Railway crew scheduling: Models, methods and applications

Abstract The railway crew scheduling problem consists of finding the most efficient duty combination for railway crews to cover all trains and related activities for a defined period of time. Crew scheduling problems in transportation originate in airline and bus industries. In the 1990s, researchers developed sophisticated algorithms which were capable of solving the larger and more complex problem instances of railway operators. Practical implementations and decision support tools received very satisfying feedback from the industry. Since then, numerous real-world problems have been studied requiring innovative algorithmic approaches to the NP-hard problem. In this paper, we review 123 articles on railway crew scheduling focusing on more recent publications since 2000. After depicting crew scheduling in railway including the differences between transportation modes, our goal is to classify the literature according to model formulations, objectives, constraints and solution methods. By systematizing the collected articles, we identify research opportunities including integrated approaches with other planning stages, real-time re-scheduling and a further investigation of the impact of robustness and employee satisfaction on the cost of railway crew schedules.

[1]  Stéphane Dauzère-Pérès,et al.  A Lagrangian heuristic framework for a real-life integrated planning problem of railway transportation resources , 2015 .

[2]  Jorge Amaya,et al.  A model and computational tool for crew scheduling in train transportation of mine materials by using a local search strategy , 2018 .

[3]  Balachandran Vaidyanathan,et al.  Railroad Crew Scheduling , 2009, Encyclopedia of Optimization.

[4]  Erik Demeulemeester,et al.  Personnel scheduling: A literature review , 2013, Eur. J. Oper. Res..

[5]  Julie Jespersen-Groth,et al.  Estimates on Rolling Stock and Crew in DSB S-tog Based on Timetables , 2004, ATMOS.

[6]  Ying Wang,et al.  A Column Generation-Based Approach for Railway Crew Scheduling Problem , 2008 .

[7]  Lasse Gerrits,et al.  Differences and similarities in European railway disruption management practices , 2018, J. Rail Transp. Plan. Manag..

[8]  Ali Haghani,et al.  Genetic Algorithm–Based Column Generation Approach to Passenger Rail Crew Scheduling , 2010 .

[9]  Guy Desaulniers,et al.  Chapter 2 Public Transit , 2007, Transportation.

[10]  Yindong Shen,et al.  A variable iterated greedy algorithm based on grey relational analysis for crew scheduling , 2017 .

[11]  Jens Clausen,et al.  Applied Railway Optimization in Production Planning at DSB S-tog - tasks, tools and challenges , 2007, ATMOS.

[12]  Yindong Shen,et al.  A column generation algorithm for crew scheduling with multiple additional constraints , 2014 .

[13]  Geraldo Robson Mateus,et al.  General hybrid column generation algorithm for crew scheduling problems using genetic algorithm , 2009, 2009 IEEE Congress on Evolutionary Computation.

[14]  Masahiro Inuiguchi,et al.  Improvement of Column Generation Method for Railway Crew Scheduling Problems , 2010 .

[15]  Anthony Wren,et al.  Experiences with a Flexible Driver Scheduler , 2001 .

[16]  J. P. Martins,et al.  Case Studies in Planning Crew Members , 2010 .

[17]  Ralf Borndörfer,et al.  Integration of duty scheduling and rostering to increase driver satisfaction , 2017, Public Transp..

[18]  Malay Dalal,et al.  Simulation modeling at Union Pacific Railroad , 2001, Proceeding of the 2001 Winter Simulation Conference (Cat. No.01CH37304).

[19]  Ulrich Wilhelm Thonemann,et al.  A graph partitioning strategy for solving large-scale crew scheduling problems , 2015, OR Spectr..

[20]  R. Guttkuhn,et al.  A discrete event simulation for the crew assignment process in North American freight railroads , 2003, Proceedings of the 2003 Winter Simulation Conference, 2003..

[21]  N. van Oort,et al.  Driver schedule efficiency vs. public transport robustness : A framework to quantify this trade-off based on passive data , 2018 .

