The article presents a comprehensive study of the possibilities of applying mathematical optimization methods to improve the efficiency of managing organizational systems, using the example of forensic expert institutions. The work focuses on a critical analysis and adaptation of classical assignment theory to the realities of managing expert activities, which are characterized by high responsibility, diverse tasks, and strict procedural limitations. The evolution from simple linear assignment models to complex, multi-criteria, and generalized formulations that can adequately reflect the requirements for quality, urgency, and workload balance is analyzed in detail. The theoretical foundations and limits of applicability of key optimization paradigms, such as scheduling theory, the transportation problem, and the traveling salesman problem, have been investigated.

Keywords: management of organizational systems, resource allocation optimization, assignment theory, multi-criteria optimization, generalized assignment problem, load balancing, expert activity management, scheduling algorithms, decision support system