The Allocation of Interstage Buffer Capacities in Production Lines

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Abstract
A flow-shop-type production line where the stations are subject to breakdown is modeled as a series of queues. The objective is to find the allocation of interstage buffer capacities that maximizes total profit. The stations, which are modeled as single-server queueing systems, have completion-time distributions of two-stage Coxian type. After a standard transformation to a phase-type state representation, the new system gives rise to a Markov chain. The balance equations for this chain are solved by successive approximations to find the steady-state probability distribution of the number of items at each station, once the buffer capacities are given. A search procedure has been employed to find the optimal buffer capacities.