A Distributed Algorithm for Dynamic Break Scheduling in Emergency Service Fleets

  • Marin LujakEmail author
  • Holger Billhardt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10621)


The quality of service and efficiency of labour utilization in emergency service fleets, such as police, fire departments, and emergency medical services (EMS), depends, among other things, on the efficiency of work break scheduling. The workload of such fleets usually cannot be forecasted with certainty and its urgency requires an immediate response. However, prolonged focused work periods decrease efficiency with related decline of attention and performance. Therefore, break schedule should be regularly updated as the work shift progresses to allow frequent and sufficiently long time for rest. In this paper, we propose a distributed and dynamic work break scheduling algorithm for crews in emergency service vehicle fleets. Based on the historical intervention data, the algorithm rearranges vehicles’ crews’ work breaks in a manner considering individual crews’ preferences. Moreover, it dynamically reallocates stand-by vehicles for best coverage of a region of interest. We analyze the proposed algorithm and show its performance and efficiency on the EMS use-case.


Emergency service Dynamic break scheduling Dynamic shift scheduling Vehicle crew assignment Service operations scheduling 


  1. 1.
    Bash, B.A., Desnoyers, P.J.: Exact distributed Voronoi cell computation in sensor networks. In: Proceedings of the 6th International Conference on Information Processing in Sensor Networks, pp. 236–243. ACM (2007)Google Scholar
  2. 2.
    Beer, A., Gartner, J., Musliu, N., Schafhauser, W., Slany, W.: An AI-based break-scheduling system for supervisory personnel. IEEE Intell. Syst. 25(2), 60–73 (2010)CrossRefGoogle Scholar
  3. 3.
    Van den Bergh, J., Beliën, J., De Bruecker, P., Demeulemeester, E., De Boeck, L.: Personnel scheduling: a literature review. Eur. J. Oper. Res. (EJOR) 226(3), 367–385 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bhandari, A., Scheller-Wolf, A., Harchol-Balter, M.: An exact and efficient algorithm for the constrained dynamic operator staffing problem for call centers. Manage. Sci. 54(2), 339–353 (2008)CrossRefzbMATHGoogle Scholar
  5. 5.
    Billhardt, H., Fernández, A., Lemus, L., Lujak, M., Osman, N., Ossowski, S., Sierra, C.: Dynamic coordination in fleet management systems: toward smart cyber fleets. IEEE Intell. Syst. 29(3), 70–76 (2014)CrossRefGoogle Scholar
  6. 6.
    Billhardt, H., Lujak, M., Sánchez-Brunete, V., Fernández, A., Ossowski, S.: Dynamic coordination of ambulances for emergency medical assistance services. Knowl.-Based Syst. 70, 268–280 (2014)CrossRefGoogle Scholar
  7. 7.
    Chiuso, A., Fagnani, F., Schenato, L., Zampieri, S.: Gossip algorithms for distributed ranking. In: American Control Conference (ACC), 2011, pp. 5468–5473. IEEE (2011)Google Scholar
  8. 8.
    Defraeye, M., Van Nieuwenhuyse, I.: Staffing and scheduling under nonstationary demand for service: a literature review. Omega 58, 4–25 (2016)CrossRefzbMATHGoogle Scholar
  9. 9.
    Di Gaspero, L., Gärtner, J., Musliu, N., Schaerf, A., Schafhauser, W., Slany, W.: Automated shift design and break scheduling. In: Uyar, A., Ozcan, E., Urquhart, N. (eds.) Automated Scheduling and Planning. SCI, vol. 505, pp. 109–127. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-39304-4_5 CrossRefGoogle Scholar
  10. 10.
    Ernst, A.T., Jiang, H., Krishnamoorthy, M., Sier, D.: Staff scheduling and rostering: a review of applications, methods and models. Eur. J. Oper. Res. 153(1), 3–27 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Huisman, D., Freling, R., Wagelmans, A.P.: Multiple-depot integrated vehicle and crew scheduling. Transp. Sci. 39(4), 491–502 (2005)CrossRefGoogle Scholar
  12. 12.
    Hur, D., Mabert, V.A., Bretthauer, K.M.: Real-time work schedule adjustment decisions: an investigation and evaluation. Prod. Oper. Manage. 13(4), 322–339 (2004)CrossRefGoogle Scholar
  13. 13.
    Lloyd, S.: Least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lujak, M., Billhardt, H.: Coordinating emergency medical assistance. In: Ossowski, S. (ed.) Agreement Technologies. LGTS, vol. 8, pp. 597–609. Springer, Dordrecht (2013). doi: 10.1007/978-94-007-5583-3_35 CrossRefGoogle Scholar
  15. 15.
    Lujak, M., Billhardt, H., Ossowski, S.: Optimizing emergency medical assistance coordination in after-hours urgent surgery patients. In: Bulling, N. (ed.) EUMAS 2014. LNCS, vol. 8953, pp. 316–331. Springer, Cham (2015). doi: 10.1007/978-3-319-17130-2_21 Google Scholar
  16. 16.
    Lujak, M., Billhardt, H., Ossowski, S.: Distributed coordination of emergency medical service for angioplasty patients. Ann. Math. Artif. Intell. 78(1), 73–100 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Mehrotra, V., Ozlük, O., Saltzman, R.: Intelligent procedures for intra-day updating of call center agent schedules. Prod. Oper. Manage. 19(3), 353–367 (2010)CrossRefGoogle Scholar
  18. 18.
    Mesquita, M., Moz, M., Paias, A., Paixão, J., Pato, M., Respício, A.: A new model for the integrated vehicle-crew-rostering problem and a computational study on rosters. J. Sched. 14(4), 319–334 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Rekik, M., Cordeau, J.F., Soumis, F.: Implicit shift scheduling with multiple breaks and work stretch duration restrictions. J. Sched. 13(1), 49–75 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Robbins, T.R., Harrison, T.P.: A stochastic programming model for scheduling call centers with global service level agreements. EJOR 207(3), 1608–1619 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Widl, M., Musliu, N.: An improved memetic algorithm for break scheduling. In: Blesa, M.J., Blum, C., Raidl, G., Roli, A., Sampels, M. (eds.) HM 2010. LNCS, vol. 6373, pp. 133–147. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-16054-7_10 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.IMT Lille DouaiDouaiFrance
  2. 2.University Rey Juan CarlosMadridSpain

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