Title: The warm-standby M/M/R machine repair problem with balking, reneging and service pressure coefficient

Authors: Kuo-Hsiung Wang; Shu-Wei Shang; Tseng-Chang Yen

Addresses: Department of Computer Science and Information Management, Providence University, Taichung 43301, Taiwan ' Department of Applied Mathematics, National Chung-Hsing University, Taichung 40227, Taiwan ' Department of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan

Abstract: This paper studies the warm-standby M/M/R machine repair problem with balking and reneging plus service pressure coefficient. Failed machines balk (do not enter) with a constant probability (1 − b) and renege (leave the queue after entering) according to a negative exponential distribution. We use the birth-and-death results to derive the steady-state probabilities, using which various system performance measures that can be obtained. A cost model is constructed to determine the joint optimal values of the number of repairmen, the number of warm standbys, and the joint optimal values of the service rate and the balking rate simultaneously by using two-stage optimisation method. Numerical results are provided to illustrate the effectiveness of the two-stage optimisation algorithm. Sensitivity analysis is also investigated.

Keywords: machine repair; balking; reneging; service pressure coefficient; direct search; two-stage optimisation; performance measures; cost modelling; warm standbys.

DOI: 10.1504/IJSOI.2013.059354

International Journal of Services Operations and Informatics, 2013 Vol.8 No.1, pp.19 - 34

Received: 05 Mar 2012
Accepted: 24 May 2013
Published online: 22 Sep 2014 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article