Optimal Issuing Policies in Inventory Management—I

The general inventory depletion problem can be described as the problem of finding an issue policy which maximizes or minimizes a prescribed function when the inventory itself is changing in quality over time. Earlier authors writing on this subject have placed many restrictive assumptions on the model. The assumption of one demand source withdrawing items from the stockpile is removed and the case of several demand sources is considered. Next, it is assumed that there is a constant penalty cost, p, each time an item is issued. It can be described as an installation or work stoppage cost. Finally, the assumption that the field life, L(S), is a concave or convex function is removed. A more general type of function is considered. L(S) is a concave nonincreasing function for Sε [0, t] and L(S) = L(t) = c > 0 for S ≧ t. When L(S) has this form, it provides a good approximation to the general decreasing S-shaped curve. In all of the foregoing cases, optimal policies or bounds on the optimal policies are presented.