Integrated vendor-buyer inventory model considering imperfect quality and inspection errors with controllable lead time

A joint production-inventory model of two-stages (vendor-buyer) for items by considering defective items and inspection errors with controllable lead time is developed in this paper. The assumption of the demand is assumed to be normal distribution. The production process is not perfect, which is produces a paticular number of defective items. An inspection process of the shipment lot is hold by the buyer to sort out the item qualities. The human inspector may missclassify a defective item as a good one or missclassify a good item item as defective one. The lead time of shipment can directly affects inventory investment in safety stock, the customer service level, and the competitive abilities of a business, so we decide to take lead time also as control object. An optimal solution for the expected integrated total annual cost is provided and for the illustrative purpose, numerical example is also presented. This paper gives complement to the current literatures that used in this study, so that this one model can cover all aspects that considered in the previous literatures.