[22]  Yoshikazu Fukuyama,et al.  Train crew scheduling using tabu search , 2017, 2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE).

[23]  Jingpeng Li,et al.  A Self-Adjusting Algorithm for Driver Scheduling , 2005, J. Heuristics.

[24]  Udo Buscher,et al.  Valid inequalities for the arc flow formulation of the railway crew scheduling problem with attendance rates , 2019, Comput. Ind. Eng..

[25]  Jihong Ou,et al.  An Optimization Based Approach to the Train Operator Scheduling Problem at Singapore MRT , 2001, Ann. Oper. Res..

[26]  J. Beasley,et al.  A tree search algorithm for the crew scheduling problem , 1996 .

[27]  David S.W. Lai,et al.  Real-time rescheduling and disruption management for public transit , 2018 .

[28]  Lucas P. Veelenturf,et al.  An overview of recovery models and algorithms for real-time railway rescheduling , 2014 .

[29]  Eric Pinson,et al.  A set packing approach for scheduling passenger train drivers: the French experience , 2015 .

[30]  Matteo Fischetti,et al.  A Heuristic Method for the Set Covering Problem , 1999, Oper. Res..

[31]  Jacques Desrosiers,et al.  Accelerating Strategies in Column Generation Methods for Vehicle Routing and Crew Scheduling Problems , 2002 .

[32]  Leo G. Kroon,et al.  Personnel scheduling in a complex logistic system: a railway application case , 2007, J. Intell. Manuf..

[33]  Zhiqiang Tian,et al.  Modeling and Algorithms of the Crew Scheduling Problem on High-speed Railway Lines☆ , 2013 .

[34]  Yoshikazu Fukuyama,et al.  Practical train crew scheduling using improved tabu search , 2017, 2017 IEEE Symposium Series on Computational Intelligence (SSCI).

[35]  Narayan Rangaraj,et al.  Scheduling and Rescheduling of Railway Operations: A Review and Expository Analysis , 2011 .

[36]  Manfred Gronalt,et al.  A two-stage approach to the depot shunting driver assignment problem with workload balance considerations , 2017, PloS one.

[37]  Bin Guo,et al.  Study of Crew Scheduling System for High-Speed Railway , 2014 .

[38]  Rolf Dornberger,et al.  Use of a genetic algorithm in a distributed resource management software , 2007, 2007 IEEE Congress on Evolutionary Computation.

[39]  Adrian A. Hopgood,et al.  Fuzzy-Logic Controlled Genetic Algorithm for the Rail-Freight Crew-Scheduling Problem , 2018, KI - Künstliche Intelligenz.

[40]  Matthias Müller-Hannemann,et al.  Robustness as a Third Dimension for Evaluating Public Transport Plans , 2018, ATMOS.

[41]  Dennis Huisman.  A column generation approach for the rail crew re-scheduling problem , 2007, Eur. J. Oper. Res..

[42]  Dennis Huisman,et al.  The New Dutch Timetable: The OR Revolution , 2008, Interfaces.

[43]  Ann S. K. Kwan,et al.  A Hybridised Integer Programming and Local Search Method for Robust Train Driver Schedules Planning , 2004, PATAT.

[44]  Xuan Su,et al.  A Crew Scheduling with Chinese Meal Break Rules , 2013 .

[45]  A Wren,et al.  A GENERAL REVIEW OF THE USE OF COMPUTERS IN SCHEDULING BUSES AND THEIR CREWS , 1980 .

[46]  Niklas Kohl,et al.  Railway Crew Pairing Optimization , 2004, ATMOS.

[47]  Kai Chen,et al.  Evolutionary crew scheduling with adaptive chromosomes , 2013 .

[48]  Anthony Wren,et al.  TRACS II: a hybrid IP/heuristic driver scheduling system for public transport , 2002, J. Oper. Res. Soc..

[49]  C.G. Guillermo,et al.  Hybrid algorithm of Tabu Search and Integer Programming for the railway crew scheduling problem , 2009, 2009 Asia-Pacific Conference on Computational Intelligence and Industrial Applications (PACIIA).

