An optimum approach of profit analysis on the machine repair system with heterogeneous repairmen

We consider a machine repair problem with queue-dependent heterogeneous repairmen. The stationary probability distribution of the number of failed machines in the system is derived. A profit model is developed to determine the optimal values of threshold to assign/add one more repairman for increasing the total service rate where the service rate is assumed adjustable. The probabilistic global search Lausanne (PGSL) method is employed to find an initial trial solution. Based on this initial solution, a direct search method is applied to obtain the optimal values of the threshold and, then, the Quasi-Newton method is implemented to adjust the corresponding service rates. Some numerical experiments are performed to justify the efficiency of the optimum approach.