Exact Delivery Under Resource Limits: Logic-Driven Project Scheduling

Project leaders frequently confront strict precedence dependencies and scarce renewable capacities; this paper presents a decision-support approach that computes optimal schedules minimizing completion time under binding resource limits for real-world projects. The method models precedence as difference constraints and captures resource usage with compact Boolean formulations that exploit natural at-most-one structures in project networks, enabling highly efficient solving by modern logic engines. Two complementary designs are provided—time-indexed and activity-indexed—augmented by preprocessing for extended precedences, energy-based lags, and feasible time windows to tighten the search space and improve tractability. Evaluated on diverse benchmark portfolios, including multi-mode activities and time-varying capacities, the approach consistently solves more instances and certifies optimality or infeasibility faster than leading exact techniques, while improving upper bounds in many challenging cases relevant to portfolio governance. For practitioners and PMOs, the contribution yields robust resource-feasible baselines, transparent trade-offs between modeling choices, and repeatable, audit-ready schedule decisions that generalize across project types without reliance on heuristics.