Abstract
Railway freight shunting is the process of forming departing trains from arriving freight trains. The process is continuously performed at rail yards. The shunting procedure is complex and rail yards constitute bottlenecks in the rail freight network, often causing delays to individual shipments. One of the problems is that planning for the allocation of tracks at rail yards is difficult, given that the planner has limited resources (tracks, shunting engines, etc.) and needs to foresee the consequences of committed actions for the current inbound trains.
The required schedules highly depend on the particular infrastructure of the rail yard, on the configuration of inbound and outbound trains, and on the business objectives. Thus, new optimization tools as active decision support for the dispatchers are closely tailored to the actual processes. Due to its practical relevance, a broad range of variants has been discussed and solved by the scientific community in recent years. For selected relevant variants, we describe their fruitful relation to scientific research topics such as graph coloring, sequence partitioning, and scheduling, we discuss their computational complexity and approximability, and we outline efficient optimization procedures.
In particular, we consider a set of models and algorithms which are applicable in practice, and discuss their application to the shunting yards in Ludwigshafen, Germany and in Hallsberg, Sweden. We also discuss similarities and differences between the different approaches and outline the need for future research.
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Ahuja RK, Jha KC, Liu J (2007) Solving real-life railroad blocking problems. Interfaces 37(5):404–419. ISSN: 0092-2102. https://doi.org/10.1287/inte.1070.0295 (cited on page 182)
Assad AA (1981) Analytical models in rail transportation: an annotated bibliography. Inf Syst Oper Res 19(1):59–80. https://doi.org/10.1080/03155986.1981.11731807 (cited on page 185)
Assad AA (1983) Analysis of rail classification policies. Inf Syst Oper Res 21(4):293–314. https://doi.org/10.1080/03155986.1983.11731905 (cited on page 185)
Avriel M, Penn M, Shpirer N (2000) Container ship stowage problem: complexity and connection to the coloring of circle graphs. Discret Appl Math 103(1):271–179. https://doi.org/10.1016/S0166-218X(99)00245-0 (cited on page 183)
Barnhart C, Jin H, Vance PH (2000) Railroad blocking: a network design application. Oper Res 48(4):603–614. https://doi.org/10.1287/opre.48.4.603.12416 (cited on page 182)
Baumann O (1959) Die Planung der Simultanformation von Nahgüterzügen für den Rangierbahnhof Zürich-Limmattal. Rangiertechnik 19:25–35 (cited on page 184)
Bodin LD, Golden BL, Schuster AD, Romig W (1980) A model for the blocking of trains. Transp Res B 14(1):115–120. https://doi.org/10.1016/0191-2615(80)90037-5 (cited on page 182)
Bodlaender HL, Jansen K (1995) Restrictions of graph partition problems. Part I. Theor Comput Sci 148(1):93–109. https://doi.org/10.1016/0304-3975(95)00057-4 (cited on page 196)
Bohlin M, Flier H, Maue J, Mihalák M (2010) Hump yard track allocation with temporary car storage. Tech. rep. T2010:09. Swedish Institute of Computer Science. HDL: 20.500.11850/99142 (cited on pages 201,206)
Bohlin M, Flier H, Maue J, Mihalák M (2011) Track allocation in freight-train classification with mixed tracks. In: Proceedings of the 11th workshop on algorithmic approaches for transportation modelling, optimization, and systems (ATMOS 2011), Schloss Dagstuhl, Wadern, Sept 2011, vol 20, pp 38–51. https://doi.org/10.4230/OASIcs.ATMOS.2011.38 (cited on page 206)
Bohlin M, Dahms F, Flier H, Gestrelius S (2012) Optimal freight train classification using column generation. In: Proceedings of the 12th workshop on algorithmic approaches for transportation modelling, optimization, and systems (ATMOS 2012), Schloss Dagstuhl, Wadern, vol 25, pp 10–22. https://doi.org/10.4230/OASIcs.ATMOS.2012.10 (cited on page 206)
