Optimizing inventory decisions for a closed–loop supply chain model under a carbon tax regulatory mechanism

Green supply chain management encompasses every level of the supply chain. The core green supply chain management strategies include closed–loop manufacturing and reduction of carbon footprint. These strategies enable firms to improve their environmental profile and to comply with environmental regulations. This paper deals with a supply chain system integrating manufacturing, remanufacturing and repair activities (closed–loop manufacturing) to face a time-varying demand under the regulatory framework for carbon tax. Initially, the total cost of the system is provided and then a mixed integer nonlinear programming problem is formulated aiming to determine the optimal policy i.e. the manufacturing, remanufacturing and repairing cycles. After decomposing the original problem into two pure manufacturing and remanufacturing sub-problems, the existence of their optimal solution is proved and then a simple method, which relies on a finite search scheme, is used to determine the overall optimal solution. Through a variety of numerical examples and a sensitivity analysis, the effect of the different system parameters on costs and environmental efficiency are provided, such as: returns, carbon emissions generated per activity and rates of any activity. The main result of this analysis indicates that the proposed model is fairly robust to the parameters’ changes, however the tax on carbon emissions has a serious impact on the system optimal cost.