An integrated inventory model for items with acceptable defective items under warranty and quality improvement investment

The purpose of this paper is to investigate a single-vendor single-retailer production-inventory for products with imperfect quality under the conditions that the retailer gives a warranty policy of non-renewing free replacement for failure of perfect items within a warranty period and makes a quality improvement investment in the defective percentage. It is assumed that the defective items of each lot that the retailer receives are screened out by a 100% inspection process and then are sold in a single batch by the end of the inspection process and that the defective items can be utilized as perfect quality, which are called acceptable defective items. First, the expected annual integrated total profit is constructed with a uniformly distributed defective percentage. Then, by maximizing the expected annual integrated total profit, the optimal quality improvement investment in the defective percentage, the optimal number of shipments in a cycle, and the optimal lot size of each shipment from the vendor to the retailer are determined. A numerical example is provided to demonstrate the proposed model.