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標題: Optimal management of the machine repair problem with working vacation: Newton's method
作者: Wang, K.H.
Chen, W.L.
Yang, D.Y.
關鍵字: Cost;Optimization;Working vacation;Newton's method;server vacations;profit analysis;gi/m/1 queue;interference problem;exhaustive service;m/g/1 queue;station;spares
Project: Journal of Computational and Applied Mathematics
期刊/報告no:: Journal of Computational and Applied Mathematics, Volume 233, Issue 2, Page(s) 449-458.
This paper studies the M/M/1 machine repair problem with working vacation in which the server works with different repair rates rather than completely terminating the repair during a vacation period. We assume that the server begins the working vacation when the system is empty. The failure times, repair times, and vacation times are all assumed to be exponentially distributed. We use the MAPLE software to compute steady-state probabilities and several system performance measures. A cost model is derived to determine the optimal values of the number of operating machines and two different repair rates simultaneously, and maintain the system availability at a certain level. We use the direct search method and Newton's method for unconstrained optimization to repeatedly find the global minimum value until the system availability constraint is satisfied. Some numerical examples are provided to illustrate Newton's method. (C) 2009 Published by Elsevier B.V.
ISSN: 0377-0427
DOI: 10.1016/
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