Price-sensitive imperfect production inventory model with exponential partial backlogging

In this paper, we present an imperfect economic production inventory model considering partially backlogged situations at the beginning of the cycle. Here, all defective/imperfect quality items are reworked after the regular production process and the reworked items are considered as similar as good quality products. During production process demand is met by non-defective items only. Rework is inevitable in those industries where end product is expensive and raw materials are inadequate. The ratio of defective item production rate and production rate is taken to be a random variable. In this model, demand is taken as price sensitive and it is a monotonic decreasing function of selling price. Our objective is to optimise the expected average profit for the model of the decision variables: selling price, order quantity and backorder level. The sensitivity of the key parameters is examined to test the feasibility of the model. Finally, a numerical example is provided to investigate the proposed model.