Extended Vidale–Wolfe model on joint emission reduction and low-carbon advertising strategy design in a secondary supply chain

Under the low-carbon economy environment, downstream retailer advertises upstream manufacturer's reduction to achieve better market performance, which is a common form of cooperation in low-carbon supply chain management. This paper assumes that the market share is dynamically influenced by product emission reduction and the retailer's low-carbon advertising. First, the Vidale–Wolfe model is extended. Second, from the perspective of centralization and decentralization, four differential game models of manufacturer and retailer in the two-level supply chain are constructed, while the optimal equilibrium strategies in various situations are compared. Finally, using Rubinstein bargaining model, the profit obtained by the secondary supply chain system is distributed. The main results are as follows: (1) The unit emission reduction and market share of manufacturer are rising with time. (2) The profit of each member of the secondary supply chain and the whole supply chain is always optimal under the centralized strategy. Although the advertising cost allocation strategy achieves the Pareto optimal under the decentralized situation, it still cannot reach the profit of the centralized strategy. (3) The manufacturer's low-carbon strategy and the retailer's advertising strategy have played a positive role in the secondary supply chain. The profits of the secondary supply chain members and the whole are on the rise. (4) As the leader of the secondary supply chain, it is more dominant in profit distribution. The results can provide theoretical basis for the joint emission strategy of supply chain members in low-carbon environment.