Optimal control of carbon emission reduction strategies in supply chain with wholesale price and consignment contract.

To further reduce carbon emissions, supply chain members implement the low-carbon production process and use varieties of contracts to coordinate the channel. Considering the effect of emission reduction, this paper studies a two-echelon supply chain consisting of one manufacturer and one retailer. Two supply chain members dedicate to maximize profits by reducing their products' carbon emissions under two different contracts: the wholesale price contract and the consignment contract. The Stackelberg differential game is used, and the optimal strategies of emission reduction effort, wholesale, and retail price in the two situations are studied. The results show that the Pareto improvement for the whole supply chain can be reached under the consignment contract. However, the specific impacts on the retailer and the manufacturer are different. When consumers have a higher level of environmental awareness, the retailer tends to decrease her proportion of sales revenue under the consignment contract. At that time, choosing the wholesale price contract is more favorable for the retailer. However, as the retailer's proportion of sales revenue becomes lower, the proportion of revenue belonging to the manufacturer will increase. It would be better for the manufacturer to choose the consignment contract.