A vendor-buyer inventory model with imperfect production considering investment to reduce lead time variability

This research develops an integrated single-vendor single-buyer inventory model considering imperfect production process and investment to reduce lead time variance. In the model, we consider a system where the buyer's lead time is uncertain and follows a normal distribution. Inspection process is performed by the buyer to classify the defective items in each lot delivered from the vendor. The defective items that were found by the buyer will be returned to the vendor at the next delivery. The shortages are allowed and assumed to be fully backordered. The objective function of the model is to minimize the expected joint total cost of the system by simultaneously determining the optimal shipment lot size, optimal safety factor, optimal target variance reduction of lead time and optimal number of shipments. Further, a numerical example is provided to illustrate the application of the proposed model. Based on the results, we understand that by applying the investment policy to reduce lead time variance, the system may improve its service level at a lower cost. Thus, we conclude that the investment policy is proved to give better outcomes to the system.