Optimal management of the machine repair problem with working vacation: Newton's method

Authors:
Kuo-Hsiung Wang;Wei-Lun Chen;Dong-Yuh Yang
Affiliations:
Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan;Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan;Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu 30050, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 6
Cited 5

Queueing systems with vacations—a survey

Queueing Systems: Theory and Applications
The GI/M/1 queue with exponential vacations

Queueing Systems: Theory and Applications
Profit analysis of the M/Ek/1 machine repair problem with a non-reliable service station

Computers and Industrial Engineering
M/M/1 queues with working vacations (M/M/1/WV)

Performance Evaluation
M/G/1 queue with multiple working vacations

Performance Evaluation
Analysis of a GI/M/1 queue with multiple working vacations

Operations Research Letters

GI/Geom/1/N/MWV queue with changeover time and searching for the optimum service rate in working vacation period

Journal of Computational and Applied Mathematics
Multi-server machine repair model with standbys and synchronous multiple vacation

Computers and Industrial Engineering
Combining a maintenance center M/M/c/m queue into the economic production quantity model with stochastic machine breakdowns and repair

Computers and Industrial Engineering
Computational analysis of machine repair problem with unreliable multi-repairmen

Computers and Operations Research
Modeling of multi-server repair problem with switching failure and reboot delay and related profit analysis

Computers and Industrial Engineering

Quantified Score

Hi-index	7.29

Visualization

Abstract

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.