Mathematical Models for Management Information Systems on Digital Platforms: from Resource Management to Demand Forecasting

In the current conditions of development of digital platforms, efficient resource management, load optimization and accurate demand forecasting are key tasks to ensure their productivity and stability. The article deals with mathematical models and algorithms used for information management systems of digital platforms. The use of optimization methods, graph algorithms, forecasting, and machine learning to improve the efficiency of digital systems is investigated. Particular attention is paid to mathematical approaches to load balancing, resource allocation, and platform scalability. The application of graph theory to analyze the relationships between users, content, and services, as well as Dijkstra and Floyd-Warshell algorithms for optimal data routing, is described. Linear and integer programming methods are considered to find optimal solutions for allocating computing power and reducing costs. Stochastic and heuristic approaches to demand forecasting, including machine learning, gradient descent, and genetic algorithms, are analyzed. The use of maximum flow and minimum cut algorithms for efficient management of network resources and minimization of delays is described. The methods of discrete event and continuous modeling for analyzing dynamic changes in digital systems are proposed. The results obtained can be used to increase the adaptability of digital platforms to changing operating conditions, reduce the risk of overloading, and improve user experience. The presented mathematical models contribute to the development of effective mechanisms for managing digital services, which is critical for their reliable and sustainable operation. Keywords: digital platforms, mathematical models, resource management, load balancing, demand forecasting, optimization, Dijkstra and Floyd-Warshell algorithms, genetic algorithms, discrete simulation.