Abstract. Agile methodologies, particularly Large-Scale Scrum (LeSS), play a crucial role in managing complex software development projects involving multiple teams. However, scaling Agile across large organizations presents challenges such as inter-team coordination, resource optimization, and backlog management. This study introduces a mathematical model designed to enhance Agile project management within the LeSS framework by quantifying and optimizing key variables, including team velocity, sprint duration, the number of teams, and backlog size. The developed model mathematically represents the relationships between these variables, enabling a systematic approach to predicting project completion time and assessing overall performance. Implemented in Python, the model was tested across various simulated scenarios to evaluate its effectiveness in real-time decision-making. The results demonstrated the model’s capability to identify bottlenecks, improve resource allocation, and enhance workflow efficiency. A comparative analysis with real project data confirmed the model’s predictive accuracy and practical utility in Agile environments.

Keywords: Agile, Large-Scale Scrum, mathematical modeling, Agile project management, resource optimization, software development efficiency.