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A heuristic for real-time crew rescheduling during small disruptions

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Abstract

Due to unforeseen problems, disruptions occur in passenger railway operations. Proper real-time crew management is needed to prevent disruptions to spread over space and time. Netherlands Railways has algorithmic support from a solver to obtain good crew rescheduling solutions during big disruptions. However, small disruptions are still manually solved by human dispatchers who have limited solving capacity. In this paper the rescheduling for crews during small disruptions is modeled as inserting an uncovered task in a feasible set of duties. The problem is solved as an iterative-deepening depth-first search in a tree. To reduce computation time, we use several ideas to prune unpromising parts of the tree. We have tested the heuristic on about 5000 test instances obtained from real-world data. These tests show that the heuristic delivers good and desirable rescheduling solutions within at most 2 s.

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Notes

  1. As we see later on, each node has over 1000 children. On average 124 children survive the basic feasibility check, which we explain in Sect. 4.1. Inserting an unplanned task in a duty is conditionally possible in about 17% of the cases. This means we branch further at on average 21 children. If the depth of the tree is bounded to 7, this already leads to more than a billion leaves. However, the depth of the tree could be much larger.

  2. This sorting is done many times in the search through the tree. Therefore, we choose bucket sorting: Bucket sorting n elements can be done in linear time \(\mathcal {O}(n)\) as shown by Shutler et al. (2008), compared to \(\mathcal {O}(n\log {}n)\) for normal sorting.

  3. Note that the higher probability in the graph between pV 750,000 and 820,000 is represented in the bucket sorting, where we place these values in a higher bucket compared to the next one.

  4. Randstad is a conurbation in the Netherlands, consisting of the four largest cities and its surroundings. We include the following cities with all its train stations as locations: Almere, Amersfoort, Amsterdam, Alphen aan den Rijn, Barendrecht, Capelle aan den IJssel, Delft, Dordrecht, Gouda, Haarlem, Hilversum, Hoofddorp, Hoek van Holland, Houten, Leiden, Maassluis, Purmerend, Rijswijk, Rotterdam, Schiedam, The Hague, Utrecht, Vlaardingen, Voorburg, Zeist, Zoetermeer.

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Authors and Affiliations

  1. Bright Cape Advanced Analytics, Le Sage Ten Broeklaan 1, 5615 CP, Eindhoven, The Netherlands

    Thijs Verhaegh

  2. Econometric Institute and ECOPT, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    Dennis Huisman

  3. Process Quality and Innovation, Netherlands Railways, P.O. Box 2025, 3500 HA, Utrecht, The Netherlands

    Dennis Huisman & Pieter-Jan Fioole

  4. Department of Econometrics and Operations Research, Tilburg University, P.O.Box 90153, 5000 LE, Tilburg, The Netherlands

    Juan C. Vera

Authors
  1. Thijs Verhaegh
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  2. Dennis Huisman
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  3. Pieter-Jan Fioole
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  4. Juan C. Vera
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Correspondence to Pieter-Jan Fioole.

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Verhaegh, T., Huisman, D., Fioole, PJ. et al. A heuristic for real-time crew rescheduling during small disruptions. Public Transp 9, 325–342 (2017). https://doi.org/10.1007/s12469-017-0155-1

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  • DOI: https://doi.org/10.1007/s12469-017-0155-1

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