Modelling and Solving the Senior Transportation Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)


This paper defines a novel transportation problem, the Senior Transportation Problem (STP), which is inspired by the elderly door-to-door transportation services provided by non-profit organizations. Building on the vehicle routing literature, we develop solution approaches including mixed integer programming (MIP), constraint programming (CP), two logic-based Benders decompositions (LBBD), and a construction heuristic. Empirical analyses on both randomly generated datasets and large real-life datasets are performed. CP achieved the best results, solving to optimality 89% of our real-life instances of up to 270 vehicles with 385 requests in under 600 s. The best LBBD model can only solve 17% of those instances to optimality. Further investigation of this somewhat surprising result indicates that, compared to the LBBD approaches, the pure CP model is able to find better solutions faster and then is able to use the bounds from these sub-optimal solutions to reduce the search space slightly more effectively than the decomposition models.


  1. 1.
    Baklagis, D., Dikas, G., Minis, I.: The team orienteering pick-up and delivery problem with time windows and its applications in fleet sizing. RAIRO-Oper. Res. 50(3), 503–517 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cordeau, J.F., Laporte, G.: The dial-a-ride problem: models and algorithms. Ann. Oper. Res. 153(1), 29 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hooker, J.N., Ottosson, G.: Logic-based benders decomposition. Math. Program. 96(1), 33–60 (2003)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Laborie, P., Rogerie, J.: Reasoning with conditional time-intervals. In: FLAIRS Conference, pp. 555–560 (2008)Google Scholar
  5. 5.
    Parragh, S.N., Doerner, K., Hartl, R.F.: A survey on pickup and delivery models: part I: transportation between customers and depot. J. für Betriebswirtschaft 58(1), 21–51 (2008)CrossRefGoogle Scholar
  6. 6.
    Parragh, S.N., Doerner, K.F., Hartl, R.F.: A survey on pickup and delivery problems: part II: transportation between pickup and delivery locations. J. für Betriebswirtschaft 58, 81–117 (2008)CrossRefGoogle Scholar
  7. 7.
    Qiu, X., Feuerriegel, S., Neumann, D.: Making the most of fleets: a profit-maximizing multi-vehicle pickup and delivery selection problem. Eur. J. Oper. Res. 259(1), 155–168 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Refalo, P.: Impact-Based Search Strategies for Constraint Programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004). Scholar
  9. 9.
    Ropke, S., Cordeau, J.F.: Branch and cut and price for the pickup and delivery problem with time windows. Transp. Sci. 43(3), 267–286 (2009)CrossRefGoogle Scholar
  10. 10.
    Vansteenwegen, P., Souffriau, W., Van Oudheusden, D.: The orienteering problem: a survey. Eur. J. Oper. Res. 209(1), 1–10 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    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

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringUniversity of TorontoTorontoCanada

Personalised recommendations