Cost analysis of the machine-repair problem with R non-reliable service stations
Abstract This paper studies the machine-repair problem with N operating machines and R non-reliable service stations under steady-state conditions. Two different types of service stations are considered. In type 1, each service station serves at an identical service rate, while in type 2, each service station serves either at a slow rate or at a fast rate. Failure and service times of the machines, and breakdown and repair times of the service stations are assumed to follow a negative exponential distribution. Matrix geometric theory is used to find the steady-state probabilities. A cost model is developed to obtain the optimal number of service stations for both types. Under the optimal operating conditions, several system characteristics are evaluated for both types.