Clustering algorithm with projection for solving problems of optimal allocation of transport facilities

The paper proposes a mathematical model and a new method for solving the problem of optimal location of logistic centers for a two-level railway transportation network based on the application of the mathematical apparatus of cluster analysis. Given the geo-information parameters of the supplier plants, as well as the railroad networks specified by the railroad stations, the task of the optimal choice of railway stations – container points (CP) – is set. The criterion is to minimize the total amount of traffic in ton-kilometers from the production plant to the CP. For this purpose, the model of dividing the object into clusters is used as an optimization mathematical model. The required clusters are subsets of production points with their own CP centers. Since cluster centers must necessarily be located at railway stations, the article suggests a new clustering algorithm “with projection”. The possibilities of such a clustering algorithm, called k-means pro, are explored. A method of optimizing the choice of location of container storage distribution centers as second-level centers for a two-level transportation network is described.