A closed-loop supply chain inventory model with stochastic demand, hybrid production, carbon emissions, and take-back incentives

This paper considers a two-echelon inventory model for a closed-loop supply chain system containing a manufacturer and a retailer under a stochastic environment with carbon emission reductions. Production and remanufacturing are performed simultaneously in a manufacturer's hybrid production system involving green production and regular production. To encourage the manufacturer to reuse products, the government offers a take-back incentive operating under a collection rate target. Motivated by this offer, the manufacturer significantly improves the system and makes an investment to increase the number of used products collected from the customers. The emissions generated from transportation, production, and storage activities are incorporated into the model and intended to be reduced by a carbon tax regulation. To achieve this, a mathematical inventory model that aims to minimize the joint total cost is built and solved using an efficient procedure. The results show that by controlling the collection rate and the production allocation, the system can minimize the cost and the emissions. Further, the take-back incentive and the manufacturer's investment in collection efforts can effectively increase the return rate of used products, but these policies will lead to an undesirable increase in total emissions.