Advertisement

Journal of Scheduling

, Volume 20, Issue 1, pp 43–55 | Cite as

Optimizing railway crew schedules with fairness preferences

  • Silke JütteEmail author
  • Daniel Müller
  • Ulrich W. Thonemann
Article

Abstract

Railway crew scheduling deals with generating duties for train drivers to cover all train movements of a given timetable while taking into account a set of work regulations. The objective is to minimize the overall costs associated with a crew schedule, which includes workforce costs and hotel costs. A cost minimal schedule often contains duties that are unpopular to train drivers, and these unpopular duties are often unevenly distributed among crew depots. At the company that motivated our research, for example, train drivers dislike duties that start in the early morning hours. Currently, some crew depots operate large numbers of these unpopular duties, while others do not have any unpopular duties at all. The train drivers perceive this situation as unfair. They prefer schedules with fewer and more evenly distributed unpopular duties across crew depots. In this paper, we define and measure unpopularity and (un)fairness in a railway crew scheduling context. We integrate fairness conditions into a column generation-based solution algorithm and analyze the effect of increased fairness on cost. We also show how increased fairness affects the unpopularity of a schedule. Our method has been applied to test instances at a large European railway freight carrier. Compared to a standard approach that penalizes only the number of unpopular duties in a schedule, we were able to significantly improve schedule fairness with only marginal increases in schedule cost.

