We study a new class of problems—recurrent projects with random material de- lays, at the interface between project and supply chain management. Recurrent projects are those similar in schedule and material requirements. We present the model of project-driven supply chain (PDSC) to jointly optimize the safety-stock decisions in material supply chains and the crashing decisions in projects. We prove certain convexity properties which allow us to characterize the optimal crashing policy. We study the interaction between supply chain inventory decisions and project crashing decisions, and demonstrate the impact of the PDSC model using examples based on real-world practice.