$(T_i, S_i)$ inventory policy for deteriorating items with time proportional demand

Abstract

This thesis is concerned with the analysis of a ($T_i,S_i$) inventory system for a single deteriorating item with time proportional demand, for which both the period-wisely variant replenishment times $T_i``s$ and the maximum inventory levels $S_i``s$ are to be determined. For the system, it is assumed that demands change linearly with time and the rate of deterioration is a constant fraction of the on-hand inventory. Under the above assumptions, it is shown that given a number of replenishment periods m, there exists a unique vector of $T_i``s$ in m-dimension which minimizes the associated inventory system cost. Furthermore, the system cost is proven to be a convex function of m. A numerical example is given.