A Constraint Programming Approach for Solving Patient Transportation Problems

  • Quentin CappartEmail author
  • Charles Thomas
  • Pierre Schaus
  • Louis-Martin Rousseau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11008)


The Patient Transportation Problem (PTP) aims to bring patients to health centers and to take them back home once the care has been delivered. All the requests are known beforehand and a schedule is built the day before its use. It is a variant of the well-known Dial-a-Ride Problem (DARP) but it has nevertheless some characteristics that complicate the decision process. Three levels of decisions are considered: selecting which requests to service, assigning vehicles to requests and routing properly the vehicles. In this paper, we propose a Constraint Programming approach to solve the Patient Transportation Problem. The model is designed to be flexible enough to accommodate new constraints and objective functions. Furthermore, we introduce a generic search strategy to maximize efficiently the number of selected requests. Our results show that the model can solve real life instances and outperforms greedy strategies typically performed by human schedulers.



This research is financed by the Walloon Region (Belgium) as part of PRESupply Project. The problem has been proposed by the CSD, a Belgian non-profit organization operating at Liège.


  1. 1.
    Cordeau, J.F., Laporte, G.: The dial-a-ride problem: models and algorithms. Ann. Oper. Res. 153, 29–46 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Melachrinoudis, E., Min, H.: A tabu search heuristic for solving the multi-depot, multi-vehicle, double request dial-a-ride problem faced by a healthcare organisation. Int. J. Oper. Res. 10, 214–239 (2011)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Liu, R., Xie, X., Augusto, V., Rodriguez, C.: Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care. Eur. J. Oper. Res. 230, 475–486 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Detti, P., Papalini, F., de Lara, G.Z.M.: A multi-depot dial-a-ride problem with heterogeneous vehicles and compatibility constraints in healthcare. Omega 70, 1–14 (2017)CrossRefGoogle Scholar
  5. 5.
    Cordeau, J.F., Laporte, G.: A tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transp. Res. Part B Methodol. 37, 579–594 (2003)CrossRefGoogle Scholar
  6. 6.
    Parragh, S.N.: Introducing heterogeneous users and vehicles into models and algorithms for the dial-a-ride problem. Transp. Res. Part C Emerg. Technol. 19, 912–930 (2011)CrossRefGoogle Scholar
  7. 7.
    Parragh, S.N., Cordeau, J.F., Doerner, K.F., Hartl, R.F.: Models and algorithms for the heterogeneous dial-a-ride problem with driver-related constraints. OR Spectr. 34, 593–633 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Psaraftis, H.N.: An exact algorithm for the single vehicle many-to-many dial-a-ride problem with time windows. Transp. Sci. 17, 351–357 (1983)CrossRefGoogle Scholar
  9. 9.
    Melachrinoudis, E., Ilhan, A.B., Min, H.: A dial-a-ride problem for client transportation in a health-care organization. Comput. Oper. Res. 34, 742–759 (2007)CrossRefGoogle Scholar
  10. 10.
    Cordeau, J.F., Gendreau, M., Laporte, G.: A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30, 105–119 (1997)CrossRefGoogle Scholar
  11. 11.
    Parragh, S.N., Doerner, K.F., Hartl, R.F., Gandibleux, X.: A heuristic two-phase solution approach for the multi-objective dial-a-ride problem. Networks 54, 227–242 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Berbeglia, G., Cordeau, J.F., Gribkovskaia, I., Laporte, G.: Static pickup and delivery problems: a classification scheme and survey. Top 15, 1–31 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Attanasio, A., Cordeau, J.F., Ghiani, G., Laporte, G.: Parallel tabu search heuristics for the dynamic multi-vehicle dial-a-ride problem. Parallel Comput. 30, 377–387 (2004)CrossRefGoogle Scholar
  14. 14.
    Berbeglia, G., Pesant, G., Rousseau, L.M.: Checking the feasibility of dial-a-ride instances using constraint programming. Transp. Sci. 45, 399–412 (2011)CrossRefGoogle Scholar
  15. 15.
