Two-Stage Production Systems with Intermediate Storage

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Abstract
This paper presents an analytical study of several aspects of two-stage production systems with variable operation times and provision for intermediate storage. For the exponential service times assumed at one of the stages, the set of simultaneous equations satisfied by the steady-state probabilities are shown to involve the Laplace transform of the density function at the other stage and its various order derivatives. An analysis of this set of equations leads to a recursive solution for the mean production rate of a system with any number of storages. The realistic cases of Erlang and normal density functions are worked out in detail. It turns out that for moderate coefficients of variation the production rates for these two distributions differ only marginally. That this is not generally true is illustrated by considering a uniform distribution, for which the results are significantly different. The problem of balancing the production system is discussed at some length. It is shown that the production rate improves on allotting a slightly higher load to the less variable stage.

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