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Optimal capacitated ring trees

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EURO Journal on Computational Optimization

Abstract

We study a new network design model combining ring and tree structures under capacity constraints. The solution topology of this capacitated ring tree problem (CRTP) is based on ring trees which are the union of trees and 1-trees. The objective is the minimization of edge costs but could also incorporate other types of measures. This overall problem generalizes prominent capacitated vehicle routing and Steiner tree problem variants. Two customer types have to be connected to a distributor ensuring single and double node connectivity, respectively, while installing optional Steiner nodes. The number of ring trees and the number of customers supplied by such a single structure are bounded. After embedding this combinatorial optimization model in existing network design concepts, we develop a mathematical formulation and introduce several valid inequalities for the CRTP that are separated in our exact algorithm. For a set of literature-derived instances we consider various reliability scenarios and present computational results.

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Notes

  1. The instances can be obtained from the corresponding author.

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Acknowledgments

We would like to thank the anonymous reviewers for their detailed comments which led to an improvement of this work. Moreover, we thank Edna Hoshino for discussion.

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Authors and Affiliations

  1. Department of Engineering Management, University of Antwerp, Prinsstraat 13, 2018, Antwerp, Belgium

    Alessandro Hill

  2. Institute of Information Systems (IWI), University of Hamburg, Von-Melle-Park 5, 20146, Hamburg, Germany

    Stefan Voß

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  1. Alessandro Hill
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  2. Stefan Voß
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Correspondence to Alessandro Hill.

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Hill, A., Voß, S. Optimal capacitated ring trees. EURO J Comput Optim 4, 137–166 (2016). https://doi.org/10.1007/s13675-015-0035-x

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