Fill Rate Approximations for a Perishable Inventory System with Positive Lead Time and Fixed Case Pack Size Using a Modified (R,S,Nq)-Replenishment Policy in a Lost Sales Environment

Abstract

This paper provides an approximation for the customer service level for a perishable item in a stochastic lost sales environment using a periodic review inventory control system in which demand is discrete and case pack sizes are fixed. We first show that the customer service level is virtually independent of the shelf life, when using an inventory replenishment policy which has been developed specifically for perishables. This result enables us to approximate the service level for perishables in a lost sales environment by using available results for the non-perishable lost sales problem. Since the lost sales problem for non-perishable items is also notoriously difficult to analyse, we develop new approximations which link the service level in a lost sales system to the service level in a backordering system for non-perishable items. The backordering system for non-perishable items is relatively simple to analyse. In this way we provide new approximations for the lost sales system for both non-perishable items and (due to the result that the service level is virtually independent of the shelf life) also for perishable items. These new approximations are tested for perishable items in a typical retail environment in which the lead time, review period and case pack size are relatively small and in which demand may follow a week pattern or not. The best approximation performs very well: it has an average approximation error equal to -0,19%.