Two Echelon Supply Chain Model with lead time and effect of carbon emission under fuzzy environment

Carbon emission has become a major challenge everywhere, such as in the production process, holding items, deteriorating items, waste disposal, and transporting items. Two warehouses are a realistic approach in inventory modeling. Inflation and lead time play a key role in making this study closer to reality. Uncertainty is also a very realistic approach for any organization. In this study, we developed a supply chain model in which there is one retailer and one supplier. The retailer holds its inventory in two warehouses. Our objective is to find the optimal total cost, cycle length, and supplier's lead time. In this study, we calculate the total cost in three different ways: first, for the crisp model; second, for the fuzzy model using the signed distance method; and third, using the graded mean integration method. We carried out the numerical solution using the software MATHEMATICA 12.0. From numerical illustration, we find that the total cost is minimum for the fuzzy model using the graded mean integration method. Sensitivity analysis is carried out to see the behavior of different parameters on the total cost.