MATHEMATICAL METHODS IN LOGISTICS AND MARKETING: ENHANCING MANAGEMENT EFFICIENCY AND PROCESS OPTIMIZATION

The article explores the application of mathematical methods in logistics and marketing to enhance management efficiency, optimize processes, and increase the competitiveness of enterprises. Logistics and marketing processes are becoming increasingly complex, necessitating the implementation of modern mathematical approaches to planning, forecasting, and decision-making. In particular, linear programming methods are examined, which are used for resource allocation, cost minimization, and determining optimal transportation routes. Graph theory enables the analysis of transportation and communication networks, as well as the identification of the most efficient delivery routes and interactions between marketing entities. Queueing theory helps manage queues and distribute workloads in logistics centers and service systems. Simulation modeling allows for the assessment of the effectiveness of logistics schemes and marketing campaigns in a virtual environment before their implementation. A separate focus is given to the application of machine learning and big data analysis in logistics and marketing. Artificial intelligence algorithms contribute to improving demand forecasting accuracy, analyzing consumer behavior, automating inventory management, and selecting personalized marketing offers. The study explores the use of clustering methods, neural networks, and genetic algorithms for business process optimization. The article also presents an analytical review of real-world cases of mathematical methods applied in logistics and marketing. It demonstrates how mathematical models help international corporations reduce transportation costs, enhance customer service levels, effectively manage inventories, and adapt marketing strategies to market changes. The study analyzes sales forecasting methods, distribution management, selection of optimal supply channels, and the personalization of advertising campaigns. Thus, the research substantiates that the use of mathematical methods in logistics and marketing is a key success factor for enterprises in the modern competitive environment. Optimization algorithms, graph models, simulation modeling methods, and artificial intelligence not only improve business process management efficiency but also facilitate the implementation of innovative approaches in logistics and marketing.