An economic production lot size model for product life cycle (maturity stage) with defective items with shortages

A product life cycle is the life span of a product which the period begins with 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. The purpose of this paper is to investigate the optimal production lot size and total cost during the Product Life Cycle which consists of introduction, growth, maturity and decline stages. The defective rate is considered as a variable of known proportions. The relevant model is built and it is also solved. Necessary and sufficient conditions for a unique and global optimal solution are derived. A numerical example is provided and numerically verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.