Inventory system with defective products and investment opportunity for reducing defective proportion

This paper proposes a production‐inventory model with defective items. The model incorporates additional investment opportunity on quality improvement for reducing the proportion of defective products. Defective proportion depends upon production rate and the amount of this additional investment on quality improvement. Shortages are allowed and are fully backlogged. Only a random proportion of defective items can be resold at a highly discounted price and rest are to be disposed. Demand rate is assumed to be dependent on selling price. Unit cost is assumed to be a decreasing function of production rate. Profit maximization criterion is used to develop the model. The model jointly determines the optimum values of additional investment, selling price, production rate, production cycle, and production period. Concavity of the expected average net profit is proved. An iteration‐based simple algorithm is provided to solve the developed model. The model is illustrated by a numerical example. A sensitivity analysis has been performed.