[50]  François Soumis,et al.  Airline crew scheduling: models, algorithms, and data sets , 2014, EURO J. Transp. Logist..

[51]  Ulrich Wilhelm Thonemann,et al.  Optimizing railway crew schedules with fairness preferences , 2017, J. Sched..

[52]  Leo G. Kroon,et al.  Reinventing Crew Scheduling at Netherlands Railways , 2004, Interfaces.

[53]  Chi-Kang Lee,et al.  SCHEDULING OF TRAIN DRIVER FOR TAIWAN RAILWAY ADMINISTRATION , 2003 .

[54]  Güvenç Şahin,et al.  Tactical crew planning in railways , 2011 .

[55]  Ann S. K. Kwan,et al.  Effective search space control for large and/or complex driver scheduling problems , 2007, Ann. Oper. Res..

[56]  Nikolaj A. Kuznetsov,et al.  Design and Comparison of Freight Scheduling Algorithms for Intelligent Control Systems , 2016, EUSPN/ICTH.

[57]  Lucas P. Veelenturf,et al.  A Quasi-Robust Optimization Approach for Crew Rescheduling , 2016, Transp. Sci..

[58]  Guy Desaulniers.  Managing large fixed costs in vehicle routing and crew scheduling problems solved by column generation , 2007, Comput. Oper. Res..

[59]  Yindong Shen,et al.  Tabu Search for Time Windowed Public Transport Driver Scheduling , 2002 .

[60]  Silke Jütte.  Large-Scale Crew Scheduling: Models, Methods, and Applications in the Railway Industry , 2012 .

[61]  Peter Sanders,et al.  Parallel Integer Optimization for Crew Scheduling , 2000, Ann. Oper. Res..

[62]  Udo Buscher,et al.  Solving Practical Railway Crew Scheduling Problems with Attendance Rates , 2017, Bus. Inf. Syst. Eng..

[63]  Lei Nie,et al.  Crew Planning Optimization Model of High-Speed Railway , 2013 .

[64]  J. P. Arabeyre,et al.  The Airline Crew Scheduling Problem: A Survey , 1969 .

[65]  Jesper Larsen,et al.  A survey on robustness in railway planning , 2018, Eur. J. Oper. Res..

[66]  Ta-Hui Yang,et al.  Ant colony optimization for railway driver crew scheduling: from modeling to implementation , 2011 .

[67]  Dennis Huisman,et al.  Integrating Timetabling and Crew Scheduling at a Freight Railway Operator , 2014, Transp. Sci..

[68]  Luis Cadarso,et al.  A hybrid model for crew scheduling in rail rapid transit networks , 2019 .

[69]  Ernesto M. Morgado,et al.  Scheduling and managing crew in the Portuguese railways , 1992 .

[70]  Mohammad Tamannaei,et al.  Two Mathematical Models for Railway Crew Scheduling Problem , 2017 .

[71]  Matteo Fischetti,et al.  Algorithms for railway crew management , 1997, Math. Program..

[72]  Luis Cadarso,et al.  A New Approach to Crew Scheduling in Rapid Transit Networks , 2015 .

[73]  Balachandran Vaidyanathan,et al.  Crew Scheduling Problem , 2015 .

[74]  Kirsten Hoffmann.  A Hybrid Solution Approach for Railway Crew Scheduling Problems with Attendance Rates , 2015, OR.

[75]  Masahiro Inuiguchi,et al.  Column generation with dual inequalities for railway crew scheduling problems , 2011, Public Transp..

[76]  Natalia Kliewer,et al.  Robust Efficiency in Urban Public Transportation: Minimizing Delay Propagation in Cost-Efficient Bus and Driver Schedules , 2019, Transp. Sci..

[77]  Ulrich Wilhelm Thonemann,et al.  Optimizing Railway Crew Scheduling at DB Schenker , 2011, Interfaces.

