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Variable neighborhood search for the stochastic and dynamic vehicle routing problem

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Abstract

In this paper, the authors consider the vehicle routing problem (VRP) with stochastic demand and/or dynamic requests. The classical VRP consists of determining a set of routes starting and ending at a depot that provide service to a set of customers. Stochastic demands are only revealed when the vehicle arrives at the customer location; dynamic requests mean that new orders from previously unknown customers can be received and scheduled over time. The variable neighborhood search algorithm (VNS) proposed in this study can be extended by sampling for stochastic scenarios and adapted for the dynamic setting. We use standard sets of benchmark instances to evaluate our algorithms. When applying sampling based VNS, on average we were able to improve results obtained by a classical VNS by 4.39 %. Individual instances could be improved by up to 8.12 %. In addition, the proposed VNS framework matches 32 out of 40 best known solutions and provides one new best solution. In the dynamic case, VNS improves on existing results and provides new best solutions for 7 out of 21 instances. Finally, this study offers results for stochastic and dynamic scenarios. Our experiments show that the sampling based dynamic VNS provides better results when the demand deviation is small, and reduces the excess route duration by 45–90 %.

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Acknowledgments

We acknowledge funds from the Spanish Ministry of Sciences and Innovation European FEDER, under contracts TIN2008-06491-C04-01 (M* project, http://mstar.lcc.uma.es) and TIN2011-28194 (roadME project, http://roadme.lcc.uma.es), as well as CICE, Junta de Andalucía, under contract P07-TIC-03044 (DIRICOM project, http://diricom.lcc.uma.es). Briseida Sarasola received support from grant AP2009-1680 provided by the Spanish government. The financial support by the Austrian Federal Ministry of Economy, Family and Youth and the National Foundation for Research, Technology and Development is gratefully acknowledged.

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Authors and Affiliations

  1. Christian Doppler Laboratory for Efficient Intermodal Transport Operations, Department of Business Administration, University of Vienna, Vienna, Austria

    Briseida Sarasola, Karl F. Doerner & Verena Schmid

  2. Departamento de Lenguajes y Ciencias de la Computación, University of Malaga, Málaga, Spain

    Enrique Alba

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  1. Briseida Sarasola
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  2. Karl F. Doerner
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  3. Verena Schmid
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  4. Enrique Alba
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Correspondence to Briseida Sarasola.

Appendix

Appendix

See Tables 8, 9, 10, 11, 12, 13, 14, 15, and 16.

Table 8 Results obtained by VNS and S-VNS on the VRPSD with demands deviation equal to \(\pm \)5.0 %
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Table 9 Results obtained by VNS and S-VNS on the VRPSD with demands deviation equal to \(\pm \)15.0 %
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Table 10 Results obtained by VNS and S-VNS on the VRPSD with demands deviation equal to \(\pm \)20.0 %
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Table 11 Results obtained by VNS and S-VNS on the VRPSD with demands deviation equal to \(\pm \)25.0 %
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Table 12 Results obtained by S-VNS, MSSH (Mendoza and Villegas 2013), and SA (Goodson et al. 2012) for the Christiansen and Lysgaard benchmark
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Table 13 Results obtained by D-VNS and SD-VNS on the VRPSDDR with demands deviation equal to \(\pm 5.0\) %
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Table 14 Results obtained by D-VNS and SD-VNS on the VRPSDDR with demands deviation equal to \(\pm \)15.0 %
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Table 15 Results obtained by D-VNS and SD-VNS on the VRPSDDR with demands deviation equal to \(\pm \)20.0 %
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Table 16 Results obtained by D-VNS and SD-VNS on the VRPSDDR with demands deviation equal to \(\pm \)25.0 %
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Sarasola, B., Doerner, K.F., Schmid, V. et al. Variable neighborhood search for the stochastic and dynamic vehicle routing problem. Ann Oper Res 236, 425–461 (2016). https://doi.org/10.1007/s10479-015-1949-7

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