Machine Repair Problem in Production Systems with Spares and Server Vacations

This paper studies the machine repair problem consisting of M operating machines with S spare machines, and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return to the repair facility and operate one of three vacation policies: single vacation, multiple vacation, and hybrid single/multiple vacation. The Markov process and the matrixgeometric approach are used to develop the steady-state probabilities of the number of failed machines in the system as well as the performance measures. A cost model is developed to obtain the optimal values of the number of spares and the number of servers while maintaining a minimum specified level of system availability. Some numerical experiments are performed and some conclusions are drawn.