Abstract: Recently, more and more firms are paying attention to improving corporate social responsibility (CSR). Many researchers have realized this important issue in supply chain management, and further attempt to analyze how to effectively make CSR investment under various decision-making environments. However, few studies have addressed the joint pricing and CSR investment decisions in the closed loop supply chain. On this basis, we aim to fill this research gap by exploring the effect of CSR investment on the optimal decisions and profits in the closed loop supply chain.
Based on observations in the industry, Four following types of CSR investment are considered:(1) No CSR investment:neither of the manufacturernor the retailer makes CSR investment; (2) Manufacturer CSR investment:only the manufacturer makes CSR investment. (3) Retailer CSR investment:only the retailer undertakes the CSR investment activity; and (4) Joint CSR investment:both the manufacturer and the retailer jointly make CSR investment. In the closed loop supply chain, the manufacturer is responsible for collecting the used product. The standard Stakelberg game is used to model the interplay between the manufacturer and the retailer in the closed loop supply chain, the manufacturer is the channel leader and the retailer is the follower. Then, using first-order conditions, the equilibrium prices, equilibrium CSR investment level, equilibrium return rates and the optimal profits are obtained for each channel player and the system under the centralized and the decentralized models. By comparing the equilibrium decisions and profits among different models, it is found that the type of joint CSR investment is optimal for the manufacturer, the retailer and the chain system.In addition, the retailer is the better undertaker of the CSR activity than the manufacturer. However, the result shows that the equilibrium price is the highest under the joint CSR investment case compared with other CSR investment types. Hence, the consumers need to share a larger portion of the CSR investment costs under this case.
The decentralized models have an efficiency loss because of the "double marginalization" effect in the closed loop supply chain. Therefore, how to coordinate the decentralized closed loop supply chains with the CSR constraint is explored. The result shows that the two-part tariff contract can perfectly coordinate the channel under different CSR investment types. By comparing the optimal parameters of the contract, it is found that the manufacturer's bargaining power in the contract is the lowest under the case of joint CSR investment; on the contrary, the retailer's bargaining power is the strongest under this scenario. Finally, a numerical example is used to analyze the impact of some key parameters on equilibrium decisions and explore the effectiveness of the contracts. Our results are helpful for the future research of the closed loop supply chain management. Furthermore, our research also provides certain support for firms in making CSR and collecting decisions, and helps the government to set relevant policies.

Key words: closed-loop supply chain, corporate social responsibility (CSR), pricing, supply chain coordination, two-part tariff contract