DEVELOPMENT AND IMPLEMENTATION OF DIGITAL TOOLS FOR MULTI-LEVEL OPTIMIZATION OF MANAGEMENT PROCESSES IN VARIOUS ECONOMIC SECTORS: MATHEMATICAL MODELING OF LOGISTICS RISKS

This study is devoted to a comprehensive analysis of modern digital tools for multilevel optimization of management processes in logistics systems across various economic sectors, with a focus on mathematical modeling of risks. The paper presents a fundamental theoretical and methodological framework for optimizing logistics processes, including systematization of modern digital tools, methods of mathematical modeling, and risk prediction algorithms in the context of digital economic transformation. The analysis demonstrates that effective functioning of logistics systems under uncertainty requires the development of comprehensive integrated risk assessment models using advanced artificial intelligence technologies, big data, and multi-agent systems. Key components of such models include predictive analytics based on self-learning algorithms, realtime decision support systems, and mechanisms for processing heterogeneous information from multiple sources. The study revealed significant differentiation in approaches to mathematical modeling of logistics risks across various industries, determined by the specifics of production processes, characteristics of goods flows, and features of transport and warehouse infrastructure. It has been established that integrated TMS (Transportation Management Systems) and specialized software complexes for logistics process analytics demonstrate the highest effectiveness in the modern economy, providing multi-level optimization taking into account dynamic characteristics of risk factors. The paper identifies key determinants that define the effectiveness of digital tools implementation, including the degree of interoperability of logistics system components, adaptability of algorithms to changing environmental conditions, scalability of architectural solutions, and integration capabilities with existing enterprise information systems. Special attention is paid to the methodology of mathematical modeling of logistics risks, including probabilistic-statistical methods, fuzzy-set models, simulation modeling, and machine learning algorithms. An author's methodology for comprehensive risk assessment based on hybrid mathematical models has been developed and tested, combining the advantages of deterministic and stochastic approaches with big data processing technologies. The study demonstrates that the implementation of modern digital tools for logistics management can significantly reduce operational costs (by 15-30%), minimize logistics risks (by 25-40% on average), and optimize key business processes in supply chains. Based on the research, practical recommendations have been developed for implementing digital tools for multi-level optimization of logistics processes, taking into account industry specifics, business scale, and characteristics of existing IT infrastructure.