A Replenishment Inventory Model with a Stock-Dependent Demand and Age-Stock-Dependent Cost Functions in a Random Environment

This paper investigates an (S,s) continuous-review perishable inventory model with a stock-dependent Poisson demand process, full backordering (with an extension for lost sales) and uncertainty in lead time and shelf life. Four types of costs are considered: a fixed cost of an order and each outdated item; age-dependent costs of an item (i.e., holding and salvage costs), given by a function of its remaining shelf life; and a delay cost of a backlogged demand unit, which is a function of its delay duration. Applying the supplementary variable technique, we obtain the joint probability-density function of the number of items in the system and the remaining time and thereby obtain the optimal parameters minimizing the long-run average total cost. Numerical experiments show that supply chain profits are enhanced by integrating the age components into replenishment decisions, and ignoring the shelf age- and delay-dependent costs may result in a substantial loss (up to 25%). It further appeared that estimating the lead-time distribution by an exponential one is significantly more costly, in particular as the c.v. differs from 1. In contrast, an exponential shelf life may provide a good heuristic for other shelf-life distributions.