An Exact Branch and Cut Algorithm for the Vehicle and Crew Scheduling Problem

  • Christian Friberg
  • Knut Haase
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 471)

Abstract

We present a new model for the vehicle and crew scheduling problem in urban public transport systems by combining models for vehicle and crew scheduling that cover a great variety of real world aspects, including constraints for crews resulting from wage agreements and company regulations. The main part of the model consists of a set partitioning formulation to cover each trip. A column generation algorithm is implemented to calculate the continuous relaxation which is embedded in a branch and bound approach to generate an exact solution for the problem. To improve the lower bounds, polyhedral cuts basing on clique detection and a variant of the column generation algorithm that suits the cuts were tested.

Keywords

Transportation Dial 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ball, M./Bodin, L./Dial, R. (1983): A matching based heuristic for scheduling mass transit crews and vehicles. in: Transportation Science 17, 4–31.Google Scholar
  2. Dell’Allmico, M./Fischetti, M./Toth, P. (1993): Heuristic algorithms for the multiple depot vehicle scheduling problem. in: Management Science 39, 115–125.Google Scholar
  3. Desrochers, M. (1988): An algorithm for the shortest path problem with resource constraints. Cahiers du GÉRAD G-88–27, École des H.E.C., Montreal, Canada.Google Scholar
  4. Desrochers, M./Desrosiers, J./Solomon, M. (1992): A new optimization algorithm for the vehicle routing problem with time windows. in: Operations Research 40, 342–354.Google Scholar
  5. Desrochers, M./Gilbert, J./Sauvé, M./Soumis, F. (1992): CREW-OPT: Subproblem modeling in a column generation approach to urban crew scheduling. in: Desrochers, M./Rousseau, J.M. (eds.): Computer-Aided Transit Scheduling: Proceedings of the Fifth International Workshop. (Springer) Berlin, 395–406.Google Scholar
  6. Desrochers, M./Soumis, F. (1989): A column generation approach to the urban transit crew scheduling problem. in: Transportation Science 23, 1–13.Google Scholar
  7. Falkner, J.C./Ryan, D.M. (1992): Express: Set partitioning for bus crew scheduling in Christchurch. in: Desrochers, M./Rousseau, J.M. (eds.): Computer-Aided Transit Scheduling: Proceedings of the Fifth International Workshop. (Springer) Berlin, 359–378.Google Scholar
  8. Freling, R./Boender, G./Paixão, A. (1995): An integrated approach to vehicle and crew scheduling, Report 9503/A, Erasmus University Rotterdam.Google Scholar
  9. Freling, R. (1997): Models and techniques for integrating vehicle and crew scheduling, Tinbergen Institute Research Series 157, (Thesis Publishers), Amsterdam.Google Scholar
  10. Friberg, C./Haase, K. (1997): An exact branch and bound algorithm for the vehicle and crew scheduling problem, Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel, 416, University of Kiel.Google Scholar
  11. Hoffman, K.L./Padberg, M. (1993): Solving airline crew scheduling problems by branch-and-cut. in: Management Science 39, 657–682.Google Scholar
  12. Lasdon, L.S. (1970): Optimization Theory for Large Systems. (MacMillan) New York.Google Scholar
  13. Lawler, E.L. (1972): A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem. in: Management Science 18, 401–405.Google Scholar
  14. Nemhauser, G.L./Wolsey, L.A. (1988): Integer and combinatorial optimization. (Wiley) New York.Google Scholar
  15. Patrikalakis, I./Xerocostas, D. (1992): A new decomposition scheme of the urban public transport scheduling problem. in: Desrochers, M./Rousseau, J.M. (eds.): Computer-Aided Transit Scheduling: Proceedings of the Fifth International Workshop. (Springer) Berlin, 407–425.Google Scholar
  16. Ribeiro, C.C./Soumis, F. (1994): A column generation approach to the multiple-depot vehicle scheduling problem. in: Operations Research 42, 41–52.Google Scholar
  17. Tosini, E./ Vercellis, C. (1988): An interactive system for extra-urban vehicle and crew scheduling problems. in: J.R. Daduna and A. Wren (eds.), Computer-Aided Transit Scheduling: Proceedings of the Fourth International Workshop, (Springer) Berlin, 41–53.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Christian Friberg
    • 1
  • Knut Haase
    • 2
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität zu KielKielGermany
  2. 2.Produktion und Logistik, Institut für BetriebswirtschaftslehreChristian-Albrechts-Universität zu KielKielGermany

Personalised recommendations