Supply Chain Coordination with Energy Price Uncertainty, Carbon Emission Cost, and Product Return

An EOQ model for a coordinated two-level supply chain is developed under energy (gasoline) price uncertainty and defective items in transhipment. It is assumed that the transportation cost not only depends on the lot size, but also depends on the gasoline price uncertainty. The purpose is to determine the optimal production–shipment policy for the proposed model by taking into account the percentage of defective items, transportation cost, setup cost, screening cost, holding cost, and carbon emission cost. The objective is to determine the optimal number of shipments and the optimal order quantity that minimize the expected total cost per unit time. Expressions for the optimal order quantity, the optimal number of shipments, the optimal number of buyer’s cycle during which the defective items are stored at the buyer’s warehouse before shipping them to the vendor are derived by minimizing the expected total cost per unit time. In order to illustrate the proposed model, a numerical example is presented and results are discussed. It is found that as the gasoline price uncertainty increases, both the total cost and shipment size increase. This shows that the gasoline price influences the supply chain coordination. Moreover, when the fixed gasoline consumption depending on the vehicle size, type, or age increases, shipment size increases, the number of shipments decreases, and the total cost increases. This implies that when the truck size or type used for shipping changes, the supply chain coordination decision will also change. The variable gasoline consumption increases the total cost of the supply chain. Finally, a similar behavior is observed with respect to fixed and variable carbon emissions costs for the buyer.