Profit analysis of the M/E-k/1 machine repair problem with a non-reliable service station

This paper studies the machine repair problem in which N identical automatic machines are maintained by a single non-reliable service station. Failure time and service time of the machines are assumed to follow the negative exponential distribution and the Erlang k type distribution, respectively. Breakdown time and repair time of the service station are also assumed to follow the negative exponential distribution and the Erlang m type distribution, respectively. Matrix geometric techniques are utilized to derive the steady-state probabilities of the number of failed machines in the system. A profit model is developed to determine the optimum number of machines to be assigned to the service station in order to maximize the total expected profit per machine per unit time. (C) 1997 Elsevier Science Ltd.