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Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization

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Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization This article was downloaded by: [160.45.229.23] On: 16 April 2021, At: 01:51 Publisher: Institute for Operations Research and the Management Sciences (INFORMS) INFORMS is located in Maryland, USA INFORMS Journal on Applied Analytics Publication details, including instructions for authors and subscription information: http://pubsonline.informs.org Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization Ralf Borndörfer, Thomas Eßer, Patrick Frankenberger, Andreas Huck, Christoph Jobmann, Boris Krostitz, Karsten Kuchenbecker, Kai Mohrhagen, Philipp Nagl, Michael Peterson, Markus Reuther, Thilo Schang, Michael Schoch, Hanno Schülldorf, Peter Schütz, Tobias Therolf, Kerstin Waas, Steffen Weider To cite this article: Ralf Borndörfer, Thomas Eßer, Patrick Frankenberger, Andreas Huck, Christoph Jobmann, Boris Krostitz, Karsten Kuchenbecker, Kai Mohrhagen, Philipp Nagl, Michael Peterson, Markus Reuther, Thilo Schang, Michael Schoch, Hanno Schülldorf, Peter Schütz, Tobias Therolf, Kerstin Waas, Steffen Weider (2021) Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization. INFORMS Journal on Applied Analytics 51(1):42-62. https://doi.org/10.1287/inte.2020.1069 Full terms and conditions of use: https://pubsonline.informs.org/Publications/Librarians-Portal/PubsOnLine-Terms-and- Conditions This article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. For more information, contact [email protected]. The Publisher does not warrant or guarantee the article’s accuracy, completeness, merchantability, fitness for a particular purpose, or non-infringement. Descriptions of, or references to, products or publications, or inclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, or support of claims made of that product, publication, or service. Copyright © 2021, The Author(s) Please scroll down for article—it is on subsequent pages With 12,500 members from nearly 90 countries, INFORMS is the largest international association of operations research (O.R.) and analytics professionals and students. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org INFORMS JOURNAL ON APPLIED ANALYTICS Vol. 51, No. 1, January–February 2021, pp. 42–62 http://pubsonline.informs.org/journal/inte ISSN 0092-2102 (print), ISSN 1526-551X (online) Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization Ralf Borndorfer,¨ a Thomas Eßer,b Patrick Frankenberger,c Andreas Huck,c Christoph Jobmann,c Boris Krostitz,c Karsten Kuchenbecker,c Kai Mohrhagen,c Philipp Nagl,d Michael Peterson,d Markus Reuther,e Thilo Schang,f Michael Schoch,c Hanno Schülldorf,c Peter Schütz,g Tobias Therolf,h Kerstin Waas,i Steffen Weidere a Mathematics Department, Freie Universitat¨ Berlin, and Network Optimization Department, Zuse Institute Berlin, 14195 Berlin, Germany; b Deutsche Bahn Cargo AG, 55116 Mainz, Germany; c Deutsche Bahn AG, 60329 Frankfurt am Main, Germany; d Deutsche Bahn Fernverkehr AG, 60326 Frankfurt am Main, Germany; e LBW Optimization GmbH, 14195 Berlin, Germany; f Deutsche Bahn Netz AG, 60486 Frankfurt am Main, Germany; g Deutsche Bahn AG, 60528 Frankfurt am Main, Germany; h Deutsche Bahn Regio AG, 68163 Mannheim, Germany; i Deutsche Bahn Netz AG, 60326 Frankfurt am Main, Germany Contact: [email protected], https://orcid.org/0000-0001-7223-9174 (RB); [email protected] (TE); [email protected] (PF); [email protected] (AH); [email protected] (CJ); [email protected] (BK); [email protected] (KK); [email protected] (KM); [email protected] (PN); [email protected] (MP); [email protected] (MR); [email protected] (TS); [email protected] (MS); [email protected] (HS); [email protected] (PS); [email protected] (TT); [email protected] (KW); [email protected] (SW) Received: February 8, 2020 Abstract. Deutsche Bahn (DB) operates a large fleet of rolling stock (locomotives, wagons, Accepted: November 5, 2020 and train sets) that must be combined into trains to perform rolling stock rotations. This https://doi.org/10.1287/inte.2020.1069 train composition is a special characteristic of railway operations that distinguishes rolling stock rotation planning from the vehicle scheduling problems prevalent in other industries. Copyright: © 2021 The Author(s) DB models train compositions using hyperarcs. The resulting hypergraph models are addressed using a novel coarse-to-fine