Replenishment Policies for Deteriorating Items with Ramp Type Demand and a Fixed Shelf-Life under Shortage

This study proposes a single-supplier, single-retailer inventory and pricing strategies for deteriorating items with ramp type demand and a fixed shelf-life u nder s hortage . In practice, there are many commodity such as food, medication exist the shelf life . Therefore the shelf life expiration date has become an important research topic in inventory management. We will discuss three cases. We assume that the inventory objective is to minimize the total cost per unit time of the system. By using the subroutine FindRoot in commercial software Mathematica 5.2, we obtain the optimal solutions