Analysis of (S, s) Inventory System with Decaying Items

This article obtains the stationary distribution of the inventory level of an (S, s) inventory model with decaying items. The demand to this inventory system is governed by a general renewal process. Items decay at a constant rate independently and identically. When the inventory reduces to a level <s, at a demand point an order for replenishment is placed and is received after a random duration whose distribution is arbitrary. The quantity realised is variable and is such that the resulting inventory level is equal to S. Both the cases of complete becklogging and lost sales are treated in the present analysis. The stochastic process L(t) representing the inventory level at any time t is analysed by identifying an embedded MRP. The intensity of decay events and shortages are obtained in an explicit form. Based on the results a total cost expression is derived. Numerical results are presented to illustrate the use of the cost expression in identifying the optimal reorder level.