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 aut omatic machines are maintained by a single non-reliable service statio n. Failure time and service time of the machines are assumed to follow the negative exponential distribution and the Erlang k type distribut ion, respectively. Breakdown time and repair time of the service stati on are also assumed to follow the negative exponential distribution an d the Erlang m type distribution, respectively. Matrix geometric techn iques are utilized to derive the steady-state probabilities of the num ber of failed machines in the system. A profit model is developed to d etermine 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.