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A Flexible, Fast, and Optimal Modeling Approach Applied to Crew Rostering at London Underground

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  • ManMohan Sodhi
  • Stephen Norris

Abstract

We present a general modeling approach to crew rostering and its application to computer-assisted generation of rotation-based rosters (or rotas) at the London Underground. Our goals were flexibility, speed, and optimality, and our approach is unique in that it achieves all three. Flexibility was important because requirements at the Underground are evolving and because specialized approaches in the literature did not meet our flexibility-implied need to use standard solvers. We decompose crew rostering into stages that can each be solved with a standard commercial MILP solver. Using a 167 MHz Sun UltraSparc 1 and CPLEX 4.0 MILP solver, we obtained high-quality rosters in runtimes ranging from a few seconds to a few minutes within 2% of optimality. Input data were takes from different depots with crew sizes ranging from 30–150 drivers, i.e., with number of duties ranging from about 200–1000. Using an argument based on decomposition and aggregation, we prove the optimality of our approach for the overall crew rostering problem. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • ManMohan Sodhi & Stephen Norris, 2004. "A Flexible, Fast, and Optimal Modeling Approach Applied to Crew Rostering at London Underground," Annals of Operations Research, Springer, vol. 127(1), pages 259-281, March.
    • Handle: RePEc:spr:annopr:v:127:y:2004:i:1:p:259-281:10.1023/b:anor.0000019092.76669.a1
    DOI: 10.1023/B:ANOR.0000019092.76669.a1
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    Cited by:

    1. Breugem, T. & van Rossum, B.T.C. & Dollevoet, T. & Huisman, D., 2022. "A column generation approach for the integrated crew re-planning problem," Omega, Elsevier, vol. 107(C).
    2. Dennis Huisman & Leo G. Kroon & Ramon M. Lentink & Michiel J. C. M. Vromans, 2005. "Operations Research in passenger railway transportation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(4), pages 467-497, November.
    3. Hartog, A. & Huisman, D. & Abbink, E.J.W. & Kroon, L.G., 2006. "Decision support for crew rostering at NS," Econometric Institute Research Papers EI 2006-04, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Tristan Becker & Maximilian Schiffer & Grit Walther, 2022. "A General Branch-and-Cut Framework for Rotating Workforce Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1548-1564, May.
    5. Nishi, Tatsushi & Sugiyama, Taichi & Inuiguchi, Masahiro, 2014. "Two-level decomposition algorithm for crew rostering problems with fair working condition," European Journal of Operational Research, Elsevier, vol. 237(2), pages 465-473.
    6. Breugem, T. & Dollevoet, T.A.B. & Huisman, D., 2019. "A Column Generation Approach for the Integrated Crew Re-Planning Problem," Econometric Institute Research Papers EI2019-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Safae Er-Rbib & Guy Desaulniers & Issmail Elhallaoui & Patrick Munroe, 2021. "Preference-based and cyclic bus driver rostering problem with fixed days off," Public Transport, Springer, vol. 13(2), pages 251-286, June.
    8. Breugem, T. & Dollevoet, T.A.B. & Huisman, D., 2017. "Is Equality always desirable?," Econometric Institute Research Papers EI2017-30, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Jaime Miranda & Pablo A. Rey & Antoine Sauré & Richard Weber, 2018. "Metro Uses a Simulation-Optimization Approach to Improve Fare-Collection Shift Scheduling," Interfaces, INFORMS, vol. 48(6), pages 529-542, November.
    10. F. Zeynep Sargut & Caner Altuntaş & Dilek Cetin Tulazoğlu, 2017. "Multi-objective integrated acyclic crew rostering and vehicle assignment problem in public bus transportation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1071-1096, October.
    11. Breugem, T. & Dollevoet, T.A.B. & Huisman, D., 2018. "Analyzing a Family of Formulations for Cyclic Crew Rostering," Econometric Institute Research Papers EI2018-35, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Thomas Breugem & Twan Dollevoet & Dennis Huisman, 2022. "Is Equality Always Desirable? Analyzing the Trade-Off Between Fairness and Attractiveness in Crew Rostering," Management Science, INFORMS, vol. 68(4), pages 2619-2641, April.
    13. Margarida Moz & Ana Respício & Margarida Vaz Pato, 2009. "Bi-objective evolutionary heuristics for bus driver rostering," Public Transport, Springer, vol. 1(3), pages 189-210, August.

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