A multi-objective model for closed-loop supply chain network based on carbon tax with two fold uncertainty: An application to leather industry

The sustainable development goals give very keen importance to the reduction of total carbon emission through industries round the globe. Industries are thus focussing on the reduction of their total carbon emission in accordance with the government and other environmental organizations' policies. In this paper, we focus on developing a multi-objective Closed-Loop Supply Chain model to optimize the distribution plan that minimizes the transportation and other operational costs and carbon footprint. Also, we use the concept of carbon tax in the mathematical model, which can help the decision-maker to decide optimal internal carbon price for the firm. Keeping in mind the uncertainty that inherently exists in data, we consider the parameters as fuzzy rough numbers, and to deal with such numbers we use the concept of two fold uncertainty. To exhibit the effectiveness of the model, we discuss a case study of a small-scale leather industry based in India. The results show that the carbon price of INR 2500 is best for the firm to reduce the carbon emission up to required level. The present study will be of much use for the industries to control carbon emissions by internally adopting the optimal carbon tax. In the numerical application, we have done a sensitivity analysis to check the impact of different carbon taxing scenarios on the carbon emission and total supply chain optimization cost.