Article information

2018 , Volume 23, ¹ 6, p.94-106

Takmazian A.K., Shabunin A.B.

Application of the optimal network flow method to the problem of locomotive selection for freight trains on the Eastern Polygon

The selection of traction resources (locomotives) for the transport of freight trains is modelled. The input data are the train route, the readiness time of the train for departure, the average speed and weight of the train. In addition, there are many locomotives with a carrying capacity and an area of permitted action. The research objective is to optimally select a resource for each segment of the train route. The solution is sought by the resource flow method of the minimum total cost through a specially designed network. The network includes edges created from train schedule segments whose filling means locomotive assignment to train at the segment, and special alternative edges, passing through which a locomotive alternates its assignment. The algorithm for finding the optimal solution is the method of pushing through the pre-flow proposed by A. Goldberg and R. Tarjan. This is one of the fastest algorithms converging to a global optimum. Two test cases were investigated: a trivial one, out of six trains and three locomotives, and a more complicated one, which is a model example the size of 10% of the full scale model and consists of 150 trains. Full scale calculations provide planning of the freight transportation on the Eastern Operational domain of the Russian Railways. The model includes 1800 locomotives and about 3000 trains on the time horizon of 48 hours. Solution is found in less than 5 minutes of processor time for a PC powered by Intel(R) Pentium(R) G2010 2.80 GHz processor.

[full text] [link to elibrary.ru]

Keywords: freight trains, locomotive-to-train assignment, scheduling problem, alternative graph, minimum cost flow, real-time calculations

doi: 10.25743/ICT.2018.23.6.009

Author(s):
Takmazian Andrey Kurkenovich
Office: Institute of Mechanics Lomonosov Moscow State University, Research and Design Institute for Information Technology, Signaling and Telecommunications on Railway Transport
Address: 119192, Russia, Moscow
E-mail: takmazian@gmail.com

Shabunin Alexander Borisovich
Office: Research and Design Institute for Information Technology, Signaling and Telecommunications on Railway Transport
Address: 107996, Russia, Moscow

References:
[1] Piu, F., Speranza, M.G. The locomotive assignment problem: a survey on optimization models. International Transactions in Operational Research. 2014; 24(3):327–352.

[2] Matyukhin, V.G., Shabunin, A.B., Nemtsov, E.F. Traction resources management at Eastern operating domain of Russia. Locomotiv. 2017; 1(721):8–9. (In Russ.)

[3] Kuztetsov, N.A., Minashina, I.K., Paschenko, F.F., Ryabykh, N.G., Zakharova, E.M. Optimization algorithms in scheduling problems of the rail transport. Journal of Communications Technology and Electronics. 2015; 60(6):637–646.

[4] Azanov, V.M., Buyanov, M.V., Gaynanov, D. N., Ivanov, S.V. Algorithm and software development to allocate locomotives for transportation of freight trains. Bulletin of the South Ural State University.Series «Mathematical Modelling, Programming & Computer Software». 2016; 9(4):73–85.

[5] Bertsekas, D.P. The auction algorithm: a ditributed relaxation method for the assignment problem. Annals of operations research. 1988; (14):105–123.

[6] Noori, S., Ghannadpour, S.F Locomotive assignment problem with train precedence using genetic algorithm. Journal of Industrial Engineering International. 2012; (8:9). Available at: https://doi.org/10.1186/2251-712X-8-9

[7] Arkhipov, D.I., Lazarev, A.A., Musatova E.G. Constraint programming approach applied to locotive and locomotive crew assignment problem for freight transportation. Proceedings of the 6th International science and technology conference .Intelligence control systems for railroad transportation. Research and Design Institute for Information Technology, Signalling and Telecommunications in Railway Transportation. Moscow; 2017: 56–59.

[8] Zhilyakova, L.Yu., Kuznetsov, N.A., Matyukhin, V.G., Shabunin, A.B., Takmaz'yan, A.K. Locomotive assignment graph model for freight traffic on linear section of railway. The problem of finding a maximal independent schedule coverage. Control Sciences. 2018; (3):65–75. ( In Russ.)

[9] Gainanov, D.N., Kibzun, A.I., Rasskazova, V.A. Theoretical-graph algorithm in the problem on the assignments and transportations of locomotives. Computers and information technology bulletin. 2017; (5):51–56. Doi: 10.14489/vkit.2017.05.pp.051-056. ( In Russ.)

[10] Forbes, M.A., Holt, J.N., Watts, A.M. Exact Solution of Locomotive Scheduling Problems. Journal of the Operational Research Society. 1991; 42(10):825—831.

[11] Noble, D.H., Al-Amin, M., Mills, R.G.J. Production of locomotive rosters for a multi-class multi-locomotive problem. The journal of the operational research society. 2001; 52(11):1191–1200. Available at http://www.jstor.org/stable/822929.

[12] Ahuja, R.K., Liu, J., Orlin, J.B., Sharma, D., Shughart, L.A. Solving Real-Life Locomotive-Scheduling Problems. Transportation Science. 2005; 36(4):503–517.

[13] Vaidyanathan, B, Ahuja, R.K., Orlin, J.B. The locomotive routing problem. Transportation Science. 2008; (42):492—507.

[14] Jaumard, B., Tian, H. Multi-column generation model for the locomotive assignment problem. Proceedings of 16th workshop on algorithmic approaches for transportation modelling, optimization, and systems (ATMOS’16). Aarhus, Denmark. Open-Access Series in Informatics. P. 6:1—6:13. Available at http://www.dagstuhl.de/dagpub/978-3-95977-021-72016.

[15] Pacciarelli, D. Alternative graph formulation for solving complex factory-scheduling problems. International journal of production research. 2002; (40):3641–3653. Doi:10.1080/00207540210136478.

[16] Goldberg, A.V., Tarjan, R.E. A new approach to the maximum flow problem. Proceedings of the eighteenth annual Association for Computing Machinery (ACM) symposium on Theory of computing. New York, USA: Association for Computing Machinery; 1986: 136–146.

[17] Goldberg, A.V., Tarjan, R.E. Solving minimum cost flow problems by successive approximation. Proceedings of the nineteenth annual Association for Computing Machinery (ACM) symposium on Theory of computing. New York, USA: Association for Computing Machinery; 1987: 7–18. Doi: 10.1145/28395.28397.

[18] Bertsekas, D.P. Distributed asynchronous relaxation methods for linear network flow problems. Laboratory for information and decision systems report LIDS-P-1606. Cambridge, MA, USA: Massachusetts Institute of Technology; 1986: 26.

[19] Bertsekas, D.P., Castanon, D.A. The auction algorithm for the minimum cost network flow problem. Laboratory for information and decision systems report LIDS-P-1925. Cambridge, MA, USA: Massachusetts Institute of Technology; 1989: 32.

Bibliography link:
Takmazian A.K., Shabunin A.B. Application of the optimal network flow method to the problem of locomotive selection for freight trains on the Eastern Polygon // Computational technologies. 2018. V. 23. ¹ 6. P. 94-106
Home| Scope| Editorial Board| Content| Search| Subscription| Rules| Contacts
ISSN 1560-7534
© 2024 FRC ICT