Skip to main content
Log in

A Flexible System for Scheduling Drivers

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

A substantial part of the operating costs of public transport is attributable to drivers, whose efficient use therefore is important. The compilation of optimal work packages is difficult, being NP-hard. In practice, algorithmic advances and enhanced computing power have led to significant progress in achieving better schedules. However, differences in labor practices among modes of transport and operating companies make production of a truly general system with acceptable performance a difficult proposition. TRACS II has overcome these difficulties, being used with success by a substantial number of bus and train operators. Many theoretical aspects of the system have been published previously. This paper shows for the first time how theory and practice have been brought together, explaining the many features which have been added to the algorithmic kernel to provide a user-friendly and adaptable system designed to provide maximum flexibility in practice. We discuss the extent to which users have been involved in system development, leading to many practical successes, and we summarize some recent achievements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  • Wren, A., “Heuristics ancient and modern: Transport scheduling through the ages,” J. Heuristics, 4, 87-100 (1998).

    Google Scholar 

  • Fores, Sarah, Les Proll, and Anthony Wren, “TRACS II: A hybrid IP/heuristic driver scheduling system for public transport,” J. Oper. Res. Soc., 53, 1093-1100 (2002).

    Google Scholar 

  • Hamer, N. and L. Séguin, “The HASTUS system: New algorithms and modules for the 90s,” in M. Desrochers and J.-M. Rousseau (eds), Computer-Aided Transit Scheduling, Springer-Verlag, Berlin, 1992, pp. 17-29.

    Google Scholar 

  • Wolsey, L. A., Integer Programming, John Wiley & Sons, New York, 1998.

    Google Scholar 

  • Johnson, C., E. L. Barnhart, G. L. Nemhauser, M. W. P. Savelsbergh, P. Vance, “Branch-and-price: column generation for solving huge integer programs,” Oper. Res., 46, 316-329 (1998).

    Google Scholar 

  • Kwan, R. S. K., A. S. K. Kwan, and A. Wren, “Evolutionary driver scheduling with relief chains,” Evol. Comput., 9, 445-460 (2001).

    Google Scholar 

  • Smith, Barbara M., Colin J. Layfield, and Anthony Wren, “A constraint programming pre-processor for a bus driver scheduling system,” in E. C. Freuder and R. J. Wallace (eds), Constraint Programming and Discrete Optimization, American Mathematical Society, 2001, pp. 131-148.

  • Shen, Yingdong and Raymond S. K. Kwan, “Tabu search for driver scheduling,” in S. Voss and J. R. Daduna (eds), Computer-Aided Scheduling of Public Transport, Springer-Verlag, Berlin, 2001, pp. 121-135.

    Google Scholar 

  • Smith, B. M. and A. Wren, “A bus crew scheduling system using a set covering formulation,” Transporto. Res., 22A, 97-108, (1988).

    Google Scholar 

  • Wren, A. and B. M. Smith, “Experiences with a crew scheduling system based on set covering,” in J. R. Daduna and A. Wren (eds), Computer-Aided Transit Scheduling, Springer-Verlag, Berlin, 1988, pp. 104-118.

    Google Scholar 

  • Parker, M. E., A. Wren, R. S. K. Kwan, “Modelling the scheduling of train drivers,” in J. R. Daduna, I. Branco and J. M. P. Paixao (eds), Computer-Aided Transit Scheduling, Springer-Verlag, Berlin, 1995, pp. 213-235.

    Google Scholar 

  • Willers, W. P., L. G. Proll, A. Wren, “A dual strategy for solving the linear programming relaxation of a driver scheduling system,” Ann. Oper. Res., 58, 519-531 (1995).

    Google Scholar 

  • Fores, Sarah and Les Proll, “Driver scheduling by integer linear programming—the TRACS II approach,” in A. El Kamel P Borne, M. Ksouri (eds.), Proceedings CESA'98 Computational Engineering in Systems Applications Symposium on Industrial and Manufacturing Systems, LÚnion des Chercheurs et Ingenieurs Scientifiques (UCIS), Villeneuve d'Ascq, 1998.

    Google Scholar 

  • Fores, Sarah, Les Proll, Anthony Wren, “An improved ILP system for driver scheduling,” in N. H. M. Wilson (ed.), Computer-Aided Transit Scheduling, Springer Verlag, Berlin, 1999, pp. 43-62.

    Google Scholar 

  • Kwan, A. S. K., R. S. K. Kwan, M. E. Parker, A. Wren, “Producing train driver schedules under different operating strategies,” in N.H.M. Wilson (ed.), Computer-Aided Transit Scheduling, Springer-Verlag, Berlin, 1999, pp. 129-154.

    Google Scholar 

  • Bixby, R. E., J. W. Gregory, I. L. Lustig, R. J. Marsten, and D. F. Shanno, “Very large-scale linear programming: A case study in combining interior point and simplec methods,” Oper. Res., 40, 85-897, (1992).

    Google Scholar 

  • Forrest, J. J. and D. Goldfarb, “Steepest-edge simplex algorithms for linear programming,” Math. Prog., 57, 341-374 (1992).

    Google Scholar 

  • Chamberlain, M. and A. Wren, “Developments and recent experience with the BUSMAN and BUSMAN II systems,” in M. Desrochers and J.-M. Rousseau (eds), Computer-Aided Transit Scheduling, Springer-Verlag, Berlin, 1992, pp. 1-15.

    Google Scholar 

  • Kwan, A. S. K., R. S. K. Kwan, M. E. Parker, A. Wren, “Producing train driver shifts by computer,” in J. Allan, C. A. Brebbia, R.J. Hill, G. Sciutto and S. Sone (eds), Computer in Railways V, Vol. 1: Railway Systems-and Management, Computational Mechanics Publications, 1996, pp. 421-435.

  • Desrochers, M., J. Gilbert, M. Sauvé, and F. Soumis, “CREW-OPT: Subproblem modelling in a column generation approach to urban crew scheduling,” in M. Desrochers and J.-M. Rousseau (eds), Computer-Aided Transit Scheduling, Springer-Verlag, Berlin, 1992, pp. 395-406.

    Google Scholar 

  • Caprara, A., M. Fischetti, P. L. Guida, P. Toth, and D. Vigo, “Solution of large-scale railway crew planning problems: The Italian experience,” in N.H.M. Wilson (ed.), Computer-Aided Transit Scheduling, Springer-Verlag, Berlin, 1999, pp. 1-18.

    Google Scholar 

  • Fahle, Torsten, Ulrich Junker, Stefan E. Karisch, Niklas Kohl, Meinolf Sellmann, and Bo Vaaben, “Constraint programming based column generation for crew assignment,” J. Heuristics, 8, 59-82 (2002).

    Google Scholar 

  • Fores, Sarah, Les Proll, and Anthony Wren, “Experiences with a flexible driver scheduler,” in S. Voss and J. R. Daduna (eds), Computer-Aided Scheduling of Public Transport, Springer-Verlag, Berlin, 2001, pp. 137-152.

    Google Scholar 

  • Wren, A., and R. S. K. Kwan, “Installing an urban transport scheduling system,” J. Sched., 2, 3-17 (1999).

    Google Scholar 

  • Meilton, M., “Selecting and implementing a computer aided scheduling system for a large bus company,” in S. Voss and J. R. Daduna (eds), Computer-Aided Scheduling of Public Transport, Springer-Verlag, Berlin, 2001, pp. 203-214.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wren, A., Fores, S., Kwan, A. et al. A Flexible System for Scheduling Drivers. Journal of Scheduling 6, 437–455 (2003). https://doi.org/10.1023/A:1024854522373

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024854522373

Navigation