Supply chain project management is a comprehensive process allowing managers to coordinate resources, functions and actions to achieve a specific goal within a set time frame, scope and budget. One of the problems in the context of improving the quality of the Supply Chain Project Management is the creation of a favorable social environment for employees who are a crucial part of the supply chain management (SCM) system. In this article, this issue is considered from the perspective of the assignment problem. First, this article proposes the Corporate Social Responsibility (CSR) as a platform for introducing Lean practices within the supply chain. It strongly contributes to filling the research gap in the field of the CSR and Lean philosophy coordination. The ultimate goal is to promote the culture of continuous improvements, human resources (HR) development and satisfaction of workers’ social needs for the sustainability of the Supply Chain Project Management. Second, the Hungarian method is implemented in the context of the coordination of CSR and Lean management for right decisions in assignment problem concerning the issues of supply chain employees’ engagement and development. The results reveal the possibility of achieving positive effects in creating an employee-friendly supply chain environment and unlocking untapped human potential while maintaining long-term benefits. The research findings would assist the scientific community and practitioners in applying proposed ways to enhance labor productivity and ensure the development of employee-friendly social environment.