Due to heavy transportation for single-setup multidelivery (SSMD) policy in supply chain management, this model assumes carbon emission cost to obtain a realistic behavior for world environment. The transportation for buyer and vendor is considered along with setup cost reduction by using an investment function. It is assumed that the shipment lot size of each delivery is unequal and variable. The buyer inspects all received products and returns defective items to vendor for reworking process. Because of this policy, end customers will only obtain nondefective items. The analytical optimization is considered to obtain the optimum solution of the model. The main goal of this paper is to reduce the total cost by considering carbon emission during the transportation. A numerical example, graphical representation, and sensitivity analysis are given to illustrate the model.
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