A Hetero-functional Network Minimum Cost Flow Formulation to Resource Constrained Project Scheduling

In engineering management, project scheduling is an indispensable function in the planning, monitoring, and control of projects. The presence of scarce resources and precedence relationships among activities makes project scheduling inherently complex. Although the resource-constrained project scheduling problem (RCPSP) lies at the core of project management, it remains largely disconnected from the broader literature on model-based systems engineering (MBSE), thereby limiting its integration into the design and management of enterprises as complex systems. This paper specializes the hetero-functional network minimum-cost flow (HFNMCF) formulation to the RCPSP context. Using an illustrative instance with renewable resources, the specialized HFNMCF formulation reproduces identical schedules to those of the resourceconstrained project scheduling problem while providing additional explicit insight into project states, facilitating more precise project monitoring and control. Therefore, these results show that model-based systems engineering and hetero-functional graph theory (HFGT) are a formal generalization of the RCPSP that are amenable to systematic extension through comprehensive taxonomies, enabling the incorporation of a wide range of real-world conditions and project scenarios. Overall, the framework preserves the strengths of the classical RCPSP while accommodating realworld constraints and enterprise-level decision processes encountered in large, complex megaprojects.