Bohlin M, Gestrelius S, Dahms F, Mihalák M, Flier H (2016) Optimization methods for multistage freight train formation. Transp Sci 50(3):823–840. https://doi.org/10.1287/trsc.2014.0580 (cited on pages 201,206)
Borndörfer R, Cardonha C (2009) A set partitioning approach to shunting. Electron Notes Discret Math 35:359–364. https://doi.org/10.1016/j.dam.2011.06.009 (cited on page 198)
Boysen N, Fliedner M, Jaehn F, Pesch E (2012) Shunting yard operations: theoretical aspects and applications. Eur J Oper Res 220(1):1–14. https://doi.org/10.1016/j.ejor.2012.01.043 (cited on page 185)
Boysen N, Emde S, Fliedner M (2015) The basic train makeup problem in shunting yards. OR Spectr 38(1):207–233. https://doi.org/10.1007/s00291-015-0412-0 (cited on page 183)
Büsing C, Maue J (2010) Robust algorithms for sorting railway cars. In: Proceedings of 18th annual European conference on algorithms: Part I (ESA’10). Springer, Berlin, pp 350–361. ISBN: 978-3-642-15774-5. https://doi.org/10.1007/978-3-642-15775-2_30 (cited on page 185)
Cardonha, C (2012) Applied methods for the vehicle positioning problem. Ph.D. thesis, TU Berlin. https://doi.org/10.14279/depositonce-3141 (cited on page 198)
Cicerone S, D’Angelo G, Di Stefano G, Frigioni D, Navarra A (2009) Recoverable robustness for train shunting problems. Algorithmic Oper Res 4(2):102–116. ISSN: 1718-3235 (cited on page 185)
Cornelsen S, Di Stefano G (2007) Track assignment. J Discret Algorithms 5(2):250–261. https://doi.org/10.1016/j.jda.2006.05.001 (cited on page 192)
Daganzo CF (1986) Static blocking at railyards: sorting implications and track requirements. Transp Sci 20(3):189–199. https://doi.org/10.1287/trsc.20.3.189 (cited on page 185)
Daganzo CF (1987) Static blocking at railyards: part I. Homogeneous traffic. Transp Res B 21(1):1–27. https://doi.org/10.1016/0191-2615(87)90018-X (Not cited.)
Daganzo CF (1987) Static blocking at railyards: part II. Heterogeneous traffic. Transp Res B 21(1):29–40. https://doi.org/10.1016/0191-2615(87)90019-1 (Not cited.)
Daganzo CF, Dowling RG, Hall RW (1983) Railroad classification yard throughput: the case of multistage triangular sorting. Transp Res A 17(2):95–106. https://doi.org/10.1016/0191-2607(83)90063-8 (cited on page 185)
Dahlhaus E, Horák P, Miller M, Ryan JF (2000) The train marshalling problem. Discret Appl Math 103(1–3):41–54. https://doi.org/10.1016/S0166-218X(99)00219-X (cited on page 195)
Dahlhaus E, Manne F, Miller M, Ryan JF (2000) Algorithms for combinatorial problems related to train marshalling. In: Proceedings of AWOCA 2000, Hunter Valley, NSW, pp 7–16 (cited on page 195)
Demange M, Ekim T, de Werra D (2009) A tutorial on the use of graph coloring for some problems in robotics. Eur J Oper Res 192(1):41–55. https://doi.org/10.1016/j.ejor.2007.09.018 (cited on page 183)
Di Stefano G, Koči ML (2004) A graph theoretical approach to the shunting problem. Electron Notes Theor Comput Sci 92:16–33. https://doi.org/10.1016/j.entcs.2003.12.020 (cited on pages 192, 193, 195)
Di Stefano G, Krause S, Lübbecke ME, Zimmermann UT (2008) On minimum k-modal partitions of permutations. J Discret Algorithms 6(3):381–392. https://doi.org/10.1016/j.jda.2008.01.002 (cited on page 192)
Eggermont C, Hurkens CAJ, Modelski M, Woeginger GJ (2009) The hardness of train rearrangements. Oper Res Lett 37(2):80–82. https://doi.org/10.1016/j.orl.2008.12.005 (cited on page 196)
Epstein L, Levin A (2008) On bin packing with conflicts. J Optim 19(3):1270–1298. https://doi.org/10.1137/060666329 (cited on pages 196, 197)
Fertig HR (1927) System classification plan improves yard efficiency. Railway Age 515–522, February 19, 1927 (cited on page 184)
Flandorffer H (1953) Vereinfachte Güterzugbildung. Rangiertechnik 13:114–118 (cited on page 184)
Fomin FV, Kratsch D, Novelli J-C (2002) Approximating minimum cocolourings. Inf Process Lett 84(5):285–290. https://doi.org/10.1016/S0020-0190(02)00288-0 (cited on page 192)
Freling T, Lentink RM, Kroon LG, Huisman D (2005) Shunting of passenger train units in a railway station. Transp Sci 39(2):261–272. https://doi.org/10.1287/trsc.1030.0076 (cited on page 203)
