OR Spectrum

, Volume 34, Issue 3, pp 593–633 | Cite as

Models and algorithms for the heterogeneous dial-a-ride problem with driver-related constraints

  • Sophie N. Parragh
  • Jean-François Cordeau
  • Karl F. Doerner
  • Richard F. Hartl
Open Access
Regular Article


This paper introduces models and algorithms for a static dial-a-ride problem arising in the transportation of patients by non-profit organizations such as the Austrian Red Cross. This problem is characterized by the presence of heterogeneous vehicles and patients. In our problem, two types of vehicles are used, each providing a different capacity for four different modes of transportation. Patients may request to be transported either seated, on a stretcher or in a wheelchair. In addition, some may require accompanying persons. The problem is to construct a minimum-cost routing plan satisfying service-related criteria, expressed in terms of time windows, as well as driver-related constraints expressed in terms of maximum route duration limits and mandatory lunch breaks. We introduce both a three-index and a set-partitioning formulation of the problem. The linear programming relaxation of the latter is solved by a column generation algorithm. We also propose a variable neighborhood search heuristic. Finally, we integrate the heuristic and the column generation approach into a collaborative framework. The column generation algorithm and the collaborative framework provide tight lower bounds on the optimal solution values for small-to-medium-sized instances. The variable neighborhood search algorithm yields high-quality solutions for realistic test instances.


Passenger transportation Dial-a-ride-problem Column generation Variable neighborhood search 



This work was supported by the Special Translational Research Program of the Austrian Science Fund (FWF) under Grants #L286-N04 and #L362-N15, and by the Canadian Natural Sciences and Engineering Research Council under grant 227837-09. This support is gratefully acknowledged. We thank Fabien Tricoire for his suggestions and the Austrian Red Cross for providing the real-world data.We are also grateful to the referees for their valuable comments.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Sophie N. Parragh
    • 1
  • Jean-François Cordeau
    • 2
  • Karl F. Doerner
    • 1
  • Richard F. Hartl
    • 1
  1. 1.Department of Business AdministrationUniversity of ViennaViennaAustria
  2. 2.Canada Research Chair in Logistics and Transportation and CIRRELTHEC MontréalMontréalCanada

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