Optimal Policy for a Simple Supply Chain System with Defective Items and Returned Cost under Screening Errors

Recently, one of the most interesting topics in supply chain management (SCM) is the integrated vendor-buyer production-inventory problem, in which the critical issue is to determine economic lot size per shipment and deliveries. Most researches on this issue assume that products are screened and the process is perfect; however, screening errors (including type-I and type-II) may occur with imperfect quality in practice. In this paper we consider a simple single-vendor single-buyer supply chain system in which products are received with defective quality, and 100% screening process is performed with possible inspection errors. The objective of this paper is to determine the optimal number of shipments as well as the size of each shipment in order to minimize the joint annual cost incurred by both vendor and buyer. We develop a cost model for the supply chain system and propose a solution procedure to find the optimal solution. A numerical example is given to illustrate the application of the model. Besides, based on the numerical example, a sensitivity analysis is also made to investigate the effects of five important parameters (the inspection rate, the annual demand, the defective rate, Type I error, and Type II error) on the optimal solution.