Keywords

Crew scheduling Fairness Large-scale optimization Decision support 

References

  1. Abbink, E., Fischetti, M., Kroon, L., Timmer, G., & Vromans, M. J. C. M. (2005). Reinventing crew scheduling at Netherlands railways. Interfaces, 35(5), 393–401.CrossRefGoogle Scholar
  2. Adams, J. S. (1965). Inequity in social exchange. Advances in Experimental Social Psychology, 2, 267–299.CrossRefGoogle Scholar
  3. Akerstedt, T. (1998). Is there an optimal sleep-wake pattern in shift work? Scandinavian Journal of Work, Environment & Health, 24(suppl 3), 18–29.Google Scholar
  4. Akerstedt, T. (2003). Shift work and disturbed sleep/wakefulness. Occupational Medicine, 53(2), 89–94.Google Scholar
  5. Bard, J. F., & Purnomo, H. W. (2005). Preference scheduling for nurses using column generation. European Journal of Operational Research, 164, 510–534.CrossRefGoogle Scholar
  6. Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., & Vance, P. H. (1998). Branch-and-price: Column generation for solving huge integer programs. Operations Research, 46(3), 316–329.CrossRefGoogle Scholar
  7. Blöchliger, I. (2004). Modeling staff scheduling problems. A tutorial. European Journal of Operational Research, 158, 533–542.CrossRefGoogle Scholar
  8. Bolton, G. E., & Ockenfels, A. (2000). ERC: A theory of equity, reciprocity, and competition. The American Economic Review, 90(1), 166–193.CrossRefGoogle Scholar
  9. Borndörfer, R., Grötschel, M., & Löbel, A. (2001). Scheduling duties by adaptive column generation. Technical Report 01-02, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, GermanyGoogle Scholar
  10. Caprara, A., Toth, P., Vigo, D., & Fischetti, M. (1998). Modeling and solving the crew rostering problem. Operations Research, 46(6), 820–830.CrossRefGoogle Scholar
  11. Caprara, A., Kroon, L., Monaci, M., Peeters, M., & Toth, P. (2007). Passenger railway optimization. In C. Barnhart & G. Laporte (Eds.), Handbooks in operations research and management science, Vol. 14 transportation, Chap. 3 (Vol. 14, pp. 129–187). Amsterdam: Elsevier B.V.Google Scholar
  12. Cordeau, J. F., Toth, P., & Vigo, D. (1998). A survey of optimization models for train routing and scheduling. Transportation Science, 32(4), 380–404.CrossRefGoogle Scholar
  13. De Boer, E. M., Bakker, A. B., Syroit, J. E., & Schaufeli, W. B. (2002). Unfairness at work as a predictor of absenteeism. Journal of Organizational Behavior, 23, 181–197.CrossRefGoogle Scholar
  14. De Causmaecker, P., & Vanden Berghe, G. (2011). A categorisation of nurse rostering problems. Journal of Scheduling, 14(1), 3–16.CrossRefGoogle Scholar
  15. Desrosiers, J., & Lübbecke, M. E. (2005). A primer in column generation. In G. Desaulniers, J. Desrosiers, & M. M. Solomon (Eds.), Column generation, Chap. 1 (pp. 1–32). New York: Springer.CrossRefGoogle Scholar
  16. Dowling, D., Krishnamoorthy, M., Mackenzie, H., & Sier, D. (1997). Staff rostering at a large international airport. Annals of Operations Research, 72, 125–147.CrossRefGoogle Scholar
  17. Fehr, E., & Schmidt, K. M. (1999). A theory of fairness, competition, and cooperation. The Quarterly Journal of Economics, 114(3), 817–868.Google Scholar
  18. Folkard, S., & Barton, J. (1993). Does the ‘forbidden zone’ for sleep onset influence morning shift sleep duration? Ergonomics, 36(1–3), 85–91.CrossRefGoogle Scholar
  19. Folkard, S., & Tucker, P. (2003). Shift work, safety and productivity. Occupational Medicine, 53(2), 95–101.CrossRefGoogle Scholar
  20. Gamache, M., Soumis, F., Marquis, G., & Desrosiers, J. (1999). A column generation approach for large-scale aircrew rostering problems. Operations Research, 47(2), 247–263.CrossRefGoogle Scholar
  21. Harrington, J. M. (2001). Health effects of shift work and extended hours of work. Occupational and Environmental Medicine, 58(1), 68–72.CrossRefGoogle Scholar
  22. Homans, G. C. (1961). Social behavior: Its elementary forms. San Diego: Harcourt Brace.Google Scholar
  23. Jütte, S., Albers, M., Thonemann, U. W., & Haase, K. (2011). Optimizing railway crew scheduling at DB Schenker. Interfaces, 41(2), 109–122.CrossRefGoogle Scholar
  24. Kecklund, G., & Akerstedt, T. (1995). Effects of timing of shifts on sleepiness and sleep duration. Journal of Sleep Research, 4(suppl 2), 47–50.CrossRefGoogle Scholar
  25. Knauth, P. (1993). The design of shift systems. Ergonomics, 36(1–3), 15–28.Google Scholar
  26. Kroon, L., & Fischetti, M. (2001). Crew scheduling for Netherlands railways “Destination: Customer”. In S. Voß & J. R. Daduna (Eds.), Computer-aided scheduling of public transport (Vol. 505, pp. 181–201)., Lecture notes in economics and mathematical systems Berlin: Springer.CrossRefGoogle Scholar
  27. Maenhout, B., & Vanhoucke, M. (2013). An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems. Omega, 41(2), 485–499.CrossRefGoogle Scholar
  28. Martin, S., Ouelhadj, D., Smet, P., Vanden Berghe, G., & Özcan, E. (2013). Cooperative search for fair nurse rosters. Expert Systems with Applications, 40(16), 6674–6683.CrossRefGoogle Scholar
  29. Mason, A. J., Ryan, D. M., & Panton, D. M. (1998). Integrated simulation, heuristic and optimisation approaches to staff scheduling. Operations Research, 46(2), 161–175.CrossRefGoogle Scholar
  30. Millar, H. H., & Kiragu, M. (1998). Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming. European Journal of Operational Research, 104, 582–592.CrossRefGoogle Scholar
  31. Rosa, R. R., Härmä, M., Pulli, K., Mulder, M., & Näsman, O. (1996). Rescheduling a three shift system at a steel rolling mill: Effects of a one hour delay of shift starting times on sleep and alertness in younger and older workers. Occupational and Environmental Medicine, 53, 677–685.CrossRefGoogle Scholar
  32. Schaefer, A. J., Johnson, E. L., Kleywegt, A. J., & Nemhauser, G. L. (2005). Airline crew scheduling under uncertainty. Transportation Science, 39(3), 340–348.CrossRefGoogle Scholar
  33. Simons, T. L., & Roberson, Q. (2003). Why managers should care about fairness : The effects of aggregate justice perceptions on organizational outcomes. Journal of Applied Psychology, 88(3), 432–443.Google Scholar
  34. Smet, P., Martin, S., Ouelhadj, D., Özcan, E., & Vanden Berghe, G. (2013). Fairness in nurse rostering. Techical report. University of Portsmouth, Portsmouth, United Kingdom.Google Scholar
  35. Stolletz, R. (2010). Operational workforce planning for check-in counters at airports. Transportation Research Part E: Logistics and Transportation Review, 46(3), 414–425.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Business Administration and EconomicsInternational University of Applied Sciences Bad Honnef - BonnBad HonnefGermany
  2. 2.University of CologneCologneGermany

Personalised recommendations