A Coordinated Supply Chain Inventory Model for An Imperfect Quality Item with Credit Period Protege Procurement Cost and Learning Effects

This article develops an integrated production model which consists of a single manufacturer and a retailer for imperfect quality items, where a delay in payment is offered by manufacturer to the retailer. In this model retailer’s procurement cost linearly depends on the credit period. A screening process is applied on each batch of an imperfect quality items to separate the good and defective items by the retailer. Furthermore, manufacturer's process cost is considered as a linear function of the amount of quantity purchased by retailer. The purpose of this study is to determine the position of credit period and the number of replenishments of retailer in finite time so that the integrated system gets the optimum cost. The model has been verified with the help of numerical examples and a sensitivity analysis has been carried out through numerically, graphically, and analytically with respect to some key parameters.