The subject of research in the article is the process of supporting decision-making in the tasks of optimizing closed logistics networks at the stage of reengineering. The goal of the work is to improve the efficiency of technologies for the automated design of closed logistics networks due to the improvement of mathematical models of multi-criteria problems of reengineering their topological structures. The following tasks are solved in the article: review and analysis of the current state of the problem of supporting decision-making in the tasks of optimizing logistics networks at the stage of their reengineering; decomposition of the problem of optimization of logistics networks at the main stages of their life cycles; selection of a logical scheme of the reengineering process of the logistics network as a territorially distributed object; development of a mathematical model of the general problem of multi-criteria optimization of logistics networks according to indicators of economy, efficiency, reliability and survivability; selection of models for scalar multi-criteria evaluation of reengineering options, taking into account factors that are difficult to formalize, knowledge and experience of the decision-maker. The following methods are used: system approach, theories of systems, theories of usefulness, theories of decision-making, system design, optimization and operations research. Results. Decomposition of the reengineering problem was carried out on the following tasks: determination of the purpose of reengineering and the principles of network reconstruction; network structure optimization; optimization of the topology of network elements; selection of functioning technology; determination of parameters of elements and vehicles; assessment and selection of the best network construction option. The general mathematical model of the multi-criteria task of reengineering the topological structures of centralized three-level logistics networks based on the indicators of costs, cargo delivery time, reliability and survivability has been improved. Universal functions of general utility and utility of local criteria are proposed to obtain scalar estimates for multiple indicators. Exclusion of part of local criteria and restrictions from the general model allows obtaining models of practically all interesting problems of optimization of logistics networks. Conclusions. The developed complex of mathematical models expands the methodological principles of automating the processes of designing logistics networks, allows for the correct reduction of a set of effective options for their construction for the final choice, taking into account factors that are difficult to formalize, the knowledge and experience of designers. The practical use of the proposed complex of mathematical models will reduce the time and capacity complexity of project decision-making support technologies, and due to the use of the proposed options selection procedures, increase their quality based on a number of functional and cost indicators.