An EPQ Model for Product Life Cycle (Maturity Stage) with Deteriorating Items and Shortages

A product life cycle is the life span of a product in which the period begins with the initial product specification and ends with the withdrawal from the market of both the product and its support. A product life cycle can be divided into several stages characterized by the revenue generated by the product. This study investigates inventory control policies in a manufacturing system for a single product during the product life cycle, which consists of four stages: introduction, growth, maturity and decline. In all inventory models a general assumption is that products have indefinitely long lives. In general, almost all items deteriorate over time. Often, the rate of deterioration is low and there is little need to consider the deterioration in the determination of the economic lot size. The objective is to derive the cycle time and optimal production lot size to minimize total costs for the product life cycle with deteriorating items. The relevant model is built, solved and some main results on the uniqueness of the solution using rigorous mathematical methods are obtained. Illustrative examples are provided to verify our findings numerically.