Optimal Management of the Machine Repair Problem with Working Vacation: Newton-Quasi method

• Main Authors: Wei-Lun Chen, 陳韋綸
• Other Authors: 王國雄
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/32365348583722340949

碩士 === 國立中興大學 === 應用數學系所 === 96 === 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.