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Approximation algorithms for a vehicle routing problem

Author

Listed:
  • Sven Krumke
  • Sleman Saliba
  • Tjark Vredeveld
  • Stephan Westphal

Abstract

In this paper we investigate a vehicle routing problem motivated by a real-world application in cooperation with the German Automobile Association (ADAC). The general task is to assign service requests to service units and to plan tours for the units such as to minimize the overall cost. The characteristics of this large-scale problem due to the data volume involve strict real-time requirements. We show that the problem of finding a feasible dispatch for service units starting at their current position and serving at most k requests is NP-complete for each fixed k ≥ 2. We also present a polynomial time (2k − 1)-approximation algorithm, where again k denotes the maximal number of requests served by a single service unit. For the boundary case when k equals the total number |E| of requests (and thus there are no limitations on the tour length), we provide a $${\left(2-\frac{1}{|E|} \right)}$$ -approximation. Finally, we extend our approximation results to include linear and quadratic lateness costs. Copyright Springer-Verlag 2008

Suggested Citation

  • Sven Krumke & Sleman Saliba & Tjark Vredeveld & Stephan Westphal, 2008. "Approximation algorithms for a vehicle routing problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 333-359, October.
  • Handle: RePEc:spr:mathme:v:68:y:2008:i:2:p:333-359
    DOI: 10.1007/s00186-008-0224-y
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    References listed on IDEAS

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    1. M. Haimovich & A. H. G. Rinnooy Kan, 1985. "Bounds and Heuristics for Capacitated Routing Problems," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 527-542, November.
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    Cited by:

    1. Farshad Majzoubi & Lihui Bai & Sunderesh S. Heragu, 2021. "The EMS vehicle patient transportation problem during a demand surge," Journal of Global Optimization, Springer, vol. 79(4), pages 989-1006, April.
    2. Huigenbosch, P. & van de Klundert, J. & Wormer, L., 2008. "ANWB automates and improves repair men dispatching," Research Memorandum 055, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Peter van Huigenbosch & Joris van de Klundert & Laurens Wormer, 2011. "ANWB Automates and Improves Service Personnel Dispatching," Interfaces, INFORMS, vol. 41(2), pages 123-134, April.

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