[78]  Jun Wu,et al.  Research on the Equilibrium of Train Crew Scheduling Plan of Motor Train Set , 2012 .

[79]  Yindong Shen,et al.  Integrated bus transit scheduling for the Beijing bus group based on a unified mode of operation , 2009, Int. Trans. Oper. Res..

[80]  Paolo Toth,et al.  A Global Method for Crew Planning in Railway Applications , 2001 .

[81]  Anita Schöbel,et al.  An eigenmodel for iterative line planning, timetabling and vehicle scheduling in public transportation , 2017 .

[82]  Christos Goumopoulos,et al.  Efficient trip generation with a rule modeling system for crew scheduling problems , 2004, J. Syst. Softw..

[83]  Paolo Toth,et al.  Robust Train Timetabling , 2018 .

[84]  Ulrich Derigs,et al.  Supporting strategic crew management at passenger railways—model, method and system , 2010, Public Transp..

[85]  Changfeng Zhu,et al.  Research on Optimization of Crew Scheduling for High Speed Railway , 2014 .

[86]  Leo G. Kroon,et al.  Scheduling train drivers and guards: the Dutch "Noord-Oost" case , 2000, Proceedings of the 33rd Annual Hawaii International Conference on System Sciences.

[87]  Marco A. Boschetti,et al.  An Exact Algorithm for the Simplified Multiple Depot Crew Scheduling Problem , 2004, Ann. Oper. Res..

[88]  Adrian A. Hopgood,et al.  Rail-Freight Crew Scheduling with a Genetic Algorithm , 2014, SGAI Conf..

[89]  C. Rudin-Brown,et al.  How shift scheduling practices contribute to fatigue amongst freight rail operating employees: Findings from Canadian accident investigations. , 2018, Accident; analysis and prevention.

[90]  Ellis L. Johnson,et al.  Airline Crew Scheduling: State-of-the-Art , 2005, Ann. Oper. Res..

[91]  Helena R. Lourenço,et al.  Driver scheduling problem modelling , 2006, Public Transp..

[92]  Dennis Huisman,et al.  Solving Large Scale Crew Scheduling Problems by using Iterative Partitioning , 2008, ATMOS.

[93]  Ricardo L. Saldanha,et al.  Decision support for scheduling security crews at Netherlands Railways , 2017, Public Transp..

[94]  Amin Khosravi Khosravi,et al.  A Comprehensive Approach for Railway Crew Scheduling Problem (Case Study: Iranian Railway Network) , 2017 .

[95]  Matteo Fischetti,et al.  Crew Scheduling for Netherlands Railways: "destination: customer" , 2000 .

[96]  Dennis Huisman,et al.  Railway Crew Management , 2018 .

[97]  Dennis Huisman,et al.  Models and Algorithms for Integration of Vehicle and Crew Scheduling , 2000, J. Sched..

[98]  Mohamadreza Banihashemi,et al.  A New Model for the Mass Transit Crew Scheduling Problem , 2001 .

[99]  Christian Artigues,et al.  An evolutionary and constructive approach to a crew scheduling problem in underground passenger transport , 2010, J. Heuristics.

[100]  Dung-Ying Lin,et al.  Integrated Crew Scheduling and Roster Problem for Trainmasters of Passenger Railway Transportation , 2019, IEEE Access.

[101]  Yindong Shen,et al.  An Improved Column Generation Algorithm for Crew Scheduling Problems , 2013 .

[102]  Raymond S. K. Kwan,et al.  Tabu Search for Driver Scheduling , 2001 .

[103]  Diego Klabjan,et al.  Airline Crew Scheduling , 2003 .

[104]  Kai Lu,et al.  Smart Urban Transit Systems: From Integrated Framework to Interdisciplinary Perspective , 2018 .

[105]  Giorgio Gallo,et al.  Network models for vehicle and crew scheduling , 1984 .

[106]  Xuan Su,et al.  Rail Crew Scheduling Based on a Pooling Mode for High Speed Passenger Lines , 2010, 2010 International Conference on Logistics Engineering and Intelligent Transportation Systems.

