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The effects of triangle inequality on the vehicle routing problem

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  • Fleming, Christopher L.
  • Griffis, Stanley E.
  • Bell, John E.
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    Abstract

    Routing problems often utilize experimental networks to represent real world scenarios. However most ignore the inclusion of triangle inequality violations, a phenomenon resulting from delays or rounding errors within a network. This work evaluates the effect of both frequency – the number of violations – and severity – the degree of intensity of a violation – of triangle inequality and evaluates both solution quality and solution time based on Simulated Annealing, Ant Colony Optimization and Savings Algorithm methods. Findings indicate that while both frequency and severity degrade solution quality, increased levels of frequency and severity together result in significant adverse affects to solution quality. Solution time, however, is not impacted by the presence of triangle inequality violations within the network. This information should encourage practitioners to identify delays and maintain the presence of triangle inequality violations in a network to ensure accuracy of solution quality.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 224 (2013)
    Issue (Month): 1 ()
    Pages: 1-7

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    Handle: RePEc:eee:ejores:v:224:y:2013:i:1:p:1-7

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Routing; Traffic; Logistics;

    References

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    1. Kok, A.L. & Hans, E.W. & Schutten, J.M.J., 2011. "Optimizing departure times in vehicle routes," European Journal of Operational Research, Elsevier, vol. 210(3), pages 579-587, May.
    2. Donati, Alberto V. & Montemanni, Roberto & Casagrande, Norman & Rizzoli, Andrea E. & Gambardella, Luca M., 2008. "Time dependent vehicle routing problem with a multi ant colony system," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1174-1191, March.
    3. S. P. Brooks & N. Friel & R. King, 2003. "Classical model selection via simulated annealing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 503-520.
    4. Jeromin, Bernd & Korner, Frank, 1989. "Triangle inequality and symmetry in connection with the assignment and the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 38(1), pages 70-75, January.
    5. Taillard, E., 1993. "Benchmarks for basic scheduling problems," European Journal of Operational Research, Elsevier, vol. 64(2), pages 278-285, January.
    6. Schilling, D. A. & Rosing, K. E. & ReVelle, C. S., 2000. "Network distance characteristics that affect computational effort in p-median location problems," European Journal of Operational Research, Elsevier, vol. 127(3), pages 525-536, December.
    7. Mari'n, Alfredo & Canovas, Lazaro & Landete, Mercedes, 2006. "New formulations for the uncapacitated multiple allocation hub location problem," European Journal of Operational Research, Elsevier, vol. 172(1), pages 274-292, July.
    8. Chris Groër & Bruce Golden & Edward Wasil, 2009. "The Consistent Vehicle Routing Problem," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 630-643, February.
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