This article examines the theoretical foundations and optimization methods of logistic supply chain management in the Armed Forces of Azerbaijan. It highlights the decisive role of logistics in modern warfare by analyzing lessons from recent conflicts and comparing military and commercial supply chains. The study emphasizes the importance of transport logistics systems and explores mathematical and algorithmic approaches including Mixed Integer Linear Programming (MILP), simulation models and game theoretic methods for enhancing efficiency, resilience and flexibility. Comparative analysis with International practices, particularly NATO standards and Industry 4.0 applications, reveals both strengths and areas for improvement in Azerbaijan's logistics model. The findings suggest that integrating scientific optimization methods and advanced technologies into logistic support systems can significantly strengthen combat readiness, ensure sustainable supply and improve resource utilization in both wartime and peacetime contexts.