Impact of carbon emission in two-echelon supply chain inventory decision with controllable deterioration and two-level trade-credit period

The aim of the supply chain is to integrate environmental aspects with energy efficiency consumption. This study considers an integrated two-echelon green supply chain with carbon emission from production, warehousing, transporting, deterioration of items, as well as disposing waste. The deterioration rate is controlled by utilizing preservation technology investment. Also, for the fast-growing business, the suppliers offer credit period to the retailer, and the same credit period is offered by retailer to end customers, which works as an influential strategy for attracting new customers and has a positive impact on sales. The whole model is studied in an inflationary environment. The discussed model was solved analytically and obtained the optimal solution in a quasi-closed form solution; and simultaneously optimizes the optimal time and preservation technology cost in a two-echelon supply chain model considering controllable deterioration, waste, and carbon emission. To illustrate the present study, a numerical analysis and a sensitivity analysis have been presented. The convexity is obtained analytically as well as graphically. The objective is to minimize total cost and to reduce total carbon emissions. The analysis of the proposed model shows that the optimal results are quite realistic and can be applied to minimize total cost and reduce total carbon emission of supply chain integration.