Optimization Analysis of the G/G/R Machine Repair Problem With Balking and Reneging

摘要

The G/G/R machine repair problem with balking and reneging via the diffusion approximation approach is investigated. Failed machines balk (do not enter) with a constant probability and renege (leave the queue after entering) according to a general distribution. Failure and repair times of the machines are also generally distributed. The approximate probability density functions of the number of failed machines in the system are developed using diffusion approximation approach. The Newton method and the direct search method are used, respectively, to determine the optimum number of repairmen as well as the optimum value of service rate, to maximize the profit function. Sensitivity analysis with numerical illustration is also provided.