Optimal lot-sizing integration policy under learning and rework effects in a manufacturer–retailer chain

Most research in economic manufacturing/order quantity management assumes that all products are of perfect quality and are produced at a constant production rate. One result of this assumption is that the number of units produced in a given period is constant, which is not the case in real life. Most production systems produce items which are of perfect quality along with some that are of imperfect quality. Defective items, as well as the learning effect, affect production and inventory costs, thereby shaping the performance of the manufacturer–retailer chain. The present study uses the Nash, Stackelberg, and cooperation games to model an imperfect production system to investigate the combined effects of lot-sizing size integration, the learning effect, imperfect production, and the rework process on a manufacturer–retailer channel. This study also demonstrates the optimal properties of the proposed models, develops a search algorithm for obtaining optimal solutions, and conducts a numerical study to seek structural and quantitative insights into the structure of the proposed models. In addition it analyzes the sensitivity of the solutions in relation to the major parameters.