VESTNIK of Samara University. Aerospace and Mechanical EngineeringVESTNIK of Samara University. Aerospace and Mechanical Engineering2542-04532541-7533Samara National Research University562310.18287/2541-7533-2017-16-4-108-117UnclassifiedClustering algorithm with projection for solving problems of optimal allocation of transport facilitiesEsipovB. A.<p><span lang="EN-US">Candidate of Science (Engineering)<br />Associate Professor, Department of Information Systems and Technologies</span></p>bobpereira@yandex.ruMoskvichevO. V.<p><span lang="EN-US">Candidate of Science (Economics), Associate Professor<br />Head of the Department of Operational Work Management</span></p>moskvichev063@yandex.ruSkladnevN. S.<p><span lang="EN-US">Student</span></p>author.skn@gmail.comAlyoshintsevA. O.<p><span lang="EN-US">Student</span></p>fenr1r16n@yandex.ruSamara National Research UniversitySamara State Transport University221220171641081172201201822012018Copyright © 2018, VESTNIK of Samara University. Aerospace and Mechanical Engineering2018<p>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.</p>Размещение транспортных объектовдвухуровневая сеть контейнерных перевозоклогистические центрыкластеризация с проекциейдефект проекцииLocation of transportation facilitiestwo-layer network of container transportationslogistic centersclustering with projectionprojection defect[1. Rezer S.M., Moskvichev O.V., Moskvicheva E.E. Optimization of Formation and Functioning of Container Transportation System of the Country. Transport: science, technique, management. 2016. No. 7. P. 3-7. (In Russ.)][2. Moskvichev O.V. A new approach to the organization of container train traffic in inland transport. Zheleznodorozhnyy transport. 2014. No. 2. P. 56-59. (In Russ.)][3. Razina M.A. Matematicheskie modeli i optimizatsiya razmeshcheniya stantsiy skoroy pomoshchi dlya obsluzhivaniya naseleniya zadannoy oblasti. Dis. … kand. fiz.-mat. nauk [Mathematical models and optimization of location of ambulance stations to provide healthcare services to the population of a given region: Thesis for a Candidate Degree in Physics and Mathematics]. Kazan, 2005. 110 p.][4. Mikhalevich B.C., Trubin V.A., Shor N.Z. Optimizatsionnye zadachi proizvodstvenno-transportnogo planirovaniya: Modeli, metody, algoritmy [Optimization problems of production-transportation planning]. Moscow: Nauka Publ., 1986. 260 p.][5. Protasov V.Yu. Maksimumy i minimumy v geometrii [Maxima and minima in geometry]. Moscow: Moskovskiy Tsentr Nepreryvnogo Matematicheskogo Obrazovaniya Publ., 2005. 56 p.][6. Ayvazyan S.A., Bukhshtaber V.M., Enyukov I.S., Meshalkin L.D. Prikladnaya statistika. Klassifikatsiya i snizhenie razmernosti [Applied statistics. Classification and reduction of dimensionality]. Moscow: Finansyi Statistika Publ., 1989. 607 p.][7. Mandel I.D. Klasternyy analiz [Cluster analysis]. Moscow: Finansy i Statistika Publ., 1988. 176 p.][8. Esipov B.A., Moskvichev O.V., Skladnev N.S., Aleshintsev A.O. Development and investigation of a clustering algorithm with a projection for solving the problems of optimization of transport infrastructure. Proceedings of the International Scientific Conference «Advanced Information Technologies and Scientific Computing (PIT 2017)». Samara: Samarskiy Nauchnyy Tsentr RAN Publ., 2017. P. 633-637. (In Russ.)][9. Moskvichev O.V. Models, methods and algorithms of optimization of container transport system of railway transport based on the cluster approach. Transport Urala. 2017. No. 2 (53). P. 18-27. (In Russ.)]