As institutions seek to reduce their environmental impact, administrative processes must be optimized for energy and resource efficiency. This study integrates control theory with P-graph methodology to develop a structured framework for sustainable administrative workflows, focusing on university enrollment systems. P-graph-based optimization identifies minimum-energy pathways and optimal resource configurations, while Model Predictive Control (MPC) and nonlinear control enable real-time process adaptation under dynamic conditions. A Life Cycle Analysis (LCA) compares the carbon footprint of digital and paper-based workflows, evaluating IT infrastructure energy use versus traditional operations. Simulated control strategies support energy-efficient decision-making, highlighting best practices for emission reduction and operational flexibility. The result is a decision-support framework that embeds P-graph into a dynamic control context, guiding control strategy selection to minimize energy use and emissions. This scalable approach supports sustainability-oriented process management across public service domains.