[107]  Jacques Desrosiers,et al.  Simultaneous Vehicle and Crew Scheduling in Urban Mass Transit Systems , 1998, Transp. Sci..

[108]  Andreas T. Ernst,et al.  An Annotated Bibliography of Personnel Scheduling and Rostering , 2004, Ann. Oper. Res..

[109]  Ulrich Wilhelm Thonemann,et al.  Divide-and-price: A decomposition algorithm for solving large railway crew scheduling problems , 2012, Eur. J. Oper. Res..

[110]  Matteo Fischetti,et al.  A Polyhedral Approach to Simplified Crew Scheduling and Vehicle Scheduling Problems , 2001, Manag. Sci..

[111]  Muhammet Deveci,et al.  A survey of the literature on airline crew scheduling , 2018, Eng. Appl. Artif. Intell..

[112]  Xudong Song,et al.  Study on Crew Scheduling Model for the Passenger Dedicated Line , 2012, Int. J. Pattern Recognit. Artif. Intell..

[113]  Francesco Corman,et al.  Special issue on Integrated optimization models and algorithms in rail planning and control , 2018 .

[114]  Peter Marton,et al.  Optimization of periodic crew schedules with application of column generation method , 2017 .

[115]  Yoshikazu Fukuyama,et al.  Generation methods of neighborhood schedules for practical train crew scheduling problems using tabu search , 2017, 2017 IEEE 10th International Workshop on Computational Intelligence and Applications (IWCIA).

[116]  Martin Desrochers,et al.  A Column Generation Approach to the Urban Transit Crew Scheduling Problem , 1987, Transp. Sci..

[117]  Kiran Chahar,et al.  Strategic crew planning tool in railroad: A discrete event simulation , 2011, Proceedings of the 2011 Winter Simulation Conference (WSC).

[118]  Anthony Wren,et al.  Scheduling Of Rail Driver Duties , 1970 .

[119]  Richard Freling,et al.  Scheduling train crews: a case study for the Dutch Railways , 2000 .

[120]  Peng Zhao,et al.  A Meta-Heuristics Algorithm for Train-Set Crew Scheduling , 2007 .

[121]  Marco A. Boschetti,et al.  A Set Partitioning Approach to the Crew Scheduling Problem , 1999, Oper. Res..

[122]  Anantaram Balakrishnan,et al.  Real-Time Decision Support for Crew Assignment in Double-Ended Districts for U.S. Freight Railways , 2016, Transp. Sci..

[123]  Dennis Huisman,et al.  Multiple-Depot Integrated Vehicle and Crew Scheduling , 2003, Transp. Sci..

[124]  Balachandran Vaidyanathan,et al.  Multicommodity network flow approach to the railroad crew-scheduling problem , 2007, IBM J. Res. Dev..

[125]  Ulrich W. Thonemann,et al.  Decomposition Strategies for Solving Large-Scale Crew Scheduling Problems , 2012 .

[126]  Alberto Caprara.  Timetabling and assignment problems in railway planning and integer multicommodity flow , 2015, Networks.

[127]  Natalia Kliewer,et al.  Multiple depot vehicle and crew scheduling with time windows for scheduled trips , 2012, Public Transp..

[128]  Martin Grötschel,et al.  Duty Scheduling in Public Transit , 2003 .

[129]  Ann S. K. Kwan,et al.  Hybrid genetic algorithms for scheduling bus and train drivers , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[130]  Omar J. Ibarra-Rojas,et al.  Planning, operation, and control of bus transport systems: A literature review , 2015 .

[131]  Dennis Huisman,et al.  Vehicle and crew scheduling: solving large real-world instances with an integrated approach , 2008 .

[132]  Jingpeng Li,et al.  An estimation of distribution algorithm for public transport driver scheduling , 2017 .

[133]  Luis Cadarso,et al.  Integration of timetable planning and rolling stock in rapid transit networks , 2012, Ann. Oper. Res..

