Optimal strategy in N-policy production system with early set-up

This paper considers a production system in which an early set-up is possible. The machine(server) is turned off when there are no units(customers) to process. When the accumulated number of units reaches m(<N), the operator starts a set-up that takes a random time. After the set-up, if there are Nor more units waiting for processing, the machine begins to process the units immediately. Otherwise the machine remains dormant in the system until the accumulated number of units reaches N. We model this system by M/G/1 queue with early set-up and N-policy. We use the decomposition property of a vacation queue to derive the distribution of the number of units in the system. We, then, build a cost model and develop a procedure to find the optimal values of (m, N) that minimize a linear average cost.