Gallo G, Di Miele F (2001) Dispatching buses in parking depots. Transp Sci 35(3):322–330. https://doi.org/10.1287/trsc.35.3.322.10151 (cited on page 183)
Gatto M, Maue J, Mihalák M, Widmayer P (2009) Shunting for dummies: an introductory algorithmic survey. In: Ahuja R, Möhring R, Zaroliagis C (eds) Robust and online large-scale optimization: models and techniques for transportation systems. Springer, Berlin, pp 310–337. https://doi.org/10.1007/978-3-642-05465-5_13 (cited on page 185)
Golumbic MC (2004) Algorithmic graph theory and perfect graphs. North-Holland, Amsterdam (cited on page 191)
Gorman MF (1998) An application of genetic and tabu searches to the freight railroad operating plan problem. Ann Oper Res 78:51–69. ISSN: 0254-5330. https://doi.org/10.1023/A:1018906301828 (cited on page 182)
Graßmann E (1952) Zur Geschichte der Rangiertechnik. Rangiertechnik 12:9–18 (cited on page 184)
Gurobi Optimization, Inc. (June 2017) Website of Gurobi. http:gurobi.com (cited on page 204)
Hamdouni M, Desaulniers G, Soumis F (2007) Parking buses in a depot using block patterns: a benders decomposition approach for minimizing type mismatches. Comput Oper Res 34(11):3362–3379. https://doi.org/10.1016/j.cor.2006.02.002 (cited on page 183)
Han Y-H (2004) Dynamic sequencing of jobs on conveyor systems for minimizing changeovers. Ph.D. thesis, Georgia Institute of Technology, School of Industrial and Systems Engineering. https://doi.org/10.1007/s00170-010-2704-5 (cited on page 183)
Hansmann RS (2010) Optimal sorting of rolling stock. Ph.D. thesis, Institut für Mathematische Optimierung, Technische Universität Carolo-Wilhelmina zu Braunschweig. Cuvillier, Göttingen. ISBN: 978-3-86955-659-8 (cited on pages 185, 186, 188, 193, 195, 196, 199, 201, 204)
Hansmann RS (2018, in preparation) Complexity of single-stage rail car rearrangements (cited on pages 195, 196, 197 198)
Hauser A, Maue J (2010) Experimental evaluation of approximation and heuristic algorithms for sorting railway cars. In: Festa P (ed) Proceedings of the 9th international symposium on experimental algorithms (SEA-10). Lecture notes in computer science, vol 6049. Springer, Berlin, pp. 154–165. https://doi.org/10.1007/978-3-642-13193-6_14 (cited on page 201)
Huntley CL, Brown DE, Sappington DE, Markowicz BP (1995) Freight routing and scheduling at CSX transportation. Interfaces 25(3):58–71. https://doi.org/10.1287/inte.25.3.58 (cited on page 182)
IBM ILOG (Apr 2016) CPLEX. http:ibm.com (cited on page 204)
Ivić M, Marković M, Marković A (2007) Effects of the application of conventional methods in the process of forming the pick-up trains. Yugoslav J Oper Res 17(2):245–256. https://doi.org/10.2298/YJOR0702245I (cited on page 183)
Jacob R, Márton P, Maue J, Nunkesser M (2011) Multistage methods for freight train classification. Networks 57(1):87–105. ISSN: 1097–0037. https://doi.org/10.1002/net.20385 (cited on pages 201)
Jansen K (2003) The mutual exclusion scheduling problem for permutation and comparability graphs. Inf Comput 180(2):71–81. https://doi.org/10.1016/S0890-5401(02)00028-7 (cited on page 197)
Keaton MH (1992) Designing railroad operating plans: a dual adjustment method for implementing Lagrangian relaxation. Transp Sci 26(4):263–279. https://doi.org/10.1287/trsc.26.4.263 (cited on page 182)
König FG (2009) Sorting with objectives - graph theoretic concepts in industrial optimization. Ph.D. thesis, TU Berlin. https://doi.org/10.14279/depositonce-2349 (cited on page 183)
König FG, Lübbecke ME (2008) Sorting with complete networks of stacks. In: Hong S-H, Nagamochi H, Fukunaga T (eds) International symposium on algorithms and computation (ISAAC 2008). Lecture notes in computer science, vol 5369. Springer, Berlin, pp. 896–907. https://doi.org/10.1007/978-3-540-92182-0_78 (cited on page 183)
König H, Schaltegger P (1967) Optimale Simultanformation von Nahgüterzügen in Rangierbahnhöfen. Monatsschrift der Internationalen Eisenbahn-Kongress-Vereinigung 4(1):1–18 (cited on page 184)