method that implements a hierarchical column generation over three levels of detail. This algorithm is the mathematical core of DB’s fleet employment optimization (FEO) system for rolling stock rotation planning. FEO’simpact within DB’s planning departments has been revolutionary. DB has used it to support the company’s procurements of its newest high-speed passenger train fleet and its intermodal cargo locomotive fleet for crossborder operations. FEO is the key to successful tendering in regional transport and to construction site management in daily operations. DB’s planning departments appreciate FEO’s high-quality results, ability to reoptimize (quickly), and ease of use. Both employees and customers benefit from the increased regularity of operations. DB attributes annual savings of 74 million euro, an annual reduction of 34,000 tons of CO2 emissions, and the elimination of 600 coupling operations in crossborder operations to the implementation of FEO. Open Access Statement: This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to copy, distribute, transmit and adapt this work, but you must attribute this work as “INFORMS Journal on Applied Analytics. Copyright © 2021 The Author(s). https://doi.org/ 10.1287/inte.2020.1069,usedunderaCreativeCommons Attribution License: https://creativecommons .org/licenses/by/4.0/.” Funding: The work of R. Borndorfer¨ was partially funded by the German Science Foundation’s (DFG) Research Center MATHEON–Mathematics for Key Technologies [project B22 “Rolling Stock Roster Planning for Railways”] and by the German Federal Ministry for Research and Education’s Research Campus MODAL–Mathematical Optimization and Data Analysis Laboratories [project “RailLab”]. Keywords: transportation • rail • scheduling • vehicles • large-scale systems • integer programming • graphs • hypergraphs • Edelman Award Introduction between major cities in central Europe at up to 300 The Western European railway network is among the kilometers per hour (km/h), regional passenger trans- densest in the world and is of major importance for port such as commuter services, and cargo transport with passenger and freight transport in the European heavy freight trains. Union (Figure 1). It supports a broad mix of operations, Deutsche Bahn (DB) is among the leading railway including InterCity Express (ICE) high-speed connections companies in the world, with revenue exceeding that 42 Borndorfer¨ et al.: Train Rotation Scheduling Using Hypergraph Optimization INFORMS Journal on Applied Analytics, 2021, vol. 51, no. 1, pp. 42–62, © 2021 The Author(s) 43 Figure 1. The Map Shows the Western European Railway transport (p. 221) and 19.1% for freight transport (p. 247). Network with Germany (Shaded in Light Gray) at the Center Rail transport also has a positive impact on our envi- ronment (Federal Environment Agency 2012)because it saves up to two-thirds of energy (p. 14) and 75% of CO2 (p. 16) in comparison with road transport. A key asset of every railway company is its train sets, locomotives, and wagons. These units are re- ferred to individually as vehicles, and together as rolling stock, to distinguish them from the network infrastructure of stations, tracks, switches, signals, and control centers that are fixed in place. Putting the rolling stock to efficient use is essential for every optimization strategy. Although it would seem log- ical for railway companies to use operations research methods, as airlines have used them to schedule their aircraft and public transit companies their buses since the 1980s, this was not the case at DB until recently. The main reason is mathematical. Unlike in air trans- portation or public transit, solving a railway vehicle routing problem to compute sequences of trips for individual vehicles (i.e., rotations) is not a satisfactory solution. Scheduling railway rolling stock also requires handling the composition of vehicles into trains. One of BNSF and Union Pacific combined. Each day, the option is to decompose the problem into train com- company transports about 5.7 million people using position and train routing steps, which are solved in approximately 24,000 timetabled trips (DB 2018). To sequence. In rail freight transport, for example, cars are assembled into blocks in step 1, trains are routed in do so, DB employs about 1,300 locomotives, 5,500 coaches (i.e., passenger wagons), and 4,200 train sets step 2, and locomotives are scheduled in
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