Resumen
The subject of research in the article is the network of closed logistics. The goal of the work is the creation of mathematical models and methods for solving problems of optimizing transportation routes in closed-loop logistics systems, taking into account many topological and functional limitations. The following tasks are solved in the article: the development of a systemological model for the problem of optimizing transportation routes in a closed logistics system; development of a mathematical model of the problem of structural and topological optimization of a three-level centralized network of closed micro-logistics routes for global transportation; development of a mathematical model for the optimization of ring transportation routes in a closed logistics system for local transportation; development of methods for optimizing ring transport routes in a closed logistics system. The following methods are used: methods of system theory, graph theory, methods of the theory of utility, optimization and research of operations. The following results were obtained: the decomposition of the problem of optimizing transportation routes in closed-loop logistics systems at the macro and micro levels was performed; a systemological model of the problem has been developed, which reflects the whole complex of tasks that are solved at various stages of the life cycle of logistics systems. To improve the efficiency of closed-loop logistics systems, a joint solution to the problems of network optimization for the transportation of direct product flows and return flows has been proposed. A mathematical model of the problem of structural and topological optimization of a three-level centralized network of closed micro-logistics routes for global transportation has been developed. To solve such problems, methods using directed enumeration of options are recognized effective; a mathematical model of the optimization problem of the network of closed micro-logistics routes for local transportation with the simultaneous transportation of the contents of the forward and reverse flows was developed; To solve the problem of optimizing closed-loop micro-logistics route networks at the local transportation level while simultaneously transporting the contents of the forward and reverse flows, modifications of the Clark-Wright methods are proposed, as well as a method based on coordinate-wise optimization and insertion schemes; experimental studies of the proposed modifications of the methods made it possible to obtain estimates of their temporal complexity. Conclusions: Practical use of the proposed mathematical models and modifications of methods for optimizing closed-loop logistics systems by jointly solving problems for direct and reverse flows will reduce the cost of implementing transport companies. The obtained estimates of the time complexity of the optimization methods will make it possible to predict the costs of computing and time resources in their practical use for solving optimization problems of closed-loop logistics networks.