A Time-Space Network Approach for the Integrated Vehicle- and Crew-Scheduling Problem with Multiple Depots

This paper discusses the integrated vehicle-and crew-scheduling problem in public transit with multiple depots. It is well known that the integration of both planning steps discloses additional flexibility that can lead to gains in efficiency, compared to sequential planning. We present a new modeling approach that is based on a time-space network representation of the underlying vehicle-scheduling problem. The integrated problem is solved with column generation in combination with Lagrangian relaxation. The column generation subproblem is modeled as a resource-constrained shortest-path problem based on a novel time-space network formulation. Feasible solutions are generated by a heuristic branch-and-price method that involves fixing service trips to depots. Numerical results show that our approach outperforms other methods from the literature for well-known test problems.

[1]  P. Camerini,et al.  On improving relaxation methods by modified gradient techniques , 1975 .

[2]  Samuel J. Raff,et al.  Routing and scheduling of vehicles and crews : The state of the art , 1983, Comput. Oper. Res..

[3]  L. Bodin.  ROUTING AND SCHEDULING OF VEHICLES AND CREWS–THE STATE OF THE ART , 1983 .

[4]  Y. P. Aneja,et al.  Shortest chain subject to side constraints , 1983, Networks.

[5]  Lawrence Bodin,et al.  A Matching Based Heuristic for Scheduling Mass Transit Crews and Vehicles , 1983 .

[6]  Alan A. Bertossi,et al.  On some matching problems arising in vehicle scheduling models , 1987, Networks.

[7]  Matteo Fischetti,et al.  The Fixed Job Schedule Problem with Spread-Time Constraints , 1987, Oper. Res..

[8]  Matteo Fischetti,et al.  The Fixed Job Schedule Problem with Working-Time Constraints , 1989, Oper. Res..

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

[10]  Martin Desrochers,et al.  CREW-OPT: Subproblem Modeling in a Column Generation Approach to Urban Crew Scheduling , 1992 .

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

[12]  Ioannis Patrikalakis,et al.  A New Decomposition Scheme of the Urban Public Transport Scheduling Problem , 1992 .

[13]  Michel Gamache,et al.  A METHOD FOR OPTIMALLY SOLVING THE ROSTERING PROBLEM , 1993 .

[14]  Celso C. Ribeiro,et al.  A Column Generation Approach to the Multiple-Depot Vehicle Scheduling Problem , 1991, Oper. Res..

[15]  José M. P. Paixão,et al.  Vehicle Scheduling for Public Mass Transit — An Overview , 1995 .

[16]  Maddalena Nonato,et al.  An Integrated Approach to Extra-Urban Crew and Vehicle Scheduling* , 1998 .

[17]  R. Kraut,et al.  Vehicle scheduling in public transit and Lagrangean pricing , 1998 .

[18]  Dennis Huisman,et al.  Integrated and Dynamic Vehicle and Crew Scheduling , 1999 .

[19]  Jacques Desrosiers,et al.  A Column Generation Approach for Large-Scale Aircrew Rostering Problems , 1999, Oper. Res..

[20]  Knut Haase,et al.  An Exact Branch and Cut Algorithm for the Vehicle and Crew Scheduling Problem , 1999 .

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

[22]  Dennis Huisman,et al.  Applying an Integrated Approach to Vehicle and Crew Scheduling in Practice , 2000 .

[23]  Di Yuan,et al.  A Lagrangian Heuristic Based Branch-and-Bound Approach for the Capacitated Network Design Problem , 2000, Oper. Res..

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

[25]  Ralf Borndörfer,et al.  Integrierte Umlauf- und Dienstplanung im öffentlichen Nahverkehr , 2002 .

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

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

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

[29]  Dennis Huisman,et al.  Combining Column Generation and Lagrangian Relaxation , 2005 .

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

[31]  Leena Suhl,et al.  A time-space network based exact optimization model for multi-depot bus scheduling , 2006, Eur. J. Oper. Res..

[32]  Diego Klabjan,et al.  Integrated Airline Fleeting and Crew-Pairing Decisions , 2007, Oper. Res..

[33]  Ingmar Steinzen,et al.  Topics in Integrated Vehicle and Crew Scheduling in Public Transport , 2007 .

[34]  Marta Mesquita,et al.  Set partitioning/covering-based approaches for the integrated vehicle and crew scheduling problem , 2008, Comput. Oper. Res..

[35]  Ralf Borndörfer,et al.  A Bundle Method for Integrated Multi-Depot Vehicle and Duty Scheduling in Public Transit , 2008 .

[36]  Leena Suhl,et al.  A Crew Scheduling Approach for Public Transit Enhanced with Aspects from Vehicle Scheduling , 2008 .

[37]  Natalia Kliewer,et al.  An overview on vehicle scheduling models , 2009, Public Transp..

[38]  Marta Mesquita,et al.  Branching approaches for integrated vehicle and crew scheduling , 2009, Public Transp..

[39]  Dennis Huisman,et al.  A comparison of five heuristics for the multiple depot vehicle scheduling problem , 2009, J. Sched..