Sustainability in the supply chain is becoming more and more important for industrial enterprises in different sectors. This research article focuses on construction supply chains (CSCs) in the Engineer-to-Order (ETO) industry, where every product is almost unique based on specific customer needs and requirements. The development of methods and approaches for more sustainable supply chain management in construction is becoming even more important. Engineering, fabrication of parts and their installation on-site are not always well synchronized in ETO supply chains. The results of such supply chains are long lead times, inefficient material transport and high and uncontrolled levels of work-in-progress (WIP). This article describes a conceptual approach to synchronize demand on-site with supply in manufacturing using the CONstant Work In Progress (ConWIP) concept from Lean Management to achieve Just-in-Time (JIT) supply. As a result, sustainable supply chains in ETO enterprises, with optimizations from an economic, ecological and social point of view, can be designed. The approach has been validated in an industrial case study.