A bilevel programming model for corporate social responsibility collaboration in sustainable supply chain management

•The model improves global and individual profits simultaneously.•The model helps to evaluate the distribution of profits and CSR in advance.•Sometimes proper compensations are necessary to ensure higher individual profits.•A firms with a rather high unit cost of CSR may result in no CSR investment in SC.

This study proposes a bilevel programming model in which the supply chain (SC) director determines optimal performance levels of corporate social responsibility (CSR) and compensation for all SC actors, thus maximizing total SC profits. Given the fixed CSR performance levels, the equilibrium product flows are determined in the lower-level model, in which the profit-maximizing behavior of the individual SC actor is considered and formulated as a variational inequality. The test results show that it is possible to improve not only performance of CSR, but also the profits of both individual SC actors and the whole SC through proper SC collaboration.