    Berbeglia, G., Cordeau, J.F., Laporte, G.: A hybrid tabu search and constraint programming algorithm for the dynamic dial-a-ride problem. INFORMS J. Comput. 24, 343–355 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Parragh, S.N., Schmid, V.: Hybrid column generation and large neighborhood search for the dial-a-ride problem. Comput. Oper. Res. 40, 490–497 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Jain, S., Van Hentenryck, P.: Large neighborhood search for dial-a-ride problems. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 400–413. Springer, Heidelberg (2011). Scholar
  18. 18.
    Liu, C., Aleman, D.M., Beck, J.C.: Modelling and solving the senior transportation problem. In: van Hoeve, W.-J. (ed.) CPAIOR 2018. LNCS, vol. 10848, pp. 412–428. Springer, Cham (2018). Scholar
  19. 19.
    Beldiceanu, N., Carlsson, M., Rampon, J.X.: Global constraint catalog, (revision a) (2012)Google Scholar
  20. 20.
    Gay, S., Hartert, R., Schaus, P.: Simple and scalable time-table filtering for the cumulative constraint. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 149–157. Springer, Cham (2015). Scholar
  21. 21.
    Vilím, P.: Timetable edge finding filtering algorithm for discrete cumulative resources. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 230–245. Springer, Heidelberg (2011). Scholar
  22. 22.
    Gay, S., Hartert, R., Schaus, P.: Time-table disjunctive reasoning for the cumulative constraint. In: Michel, L. (ed.) CPAIOR 2015. LNCS, vol. 9075, pp. 157–172. Springer, Cham (2015). Scholar
  23. 23.
    Ouellet, P., Quimper, C.-G.: Time-table extended-edge-finding for the cumulative constraint. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 562–577. Springer, Heidelberg (2013). Scholar
  24. 24.
    Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Explaining the cumulative propagator. Constraints 16, 250–282 (2011)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Simonis, H., Cornelissens, T.: Modelling producer/consumer constraints. In: Montanari, U., Rossi, F. (eds.) CP 1995. LNCS, vol. 976, pp. 449–462. Springer, Heidelberg (1995). Scholar
  26. 26.
    Laborie, P., Rogerie, J.: Reasoning with conditional time-intervals. In: FLAIRS Conference, pp. 555–560 (2008)Google Scholar
  27. 27.
    Laborie, P., Rogerie, J., Shaw, P., Vilím, P.: Reasoning with conditional time-intervals. Part II: an algebraical model for resources. In: FLAIRS Conference, pp. 201–206 (2009)Google Scholar
  28. 28.
    Laborie, P., Rogerie, J., Shaw, P., Vilím, P.: IBM ILOG CP optimizer for scheduling. Constraints, 1–41 (2018)Google Scholar
  29. 29.
    Dejemeppe, C., Van Cauwelaert, S., Schaus, P.: The unary resource with transition times. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 89–104. Springer, Cham (2015). Scholar
  30. 30.
    Ngatchou, P., Zarei, A., El-Sharkawi, A.: Pareto multi objective optimization. In: 2005 Proceedings of the 13th International Conference on Intelligent Systems Application to Power Systems, pp. 84–91. IEEE (2005)Google Scholar
  31. 31.
    Gay, S., Hartert, R., Lecoutre, C., Schaus, P.: Conflict ordering search for scheduling problems. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 140–148. Springer, Cham (2015). Scholar
  32. 32.
    Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998). Scholar
  33. 33.
    Lauriere, J.L.: A language and a program for stating and solving combinatorial problems. Artif. Intell. 10, 29–127 (1978)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Vilím, P., Laborie, P., Shaw, P.: Failure-directed search for constraint-based scheduling. In: Michel, L. (ed.) CPAIOR 2015. LNCS, vol. 9075, pp. 437–453. Springer, Cham (2015). Scholar
  35. 35.
    OscaR Team: OscaR: Scala in OR (2012).
  36. 36.
    Thomas, C., Cappart, Q., Schaus, P., Rousseau, L.M.: CSPLib problem 082: Patient transportation problem.
  37. 37.
    Godard, D., Laborie, P., Nuijten, W.: Randomized large neighborhood search for cumulative scheduling. ICAPS 5, 81–89 (2005)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Quentin Cappart
    • 1
    • 2
    • 3
    Email author
  • Charles Thomas
    • 1
  • Pierre Schaus
    • 1
  • Louis-Martin Rousseau
    • 2
    • 3
  1. 1.Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Ecole Polytechnique de MontréalMontréalCanada
  3. 3.Interuniversity Research Centre on Enterprise NetworksLogistics and Transportation (CIRRELT)MontréalCanada

Personalised recommendations