Critical time windowed train driver relief opportunities

Abstract

Train driver scheduling is the problem of constructing an efficient schedule of driver shifts, each of which contains a sequence of work on one or more trains separated by breaks. Relief opportunities (ROs) occur when trains stop at a station. While relieving on arrival at a train station is the preferred practice in the UK rail industry, considering relieving at other times within the full window of relief opportunities (WRO) at a stop might allow for a schedule optimization algorithm to build better schedules. However, simply expanding each WRO into ROs at individual minutes within the WRO would exponentially increase the complexity of the combinatorial optimization problem. A rational approach would be to be selective in considering the WROs when applying Generate-and-Select (GaS); this could either take the form of a pre-processing stage to GaS, or that of augmenting (or even replacing) the generation phase of GaS.

In this paper we first show a simple example where approximating WROs by a single relief point results in inefficient schedules, and hints at the complexity of exploiting WROs. We then study the potential of WROs in terms of the new spells and/or shifts they may allow to be created. We propose a heuristic extension to the GaS generation phase, where WROs are analysed in relation to individual scheduling constraints; ROs within WROs that are deemed useful are added to the set of arrival-time ROs. Results show an improvement over the traditional approach in a number of real-life instances from UK operations.

We also present a constructive method to analyse a combination of scheduling constraints. Results show that the method is effective in exploiting constraints that may be skipped or difficult to consider by non-constructive approaches.

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

References

  1. Fores S (2001) Column generation approaches to bus driver scheduling. PhD thesis, School of Computing, University of Leeds

  2. Huisman D (2004) Integrated and dynamic vehicle and crew scheduling. PhD thesis, Tinbergen Institute, Erasmus University Rotterdam

  3. Kwan RSK (2004) Bus and train driver scheduling. In: Leung JY-T (ed) Handbook of scheduling: algorithms, models, and performance analysis. CRC Press, New York. Chapter 51

    Google Scholar 

  4. Kwan RSK, Kwan ASK (2007) Effective search space control for large and/or complex driver scheduling problems. Ann Oper Res 155:417–435

    Article  Google Scholar 

  5. Laplagne I, Kwan RSK, Kwan ASK (2005) A hybridised integer programming and local search method for robust train driver schedules planning. In: Lecture notes in computer science, vol 3616. Springer, Berlin, pp 71–85

    Google Scholar 

  6. Lübbecke ME, Desrosiers J (2005) Selected topics in column generation. Oper Res 53(6):1007–1023

    Article  Google Scholar 

  7. Parker ME, Smith BM (1981) Two approaches to computer crew scheduling. In: Wren A (ed) Computer scheduling of public transport. North-Holland, Amsterdam, pp 193–222

    Google Scholar 

  8. Shen Y (2001) Tabu search for bus and train driver scheduling with time windows. PhD thesis, School of Computing, University of Leeds

  9. Shen Y, Kwan RSK (2001) Tabu search for driver scheduling. In: Voss S, Daduna JR (eds) Computer-aided scheduling of public transport. Lecture notes in economics and mathematical systems, vol 505. Springer, New York, pp 121–135

    Google Scholar 

  10. Weider S (2007) Integration of vehicle and duty scheduling in public transport. PhD thesis, Technische Universität Berlin

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ignacio Laplagne.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Laplagne, I., Kwan, R.S.K. & Kwan, A.S.K. Critical time windowed train driver relief opportunities. Public Transp 1, 73–85 (2009). https://doi.org/10.1007/s12469-008-0001-6

Download citation

Keywords

  • Crew scheduling
  • Time windows