-geometric approach are used to develop the steady-state probabilities of the number of failed machines in the system as well as the performance measures. A cost model is developed to obtain the optimal values of the number of spares and the number of servers while maintaining a minimum specified level of system availability. Some numerical experiments are performed and some conclusions are drawn. },
author = {Ke, Jau-Chuan, Lee, Ssu-Lang, Liou, Cheng-Hwai},
journal = {RAIRO - Operations Research},
keywords = {Hybrid multiple/single vacation; machine repair problem; matrix-geometric approach; multiple vacations; single vacation.; hybrid multiple/single vacation; multiple vacations; single vacation},
language = {eng},
month = {1},
number = {1},
pages = {35-54},
publisher = {EDP Sciences},
title = {Machine Repair Problem in Production Systems with Spares and Server Vacations},
url = {http://eudml.org/doc/250656},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Ke, Jau-Chuan
AU - Lee, Ssu-Lang
AU - Liou, Cheng-Hwai
TI - Machine Repair Problem in Production Systems with Spares and Server Vacations
JO - RAIRO - Operations Research
DA - 2009/1//
PB - EDP Sciences
VL - 43
IS - 1
SP - 35
EP - 54
AB - This paper studies the machine repair problem consisting of M operating machines with S spare machines, and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return to the repair facility and operate one of three vacation policies: single vacation, multiple vacation, and hybrid single/multiple vacation. The Markov process and the matrix-geometric approach are used to develop the steady-state probabilities of the number of failed machines in the system as well as the performance measures. A cost model is developed to obtain the optimal values of the number of spares and the number of servers while maintaining a minimum specified level of system availability. Some numerical experiments are performed and some conclusions are drawn.
LA - eng
KW - Hybrid multiple/single vacation; machine repair problem; matrix-geometric approach; multiple vacations; single vacation.; hybrid multiple/single vacation; multiple vacations; single vacation
UR - http://eudml.org/doc/250656
ER -

References

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