[134]  Ann S. K. Kwan,et al.  Evolutionary Driver Scheduling with Relief Chains , 2001, Evolutionary Computation.

[135]  Lianbo Deng,et al.  Crew Scheduling Considering both Crew Duty Time Difference and Cost on Urban Rail System , 2016 .

[136]  Jacques Desrosiers,et al.  Selected Topics in Column Generation , 2002, Oper. Res..

[137]  Erhan Kozan,et al.  A hybrid constructive heuristic and simulated annealing for railway crew scheduling , 2014, Comput. Ind. Eng..

[138]  Anthony F. Han,et al.  A constraint programming-based approach to the crew scheduling problem of the Taipei mass rapid transit system , 2014, Ann. Oper. Res..

[139]  Raymond S. K. Kwan.  Bus and Train Driver Scheduling , 2004, Handbook of Scheduling.

[140]  Raymond S. K. Kwan,et al.  A fuzzy genetic algorithm for driver scheduling , 2003, Eur. J. Oper. Res..

[141]  Lucas P. Veelenturf,et al.  Railway Crew Rescheduling with Retiming , 2009 .

[142]  Zhou Feng,et al.  Study on model and algorithm for urban rail transit crew scheduling system , 2010, 2010 International Conference On Computer Design and Applications.

[143]  José García,et al.  A Binary Cuckoo Search Big Data Algorithm Applied to Large-Scale Crew Scheduling Problems , 2018, Complex..

[144]  Ann S. K. Kwan,et al.  Driver Scheduling Using Genetic Algorithms with Embedded Combinatorial Traits , 1999 .

[145]  Avishai Ceder,et al.  Applied analysis for improving rail-network operations , 2015, J. Rail Transp. Plan. Manag..

[146]  Raymond S. K. Kwan.  Case studies of successful train crew scheduling optimisation , 2011, J. Sched..

[147]  Kwang Ryel Ryu,et al.  Crew pairing optimization by a genetic algorithm with unexpressed genes , 2006, J. Intell. Manuf..

[148]  Jacques Desrosiers,et al.  Time Constrained Routing and Scheduling , 1992 .

[149]  Edmund K. Burke,et al.  A hybrid Constraint Programming/Mixed Integer Programming framework for the preventive signaling maintenance crew scheduling problem , 2017, Eur. J. Oper. Res..

[150]  Jaroslav Janácek,et al.  Acceleration strategies of the column generation method for the crew scheduling problem , 2017, 2017 IEEE International Conference on Service Operations and Logistics, and Informatics (SOLI).

[151]  Masoud Yaghini,et al.  A set covering approach for multi-depot train driver scheduling , 2015, J. Comb. Optim..

[152]  Ali Çetin Suyabatmaz,et al.  A Column-and-Row Generation Algorithm for a Crew Planning Problem in Railways , 2011, OR.

[153]  Albert P. M. Wagelmans,et al.  A Decision Support System for Crew Planning in Passenger Transportation Using a Flexible Branch-and-Price Algorithm , 2004, Ann. Oper. Res..

[154]  Andreas T. Ernst,et al.  Staff scheduling and rostering: A review of applications, methods and models , 2004, Eur. J. Oper. Res..

[155]  Dennis Huisman,et al.  Operations Research in passenger railway transportation , 2005 .

[156]  Dušan Teodorović,et al.  Public Transportation Systems , 2022, Transportation Engineering.

[157]  J. Clausen,et al.  Scheduling of inspectors for ticket spot checking in urban rail transportation , 2010 .

[158]  Paolo Toth,et al.  Chapter 3 Passenger Railway Optimization , 2007, Transportation.

[159]  Ali Çetin Suyabatmaz,et al.  Railway crew capacity planning problem with connectivity of schedules , 2015 .

[160]  Erwin J. W. Abbink,et al.  Solving large scale crew scheduling problems in practice , 2010, Public Transp..

[161]  Andreas T. Ernst,et al.  An Integrated Optimization Model for Train Crew Management , 2001, Ann. Oper. Res..