{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T11:57:48Z","timestamp":1765886268765,"version":"3.40.5"},"reference-count":20,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["INFORMS Journal on Applied Analytics"],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:p> Deutsche Bahn (DB) operates a large fleet of rolling stock (locomotives, wagons, and train sets) that must be combined into trains to perform rolling stock rotations. This train composition is a special characteristic of railway operations that distinguishes rolling stock rotation planning from the vehicle scheduling problems prevalent in other industries. 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\u2019s fleet employment optimization (FEO) system for rolling stock rotation planning. FEO\u2019s impact within DB\u2019s planning departments has been revolutionary. DB has used it to support the company\u2019s 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\u2019s planning departments appreciate FEO\u2019s 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 CO<jats:sub>2<\/jats:sub> emissions, and the elimination of 600 coupling operations in crossborder operations to the implementation of FEO. <\/jats:p>","DOI":"10.1287\/inte.2020.1069","type":"journal-article","created":{"date-parts":[[2021,2,10]],"date-time":"2021-02-10T12:39:41Z","timestamp":1612960781000},"page":"42-62","source":"Crossref","is-referenced-by-count":7,"title":["Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization"],"prefix":"10.1287","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7223-9174","authenticated-orcid":false,"given":"Ralf","family":"Bornd\u00f6rfer","sequence":"first","affiliation":[{"name":"Mathematics Department, Freie Universit\u00e4t Berlin, and Network Optimization Department, Zuse Institute Berlin, 14195 Berlin, Germany;"}]},{"given":"Thomas","family":"E\u00dfer","sequence":"additional","affiliation":[{"name":"Deutsche Bahn Cargo AG, 55116 Mainz, Germany;"}]},{"given":"Patrick","family":"Frankenberger","sequence":"additional","affiliation":[{"name":"Deutsche Bahn AG, 60329 Frankfurt am Main, Germany;"}]},{"given":"Andreas","family":"Huck","sequence":"additional","affiliation":[{"name":"Deutsche Bahn AG, 60329 Frankfurt am Main, Germany;"}]},{"given":"Christoph","family":"Jobmann","sequence":"additional","affiliation":[{"name":"Deutsche Bahn AG, 60329 Frankfurt am Main, Germany;"}]},{"given":"Boris","family":"Krostitz","sequence":"additional","affiliation":[{"name":"Deutsche Bahn AG, 60329 Frankfurt am Main, Germany;"}]},{"given":"Karsten","family":"Kuchenbecker","sequence":"additional","affiliation":[{"name":"Deutsche Bahn AG, 60329 Frankfurt am Main, Germany;"}]},{"given":"Kai","family":"Mohrhagen","sequence":"additional","affiliation":[{"name":"Deutsche Bahn AG, 60329 Frankfurt am Main, Germany;"}]},{"given":"Philipp","family":"Nagl","sequence":"additional","affiliation":[{"name":"Deutsche Bahn Fernverkehr AG, 60326 Frankfurt am Main, Germany;"}]},{"given":"Michael","family":"Peterson","sequence":"additional","affiliation":[{"name":"Deutsche Bahn Fernverkehr AG, 60326 Frankfurt am Main, Germany;"}]},{"given":"Markus","family":"Reuther","sequence":"additional","affiliation":[{"name":"LBW Optimization GmbH, 14195 Berlin, Germany;"}]},{"given":"Thilo","family":"Schang","sequence":"additional","affiliation":[{"name":"Deutsche Bahn Netz AG, 60486 Frankfurt am Main, Germany;"}]},{"given":"Michael","family":"Schoch","sequence":"additional","affiliation":[{"name":"Deutsche Bahn AG, 60329 Frankfurt am Main, Germany;"}]},{"given":"Hanno","family":"Sch\u00fclldorf","sequence":"additional","affiliation":[{"name":"Deutsche Bahn AG, 60329 Frankfurt am Main, Germany;"}]},{"given":"Peter","family":"Sch\u00fctz","sequence":"additional","affiliation":[{"name":"Deutsche Bahn AG, 60528 Frankfurt am Main, Germany;"}]},{"given":"Tobias","family":"Therolf","sequence":"additional","affiliation":[{"name":"Deutsche Bahn Regio AG, 68163 Mannheim, Germany;"}]},{"given":"Kerstin","family":"Waas","sequence":"additional","affiliation":[{"name":"Deutsche Bahn Netz AG, 60326 Frankfurt am Main, Germany"}]},{"given":"Steffen","family":"Weider","sequence":"additional","affiliation":[{"name":"LBW Optimization GmbH, 14195 Berlin, Germany;"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.1050.0115"},{"key":"B2","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/978-3-319-89920-6_42","volume-title":"Operations Research Proceedings 2017","author":"Beckenbach I","year":"2018"},{"key":"B3","unstructured":"Beckenbach I (2019) Matchings and flows in hypergraphs. 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