Coordination of a socially responsible two-stage supply chain under random yield and demand

This study integrates corporate social responsibility (CSR) and channel coordination in a supply chain (SC) under random yield and random demand. In the SC, a supplier with random yield determines wholesale price and production input, and a producer with CSR decides order quantity and CSR investment facing CSR-related random demand. For centralized SCs with and without CSR, we prove the unimodality of the expected profits of the SCs for generic random yield and demand, and show the uniqueness of optimal ratio of order quantity to production input quantity. We disclose that the optimal expected profit of the SC with CSR is larger than that of the SC without CSR, and the profit difference increases with CSR effort and expected yield. We also find that the optimal CSR investment increases with the expected yield. Subsequently, the Nash equilibrium solutions of decentralized SCs under wholesale price and revenue-sharing contracts are analyzed. Next, we present a revenue and CSR sharing contract to realize channel coordination and win-win of SC members and related stakeholders. Lastly, we verify theoretical statements of centralized and decentralized SCs versus three numerical examples, and present managerial insights for the effect of yield uncertainty and CSR effort.