König FG, Lübbecke ME, Möhring RH, Schäfer G, Spenke I (2007) Solutions to real-world instances of PSPACE-complete stacking. In: Arge L, Hoffmann M, Welzl E (eds) Proceedings of the 15th European symposium on algorithms (ESA). Lecture notes in computer science. Springer, Berlin, pp 729–740. https://doi.org/10.1007/978-3-540-75520-3_64 (cited on page 183)
Krell K (1962) Grundgedanken des Simultanverfahrens. Rangiertechnik 22:15–23 (cited on page 184)
Krell K (1962) Ein Beitrag zur gemeinsamen Bildung von Nahgüterzügen. Rangiertechnik 23:16–25 (cited on page 184)
Kroon LG, Lentink RM, Schrijver A (2008) Shunting of passenger train units: an integrated approach. Transp Sci 42(4):436–449. https://doi.org/10.1287/trsc.1080.0243 (cited on page 203)
Liebchen C, Lübbecke M, Möhring R, Stiller S (2009) The concept of recoverable robustness, linear programming recovery, and railway applications. In: Ahuja RK, Möhring RH, Zaroliagis CD (eds) Robust and online large-scale optimization. Lecture notes in computer science, vol 5868. Springer, Berlin, pp 1–27. ISBN: 978-3-642-05464-8. https://doi.org/10.1007/978-3-642-05465-5_1 (cited on page 185)
Márton P, Maue J, Nunkesser M (2009) An improved classification procedure for the hump yard lausanne triage. In: Clausen J, Di Stefano G (eds) Proceedings of the 9th workshop on algorithmic methods and models for optimization of railways (ATMOS-09). Schloss Dagstuhl, Wadern, pp 1–15. https://doi.org/10.4230/OASIcs.ATMOS.2009.2142 (cited on page 203)
Nemani AK, Ahuja RK (2011) OR models in freight railroad industry. In: Cochran JJ, Cox LA, Keskinocak P, Kharoufeh JP, Smith JC (eds) Wiley encyclopedia of operations research and management science. Wiley, London. https://doi.org/10.1002/9780470400531.eorms0622 (cited on page 182)
Newton HN, Barnhart C, Vance PH (1998) Constructing railroad blocking plans to minimize handling costs. Transp Sci 32(4):330–345. https://doi.org/10.1287/trsc.32.4.330 (cited on page 182)
Pentinga KJ (1959) Teaching simultaneous marshalling. Railw Gaz 110(21):590–593 (cited on page 184)
Petersen ER (1977) Railyard modeling: part I. Prediction of put-through time. Transp Sci 11(1):37–49. https://doi.org/10.1287/trsc.11.1.37 (cited on page 185)
Petersen ER (1977) Railyard modeling: part II. The effect of yard facilities. Transp Sci 11(1):50–59. https://doi.org/10.1287/trsc.11.1.50 (cited on page 185)
Schaltegger P (1967) Optimierung eines Rangierverfahrens. Ablauf- und Planungsforschung 8(4):302–314 (cited on page 184)
Siddiqee MW (1972) Investigation of sorting and train formation schemes for a railroad hump yard. In: Newell GF (ed) Proceedings of the 5th international symposium on the theory of traffic flow and transportation. American Elsevier, New York, NY, pp 377–388 (cited on page 185)
Tarjan RE (1972) Sorting using networks of queues and stacks. J Assoc Comput Mach 19(2):341–346. https://doi.org/10.1145/321694.321704 (cited on page 185)
Van Dyke CD (1986) The automated blocking model: a practical approach to freight railroad blocking plan development. Transp Res Forum 27:116–121 (cited on page 182)
Wagner K (1984) Monotonic coverings of finite sets. Elektronische Informationsverarbeitung und Kybernetik 20(12):633–639 (cited on page 192)
Winter T (2000) Online and real-time dispatching problems. Ph.D. thesis, Abteilung für Mathematische Optimierung, Technische Universität Carolo-Wilhelmina zu Braunschweig. URN: urn:nbn:de:gbv:084-119482 (cited on page 196)
Winter T, Zimmermann UT (2000) Real-time dispatch of trams in storage yards. Ann Oper Res 96:287–315. https://doi.org/10.1023/A:1018907720194 (cited on page 196)
Wöckel F (1949) Nahgüterzugbildung im Flachbahnhof durch Ablauf. Eisenbahntechnik 1:5–12 (cited on page 184)
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Bohlin, M., Hansmann, R., Zimmermann, U.T. (2018). Optimization of Railway Freight Shunting. In: Borndörfer, R., Klug, T., Lamorgese, L., Mannino, C., Reuther, M., Schlechte, T. (eds) Handbook of Optimization in the Railway Industry. International Series in Operations Research & Management Science, vol 268. Springer, Cham. https://doi.org/10.1007/978-3-319-72153-8_9
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