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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

Funding

  • Gaul, Daniela: This work was partially supported by the state of North Rhine-Westphalia (Germany) within the project "bergisch.smart.mobility".

Acknowledgements

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.

Cite AsGet BibTex

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)
https://doi.org/10.4230/OASIcs.ATMOS.2021.8

Abstract

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
Keywords
  • Dial-a-Ride Problem
  • Ridepooling
  • Event-Based MILP
  • Rolling-Horizon
  • Dynamic Requests

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