Effect of variable transportation and carbon emission in a three-echelon supply chain model

•A three-echelon supply chain is considered with SSMD policy.•Variable transportation and fixed transportation cost are used.•Variable carbon emission and fixed carbon emission cost are used.•The total cost is reduced with analytical procedure.

Several industries controls carbon emission during transporting products due to increased transportation for obtaining the best transportation way with reduced cost. This study considers a three-echelon supply chain model where the supplier makes semi-finished products and transports to manufacturer for finished products. The manufacturer transports products by single-setup-multi-delivery policy to multi-retailer. The aim of the model is to reduce the supply chain cost by considering variable transportation and carbon emission costs are considered due to several shipments. An algebraic approach is employed to obtain the closed-form solution. Numerical example, sensitivity analysis, and graphical representations are given to illustrate the model.