A DELIVERY-LAG INVENTORY MODEL WITH AN EMERGENCY PROVISION

Edward W. Barankin

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Supply Chain and Inventory Management Management and Optimization Techniques Facility Location and Emergency Management

Abstract

An inventory model is constructed in which there is a fixed lag time of one period for delivery of orders, but in which there is also defined an emergency situation with respect to initial stock at any particular inventory point. When such an emergency situation obtains, an additional order of a specified fixed size is taken with immediate delivery. While the particular structure of emergency is laid down, there is a free parameter left to be chosen for each period to render the definition of emergency fully specific, and this parameter is determined as part of the optimization. There is no attempt to achieve the fullest generality in every respect. The principal object is to investigate the indicated emergency character of the model. It is anticipated that the n-period cases, with n > 1, will yield their essential properties by the device of inductive argument, and that from these, by suitable limit considerations, the stationary case may be studied. This first investigation is directed to the case of the single-period problem, so formulated as to present the features which may be expected to arise in the general n period case.

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