A closed-loop supply chain inventory model with stochastic demand, exchange rate, green investment, and carbon tax

In this paper, a mathematical inventory model for a closed-loop supply chain consisting of a single manufacturer and a single retailer is investigated under a stochastic environment and imperfect production. The manufacturer adopts a remanufacturing policy to recover returned products from the market. The model takes into account exchange rate disparities because the supply chain’s participants are in separate countries. The model also considers carbon emissions, which are expected to be produced from storage, transportation, and production. A carbon policy, namely carbon tax, is implemented to manage the overall emissions resulting from the supply chain. To cope with carbon restrictions, the manufacturer has an opportunity to invest in green technologies. The objective of the study is to find optimal shipment quantity, number of deliveries, safety factor, and green investment such that the joint total cost is minimized. An iterative procedure is suggested to solve the proposed problem, and a numerical example is presented for model validation. The findings imply that variations in the production rate and carbon tax have a significant influence on the model’s performance. Aside from that, the results reveal that uncertainty in the exchange rate and production flaws are important factors that must be considered by managers in making inventory decisions, especially those related to the number of deliveries, frequency of deliveries, and the amount of money invested in green technology. Finally, a sensitivity analysis is provided to explain the behavior of the model.