Inventory control with general demand and lead time distributions

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Abstract
This paper extends an earlier paper in this journal by Murphy (1975) by presenting practical approaches for determining the expected lost sales for a reorder level system of inventory control. First, a set of formulas are derived for computing the first four moments (f.f.m.) of the lead time demand, these formulas are applicable to any distribution forms of daily demand and lead time. By fitting the lead time demand's f.f.m. to either a beta or a Schmeiser-Deutsch distribution, this paper then demonstrates how the expected lost sales can be easily computed. The approaches presented provide accurate modelling for diversified situations and the computations can be easily performed manually.

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