An inventory model for product life cycle (growth stage) with defective items and shortages

A product life cycle is the life span of a product 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's life cycle can be divided into several stages characterised by the revenue generated by the product. This paper investigates inventory control policies in a manufacturing system for a single product during the product life cycle, which consists of three stages: introduction, growth and decline stage. The demand and the defective rates as well as cost parameters are assumed to be general functions of time is considered in this paper. The defective rate is considered as a variable of known proportions. The objective is to minimise the total net inventory cost and optimal quantity in product life cycle. The relevant model is built, solved and some main results about the uniqueness of this solution with the use of rigorous mathematical methods are obtained. Illustrative examples are provided and numerical verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.