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

top
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

top

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

top
  1. W. Feller, An introduction to probability theory and its applications, Vol. I. John Wiley and Sons, New York (1967).  
  2. F.J. Toft and H. Boothroyd, A queueing model for spare coal faces. Oper. Res. Quart.10 (1959) 245–251.  
  3. B.D. Sivazlian and K.-H. Wang, Economic analysis of the M/M/R machine repair problem with warm standbys. Microelectron. Reliab. 29 (1989) 25–35.  
  4. K.-H. Wang, Cost analysis of the M/M/R machine repair problem with mixed standby spares. Microelectron. Reliab.33 (1993) 1293–1301.  
  5. K.-H. Wang and H.-C. Lee, Cost analysis of the cold-standby M/M/R machine repair problem with multiple modes of failure. Microelectron. Reliab. 38. (1998) 435–441.  
  6. M. Jain, Rakhee and S. Maheshwari, N-policy for a machine repair system with spares and reneging. Appl. Math. Model.28 (2004) 513–531.  
  7. H. Ashcroft, The productivity of several machines under the care of one operator. J. R. Stat. Soc. B12 (1950) 145–151.  
  8. E.A. Elsayed, An optimum repair policy for the machine interference problem. J. Oper. Res. Soc.32 (1981) 793–801.  
  9. J.E. Hilliard, An approach to cost analysis of maintenance float systems. IIE Trans.8 (1976) 128–133.  
  10. D. Gross, H.D. Kahn and J.D. Marsh, Queueing models for spares provisioning. Nav. Res. Logist. Quart.24 (1977) 521–536.  
  11. D. Gross, D.R. Miller and R.M. Soland, A closed queueing network model for multi-echelon repairable item provisioning. IIE Trans.15 (1983) 344–352.  
  12. K.H. Wang, J.B. Ke and J.C. Ke, Profit analysis of the M/M/R machine repair problem with balking, reneging, and standby switching failures. Comput. Oper. Res.34 (2007) 835–847.  
  13. B.T. Doshi, Queueing system with vacations-a survey. Queueing Syst.1 (1986) 29–66.  
  14. H. Takagi, Queueing analysis: A foundation of performance evaluation, Vol. I. Vacation and priority systems, Part I. North-Holland, Amsterdam (1991).  
  15. S.M. Gupta, Machine interference problem with warm spares, server vacations and exhaustive service. Perform. Eval.29 (1997) 195–211.  
  16. M. Jain, Rakhee and M. Singh, Bilevel control of degraded machining system with warm standbys, setup and vacation. Appl. Math. Model28 (2004) 1015–1026.  
  17. J.C. Ke, Vacation policies for machine interference problem with an un-reliable server and state-dependent service rate. J. Chinese Institute Industrial Engineers23 (2006) 100–114.  
  18. O.C. Ibe and K.S. Trivedi, Stochastic Petri net analysis of finite population vacation queueing systems. Queueing Syst.8 (1991) 111–128.  
  19. K. Chelst, A.Z. Tilles and J.S. Pipis, A coal unloader: a finite queueing system with breakdowns. Interfaces11 (1981) 12–24.  
  20. D. Gross and C.M. Harris, Fundamentals of queueing theory. 3rd ed., John Wiley and Sons, New York (1998).  
  21. M.F. Neuts, Matrix geometric solutions in stochastic models: an algorithmic approach. The Johns Hopkins University Press, Baltimore (1981).  
  22. F. Benson and D.R. Cox, The productivity of machines requiring attention at random interval. J. R. Stat. Soc. B13 (1951) 65–82.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.