Solving the Dynamic Dial-a-Ride Problem Using a Rolling-Horizon Event-Based Graph

Authors Daniela Gaul , Kathrin Klamroth , Michael Stiglmayr

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Author Details

Daniela Gaul
  • Department of Mathematics, Universität Wuppertal, Germany
Kathrin Klamroth
  • Department of Mathematics, Universität Wuppertal, Germany
Michael Stiglmayr
  • Department of Mathematics, Universität Wuppertal, Germany


We thank WSW mobil GmbH for providing dial-a-ride data from their service. Furthermore, we kindly acknowledge three anonymous reviewers for the valuable feedback, which has improved this paper a lot.

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Daniela Gaul, Kathrin Klamroth, and Michael Stiglmayr. Solving the Dynamic Dial-a-Ride Problem Using a Rolling-Horizon Event-Based Graph. In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


In many ridepooling applications transportation requests arrive throughout the day and have to be answered and integrated into the existing (and operated) vehicle routing. To solve this dynamic dial-a-ride problem we present a rolling-horizon algorithm that dynamically updates the current solution by solving an MILP formulation. The MILP model is based on an event-based graph with nodes representing pick-up and drop-off events associated with feasible user allocations in the vehicles. The proposed solution approach is validated on a set of real-word instances with more than 500 requests. In 99.5% of all iterations the rolling-horizon algorithm returned optimal insertion positions w.r.t. the current schedule in a time-limit of 30 seconds. On average, incoming requests are answered within 2.8 seconds.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Network flows
  • Applied computing → Multi-criterion optimization and decision-making
  • Applied computing → Transportation
  • Dial-a-Ride Problem
  • Ridepooling
  • Event-Based MILP
  • Rolling-Horizon
  • Dynamic Requests


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  1. Andrea Attanasio, Jean-François Cordeau, Gianpaolo Ghiani, and Gilbert Laporte. Parallel tabu search heuristics for the dynamic multi-vehicle dial-a-ride problem. Parallel Computing, 30(3):377-387, 2004. URL:
  2. Alexandre Beaudry, Gilbert Laporte, Teresa Melo, and Stefan Nickel. Dynamic transportation of patients in hospitals. OR Spectrum, 32(1):77-107, 2008. URL:
  3. Gerardo Berbeglia, Jean-François Cordeau, and Gilbert Laporte. Dynamic pickup and delivery problems. European Journal of Operational Research, 202(1):8-15, 2010. URL:
  4. Gerardo Berbeglia, Jean-François Cordeau, and Gilbert Laporte. A hybrid tabu search and constraint programming algorithm for the dynamic dial-a-ride problem. INFORMS Journal on Computing, 24(3):343-355, 2012. URL:
  5. Dimitris Bertsimas, Patrick Jaillet, and Sébastien Martin. Online vehicle routing: The edge of optimization in large-scale applications. Operations Research, 67(1):143-162, 2019. URL:
  6. Pasquale Carotenuto and Fabio Martis. A double dynamic fast algorithm to solve multi-vehicle dial a ride problem. Transportation Research Procedia, 27:632-639, 2017. URL:
  7. Jean-François Cordeau. A branch-and-cut algorithm for the dial-a-ride problem. Operations Research, 54(3):573-586, 2006. URL:
  8. Luca Coslovich, Raffaele Pesenti, and Walter Ukovich. A two-phase insertion technique of unexpected customers for a dynamic dial-a-ride problem. European Journal of Operational Research, 175(3):1605-1615, 2006. URL:
  9. Daniela Gaul, Kathrin Klamroth, and Michael Stiglmayr. Event-based MILP models for ride-hailing applications. arXiv, 2021. submitted to European Journal of Operations Research. URL:
  10. Fred Glover. Ejection chains, reference structures and alternating path methods for traveling salesman problems. Discrete Applied Mathematics, 65(1-3):223-253, 1996. URL:
  11. Thomas Hanne, Teresa Melo, and Stefan Nickel. Bringing robustness to patient flow management through optimized patient transports in hospitals. Interfaces, 39(3):241-255, 2009. URL:
  12. Sin C. Ho, W.Y. Szeto, Yong-Hong Kuo, Janny M.Y. Leung, Matthew Petering, and Terence W.H. Tou. A survey of dial-a-ride problems: Literature review and recent developments. Transportation Research Part B: Methodological, 111:395-421, 2018. URL:
  13. Carl H. Häll and Anders Peterson. Improving paratransit scheduling using ruin and recreate methods. Transportation Planning and Technology, 36(4):377-393, 2013. URL:
  14. Lauri Häme and Harri Hakula. A maximum cluster algorithm for checking the feasibility of dial-a-ride instances. Transportation Science, 49(2):295-310, 2015. URL:
  15. Christian Liebchen, Martin Lehnert, Christian Mehlert, and Martin Schiefelbusch. Betriebliche Effizienzgrößen für Ridepooling-Systeme. In Making Connected Mobility Work, pages 135-150. Springer Fachmedien Wiesbaden, 2021. URL:
  16. Athanasios Lois and Athanasios Ziliaskopoulos. Online algorithm for dynamic dial a ride problem and its metrics. Transportation Research Procedia, 24:377-384, 2017. URL:
  17. Ying Luo and Paul Schonfeld. Online rejected-reinsertion heuristics for dynamic multivehicle dial-a-ride problem. Transportation Research Record: Journal of the Transportation Research Board, 2218(1):59-67, 2011. URL:
  18. Oli B. G. Madsen, Hans F. Ravn, and Jens Moberg Rygaard. A heuristic algorithm for a dial-a-ride problem with time windows, multiple capacities, and multiple objectives. Annals of Operations Research, 60(1):193-208, 1995. URL:
  19. Nikola Marković, Rahul Nair, Paul Schonfeld, Elise Miller-Hooks, and Matthew Mohebbi. Optimizing dial-a-ride services in maryland: Benefits of computerized routing and scheduling. Transportation Research Part C: Emerging Technologies, 55:156-165, 2015. URL:
  20. Harilaos N. Psaraftis. A dynamic programming solution to the single vehicle many-to-many immediate request dial-a-ride problem. Transportation Science, 14(2):130-154, 1980. URL:
  21. Douglas O. Santos and Eduardo C. Xavier. Taxi and ride sharing: A dynamic dial-a-ride problem with money as an incentive. Expert Systems with Applications, 42(19):6728-6737, 2015. URL:
  22. S. Vallee, A. Oulamara, and W. Ramdane Cherif-Khettaf. New online reinsertion approaches for a dynamic dial-a-ride problem. Journal of Computational Science, 47:101199, 2020. URL: