With the deepening of economic globalization and international division of labor, enterprises gradually turn to supply chain management methods that aiming at win-win cooperation. An enterprise’s corporate social responsibility (CSR) behaviors will affect the interests of other enterprises in the supply chain through transmission, diffusion, amplification, feedback, etc. Therefore, scholars are currently focusing on helping supply chain enterprises to take social responsibility. This paper takes a two-echelon supply chain as an example, which is composed of one manufacturer and one retailer. Considering the influence of lag effect on the performance level of corporate social responsibility, we discuss the optimal strategy of corporate social responsibility in supply chain under centralized and decentralized decision-making. Three incentive models are proposed to improve the implementation effect of decentralized supply chain decision. Study finds that, in real life, decentralized supply chain is more in line with the decision-making mode of supply chain participants, even though centralized decision-making has better operation effect. Under certain circumstances, the mixed contract, which is composed of advertising cooperation, cost sharing and revenue sharing, could lead to supply chain coordination. As an external stakeholder, the government's subsidy plays a positive role in promoting the fulfillment of corporate social responsibility. Multi-subsidy performs better than single-subsidy. Although the time lag promotes the manufacturer's social responsibility efforts and the retailer's advertising, it somehow compromises overall profit of the supply chain. Therefore, manufacturers should try to reduce the lag effect to maintain the overall profitability of the supply chain.
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