A joint pricing and replenishment policy for perishable products with fixed shelf life and positive lead times

Abstract

Most of the existing inventory models in the literature are based on the assumption that the items have infinite shelf life and do not deteriorate no matter how long they stay on the shelf. However this assumption may not be applicable in many situations since there are also many types of products with limited shelf lives. In the inventory literature stored items with fixed finite lifetimes are usually referred to as perishable items. Examples of perishable products include fresh foods, medical products, whole-blood units, packaged chemical products and photographic films. In this study, we consider the joint pricing and ordering policy, (Q, r, P1, P2), for an inventory model with perishable items, with constant shelf lives and positive lead times. The demand process is assumed to be Poisson. If there is a single batch on hand, the items in a batch are sold at price P1. If there are two batches in stock, the items in the older batch are sold at price P2, where P1 > P2. The younger batch is not sold until the older one is totally depleted. Although the shelf lives are constant, the sequence of remaining shelf lives of the items at the instances where stock level hits Q, is a random sequence. The limiting distribution of this sequence is obtained and the analytical derivations of the operating characteristics of the model is based on this limiting distribution. Numerical results are also presented.