Inventory decisions in a closed-loop supply chain system with learning and rework

In this study, we investigate a closed-loop supply chain model consisting of a manufacturer and a retailer. The retailer orders items from the manufacturer to satisfy the end customer's demand. The manufacturer uses both regular production and remanufacturing processes to produce items to fulfill the demand from the retailer. The returned items are collected and screened by the manufacturer for recovering process. We consider learning process in regular production and remanufacturing processes. In addition, the imperfect items produced during regular production are reworked. The model contributes to the current literature by allowing the inclusion of learning process in regular production and remanufacturing processes, imperfect items, rework and multiple cycle policy. Our objective is to optimise the percentage of the used item purchasing price per raw material cost, retailer ordering cycle, number of regular production cycles and the number of remanufacturing cycles, so that the joint expected total annual profit incurred has a minimum value. Furthermore, an algorithm is proposed to find the solutions of the proposed model. We also provide a numerical example and perform a sensitivity analysis to illustrate the model's behaviour and feasibility.