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.

Keywords: hybrid multiple/single vacation, machine repair problem, matrix-geometric approach, multiple vacations, single vacation

@article{RO_2009__43_1_35_0, author = {Ke, Jau-Chuan and Lee, Ssu-Lang and Liou, Cheng-Hwai}, title = {Machine repair problem in production systems with spares and server vacations}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {35--54}, publisher = {EDP-Sciences}, volume = {43}, number = {1}, year = {2009}, doi = {10.1051/ro/2009004}, mrnumber = {2502324}, zbl = {1158.60378}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro/2009004/} }

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 - Recherche Opérationnelle PY - 2009 SP - 35 EP - 54 VL - 43 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2009004/ DO - 10.1051/ro/2009004 LA - en ID - RO_2009__43_1_35_0 ER -

%0 Journal Article %A Ke, Jau-Chuan %A Lee, Ssu-Lang %A Liou, Cheng-Hwai %T Machine repair problem in production systems with spares and server vacations %J RAIRO - Operations Research - Recherche Opérationnelle %D 2009 %P 35-54 %V 43 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2009004/ %R 10.1051/ro/2009004 %G en %F RO_2009__43_1_35_0

Ke, Jau-Chuan; Lee, Ssu-Lang; Liou, Cheng-Hwai. Machine repair problem in production systems with spares and server vacations. RAIRO - Operations Research - Recherche Opérationnelle, Volume 43 (2009) no. 1, pp. 35-54. doi : 10.1051/ro/2009004. http://archive.numdam.org/articles/10.1051/ro/2009004/

[1] An introduction to probability theory and its applications, Vol. I. John Wiley and Sons, New York (1967). | Zbl

,[2] A queueing model for spare coal faces. Oper. Res. Quart. 10 (1959) 245-251.

and ,[3] Economic analysis of the M/M/R machine repair problem with warm standbys. Microelectron. Reliab. 29 (1989) 25-35.

and ,[4] Cost analysis of the M/M/R machine repair problem with mixed standby spares. Microelectron. Reliab. 33 (1993) 1293-1301.

,[5] Cost analysis of the cold-standby M/M/R machine repair problem with multiple modes of failure. Microelectron. Reliab. 38. (1998) 435-441.

and ,[6] Rakhee and S. Maheshwari, N-policy for a machine repair system with spares and reneging. Appl. Math. Model. 28 (2004) 513-531.

,[7] The productivity of several machines under the care of one operator. J. R. Stat. Soc. B 12 (1950) 145-151. | Zbl

,[8] An optimum repair policy for the machine interference problem. J. Oper. Res. Soc. 32 (1981) 793-801. | MR | Zbl

,[9] An approach to cost analysis of maintenance float systems. IIE Trans. 8 (1976) 128-133. | MR

,[10] Queueing models for spares provisioning. Nav. Res. Logist. Quart. 24 (1977) 521-536. | Zbl

, and ,[11] A closed queueing network model for multi-echelon repairable item provisioning. IIE Trans. 15 (1983) 344-352.

, and ,[12] Profit analysis of the M/M/R machine repair problem with balking, reneging, and standby switching failures. Comput. Oper. Res. 34 (2007) 835-847. | Zbl

, and ,[13] Queueing system with vacations-a survey. Queueing Syst. 1 (1986) 29-66. | MR | Zbl

,[14] Queueing analysis: A foundation of performance evaluation, Vol. I. Vacation and priority systems, Part I. North-Holland, Amsterdam (1991). | MR | Zbl

,[15] Machine interference problem with warm spares, server vacations and exhaustive service. Perform. Eval. 29 (1997) 195-211.

,[16] Rakhee and M. Singh, Bilevel control of degraded machining system with warm standbys, setup and vacation. Appl. Math. Model 28 (2004) 1015-1026. | Zbl

,[17] Vacation policies for machine interference problem with an un-reliable server and state-dependent service rate. J. Chinese Institute Industrial Engineers 23 (2006) 100-114.

,[18] Stochastic Petri net analysis of finite population vacation queueing systems. Queueing Syst. 8 (1991) 111-128. | MR | Zbl

and ,[19] A coal unloader: a finite queueing system with breakdowns. Interfaces 11 (1981) 12-24.

, and ,[20] Fundamentals of queueing theory. 3rd ed., John Wiley and Sons, New York (1998). | MR | Zbl

and ,[21] Matrix geometric solutions in stochastic models: an algorithmic approach. The Johns Hopkins University Press, Baltimore (1981). | MR | Zbl

,[22] The productivity of machines requiring attention at random interval. J. R. Stat. Soc. B 13 (1951) 65-82. | Zbl

and ,*Cited by Sources: *