Extending Resource Constrained Project Scheduling to Mega-Projects with Model-Based Systems Engineering & Hetero-functional Graph Theory
Amirreza Hosseini, Amro M. Farid
TL;DR
This work addresses the fragmentation between the Resource-Constrained Project Scheduling Problem ($RCPSP$) and Model-Based Systems Engineering ($MBSE$) plus Hetero-functional Graph Theory ($HFGT$) in megaproject contexts. It introduces a constructive translation pipeline from an Activity-on-Node ($AoN$) network to a SysML activity diagram ($ACT$) and an operand net, and shows that the Hetero-functional Network Minimum Cost Flow ($HFNMCF$) can be specialized to RCPSP, proving that $RCPSP$ is a formal special case of the broader $HFNMCF$ framework. The authors demonstrate, via renewable and non-renewable operand instances, that the operand-net formulation yields explicit project-state descriptions (input/output firing vectors, markings) that enhance monitoring, control, and integration with earned value/schedule analyses, while preserving RCPSP strengths. This reconciliation enables a principled pathway from enterprise architecture to executable schedules for complex megaprojects, offering a unified, state-based view that can adapt to real-world constraints beyond classical RCPSP. The approach also suggests that the broader $HFNMCF$ model can capture multi-resource, multi-method, and exogenous constraints essential for modern enterprise-scale delivery. Key mathematical constructs include the $AoN$-to-$ACT$ transformation, the operand net state transition function $Q_{Sl}[k+1]= ext{(ODE-like incidence)}$, and the RCPSP specialization equations $Z_{RCPSP}= \sum_{k=1}^{K-1} [k\cdot e_n]^T U^-_{l}[k]$ with capacity and precedence constraints, illustrating equivalence with $RCPSP$ solutions while exposing richer state information for monitoring and control.
Abstract
Within the project management context, project scheduling serves as an indispensable component, functioning as a fundamental tool for planning, monitoring, controlling, and managing projects more broadly. Although the resource-constrained project scheduling problem (RCPSP) lies at the core of project management activities, it remains largely disconnected from the broader literature on model-based systems engineering (MBSE), thereby limiting its integration into the design and management of complex systems. The original contribution of this paper is twofold. First, the paper seeks to reconcile the RCPSP with the broader literature and vocabulary of model-based systems engineering and hetero-functional graph theory (HFGT). A concrete translation pipeline from an activity-on-node network to a SysML activity diagram, and then to an operand net is constructed. Using this representation, it specializes the hetero-functional network minimum-cost flow (HFNMCF) formulation to the RCPSP context as a systematic means of HFGT for quantitative analysis and proves that the RCPSP is recoverable as a special case of a broader model. Secondly, on an illustrative instance with renewable and non-renewable operands, the specialized HFNMCF, while producing similar schedules, yields explicit explanations of the project states that enable richer monitoring and control. Overall, the framework preserves the strengths of the classical RCPSP while accommodating real-world constraints and enterprise-level decision processes encountered in large, complex megaprojects.