Mathematical Models of the Problem of Constructing Delivery Routes of Cargo in the Internal Zones of Trunk Nodes of a Hierarchical Transport Network
Authors: Vasyanin Volodymyr , Ushakova Liudmyla 
Published: June 2024

Introduction. The article discusses mathematical models of problems of constructing circular routes of vehicles in a multicommodity hierarchical network. As a rule, such networks consist of a decentralized backbone network and networks in the internal service areas of the backbone nodes (internal networks). In multicommodity networks, each node can exchange products (goods, cargo) with other nodes. In contrast to the distribution problems of a homogeneous interchangeable product, in multicommodity problems the flows of products are not interchangeable, the flow of each product must be delivered from a specific primary object to a specific customer. It is assumed that the multi-level structure of the transport network is defined and the geographical location of the main hubs and its internal service areas with a set of nodes for the delivery and collection of goods (customers) are known. Therefore, the problems of determining the main routes of vehicles and constructing circular routes of internal vehicles are considered independently of each other. The types of costs of real transport processes, which should be taken into account in the formation of the objective function of routing problems, are discussed and mathematical models of problems for constructing circular delivery routes with a heterogeneous fleet of vehicles are proposed. The possibility of solving the formulated problems with the help of well-known packages of mixed and integer linear programming is noted.
Purpose. The aim of the article is to formulate new mathematical models of the problem of constructing circular routes of vehicles in the internal networks of servicing the main nodes, which take into account the real costs of transport processes and the geographical features of internal networks.
The technique. The research methodology is based on the system analysis of many modern models, methods and algorithms for solving the problems of constructing circular routes for customer service in the internal zones of the main nodes of the hierarchical network.
Results. On the basis of the review and analysis of known mathematical models, several new variants of mathematical formulation of problems of designing routes of vehicles for the transportation of discrete cargo in the internal zones of the central nodes of the network have been developed. To solve the problems, precise, heuristic and metaheuristic methods and algorithms can be used, implemented in many commercial and non-commercial packages of mixed and integer programming programs, for example, IBM ILOG CPLEX, GAMS, AIMMS, Gurobi Optimizer, ABACUS, COIN-OR, GLPK, lp_solve. Many of them are available for free on the NEOS server (https://neos-server.org/neos/).
Scientific novelty and practical significance. The novelty of the work lies in the formulation of mathematical models of the problem of constructing circular routes of vehicles, which take into account the real costs of transport processes and geographical features of internal networks. The materials of the article form the methodological basis for the development of modern mathematical support for solving the problems of long-term, current and operational planning and management in the internal zones of the trunk nodes of the global hierarchical network. Keywords: problems of combinatorial optimization, mathematical models of circular routes of vehicles.