Inventory Lot Size Models with Vanishing Market

Abstract

The paper is concerned with equipment which is being phased out because it is superseded by a technologically more advanced product. It nevertheless still requires efficient handling for the rest of its life span.An inventory lot size model without backlogs for a single commodity with a vanishing market is used. The vanishing market is represented by- a demand function that decreases with time and eventually reaches zero, implying that the planning horizon is finite and known. It is assumed that there is no lead time for replenishments. The problem is to devise an optimal management scheme for this inventory system, namely, to determine the number of replenishments and their schedule over the predicted survival time horizon of the product.The problem is completely solved for the class of demand functions which can be approximated to by positive powers of time. The solution is given in a nearly closed form and is proven to be unique.