Optimal production policy for a closed-loop supply chain with stochastic lead time and learning in production

Document Type: Article


Department of Mathematics, Jadavpur University, Kolkata - 700032, India



This paper considers a closed-loop supply chain with one manufacturer and one retailer for trading a single product. On behalf of the manufacturer, the retailer collects the used items from the end customers for possible remanufacturing. The production of the finished product (manufactured and remanufactured) is subject to learning. The lead time at the retailer is assumed to be stochastic. The manufacturer delivers the retailer’s order quantity in a number of equal-sized shipments. The objective is to determine the optimal
number of shipments and shipment size by minimizing the average expected total cost of the closed-loop supply chain. A solution method for the model is presented and important results are obtained for numerical examples. From the numerical study, an impressive cost reduction due to consideration of learning in production and remanufacturing is observed. To investigate the impact of key model-parameters on the optimal results, a sensitivity analysis is also carried out. The proposed model is applicable to those business firms where production process is executed by the human beings.