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標題: 含有會調整工作效率的機器修理問題之最佳管理-牛頓法
Optimal Management of the Machine Repair Problem with Working Vacation: Newton-Quasi method
作者: 陳韋綸
Chen, Wei-Lun
關鍵字: cost
working vacation
direct search method
Newton-Quasi method
出版社: 應用數學系所
引用: References [1] Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations. Operations Research Letters 33 (2005) 201-209. [2] A.D. Banik, U.C. Gupta, S.S. Pathak, On the GI/M/1/N queue with multiple working vacations-analytic analysis and computation. Applied Mathematical Modelling 31 (2007) 1701-1710. [3] U. Chatterjee, S.P. Mukherjee, GI/M/1 queue with server vacations. Journal of the Operational Research Society 41 (1990) 83-87. [4] B.T. Doshi, Queueing systems with vacations- a survey. Queueing Systems 1 (1986) 29-66. [5] S.W. Fuhrmann, R.B. Cooper, Stochastic decompositions in the M/G/1 queue with generalized vacations. Operations Research 33 (1985) 1117- 1129. [6] F. Karaesmen, S.M. Gupta, The finite capacity GI/M/1 queue with server vacations. Journal of the Operational Research Society 47 (1996) 817-828. [7] T. Lee, The M/G/1/N queue with vacation and exhaustive service discipline. Operations Research 32 (1984) 774-784. [8] L.D. Servi, S.G. Finn, M/M/1 queues with working vacations (M/M/1/WV). Performance Evaluation 50 (2002) 41-52. [9] N.-S. Tian, The GI/M/1 queueing system with a single exponential vacation. Jounal of Systems and Mathematical Science 13 (1993) 1-9. [10] N.-S. Tian, The GI/M/1 queue with phase-type vacations. Acta Mathematicae Applicatae Sinica 16 (1993) 452-461. [11] N.-S Tian, D. Zhang, C. Cao, The GI/M/1 queue with exponential vacations. Queueing Systems 5 (1989) 331-344. [12] J.-H. Li, N.-S. Tian, Z.-Y. Ma, Performance analysis of GI/M/1 queue with working vacations and vacation interruption. Applied Mathematical Modelling 31 (2007) 880-894. [13] K.-H. Wang, Profit analysis of the machine-repair problem with a single service station subject to breakdowns. Journal of the Operational Research Society 41 (1990) 1153- 1160. [14] K.-H. Wang, J.-B. Ke, J.-C. Ke, Profit analysis of the M/M/R machine repair problem with balking, reneging, and standby switching failures. Computers and Operations Research 34 (2007) 835-847. [15] K.-H. Wang, M.-Y. Kuo, Profit analysis of the M/ /1 machine repair problem with a non-reliable service station. Computers and Industrial Engineering 32 (1997) 587-594. [16] D.-A. Wu, H. Takagi, M/G/1 queue with multiple working vacations. Performance Evaluation 63 (2006) 654-681.
摘要: 此篇論文研究了 M/M/1 含有會調整工作效率的機器修理問題,其中機器故障為一卜瓦松過程,修理者的休假時間長度與修理時間的分配為指數分配。我們假設當系統中沒有故障的機器的時候,修理者會調整工作效率。我們建立一個每單位時間內每台機器的成本函數,接著我們運用直接尋找跟數學上的牛頓法來尋找系統機器數跟不同修理率在一個穩定條件內的最佳解。我們也提供了一些數值的例子來解釋我們的牛頓法。
This thesis studies the M/M/1 machine repair problem with working vacation which the server works with different repair rates rather than completely terminates repair during a vacation period. We assume that the server begins a 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 computer 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 two methods direct search method and Newton-Quasi method to find the global minimum value until the system availability constraint is satisfied. Two numerical examples are provided to illustrate the Newton-Quasi method.
其他識別: U0005-2306200816065700
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