Cost Optimization and Sensitivity Analysis of the Machine Repair Problem with Variable Servers and Balking

We consider a machine repair model with M identical machines and variable servers considering balking concept. A recursive method is applied o develop analytical steady-state solutions. We also calculate various system performance measures, such as the expected number of failed machines, the expected number of operating machines, the expected number of busy and idle servers, average balking rate, machine availability, operative utilization, and so on. A cost model is constructed to determine the optimal values of the number of busy servers, and maintain the balking rate at a certain level. Numerical results are provided in which various system performance measures are evaluated under optimal operating conditions. Sensitivity analysis is performed to investigate the effect of changes in the system parameters on the expected cost function. Finally, numerical results are also given for illustrative purposes.