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.
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References
Fores S (2001) Column generation approaches to bus driver scheduling. PhD thesis, School of Computing, University of Leeds
Huisman D (2004) Integrated and dynamic vehicle and crew scheduling. PhD thesis, Tinbergen Institute, Erasmus University Rotterdam
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
Kwan RSK, Kwan ASK (2007) Effective search space control for large and/or complex driver scheduling problems. Ann Oper Res 155:417–435
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
Lübbecke ME, Desrosiers J (2005) Selected topics in column generation. Oper Res 53(6):1007–1023
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
Shen Y (2001) Tabu search for bus and train driver scheduling with time windows. PhD thesis, School of Computing, University of Leeds
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
Weider S (2007) Integration of vehicle and duty scheduling in public transport. PhD thesis, Technische Universität Berlin
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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
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DOI: https://doi.org/10.1007/s12469-008-0001-6