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Exact Algorithms for the Chance-Constrained Vehicle Routing Problem

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Integer Programming and Combinatorial Optimization (IPCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9682))

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Abstract

We study the chance-constrained vehicle routing problem (CCVRP), a version of the vehicle routing problem (VRP) with stochastic demands, where a limit is imposed on the probability that each vehicle’s capacity is exceeded. A distinguishing feature of our proposed methodologies is that they allow correlation between random demands, whereas nearly all existing methods for the stochastic VRP require independent demands. We first study an edge-based formulation for the CCVRP, in particular addressing the challenge of how to determine a lower bound on the number of trucks required to serve a subset of customers. We then investigate the use of a branch-and-cut-and-price (BCP) algorithm. While BCP algorithms have been considered the state of the art in solving the deterministic VRP, few attempts have been made to extend this framework to the stochastic VRP.

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Notes

  1. 1.

    Note that \(\mathbb {P}\{ D(S) \le b\} \ge 1-\epsilon \iff Q_{1-\epsilon }( D(S) ) \le b\).

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Acknowledgments

Fukasawa was supported by NSERC Discovery Grant RGPIN-05623. Luedtke was supported by NSF grants CMMI-0952907 and CMMI-1130266, and ONR award N00014-15-1-2268.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Thai Dinh & James Luedtke

  2. Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Ricardo Fukasawa

Authors
  1. Thai Dinh
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  2. Ricardo Fukasawa
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  3. James Luedtke
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Corresponding authors

Correspondence to Ricardo Fukasawa or James Luedtke .

Editor information

Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Quentin Louveaux

  2. Technische Universität Berlin, Berlin, Germany

    Martin Skutella

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Dinh, T., Fukasawa, R., Luedtke, J. (2016). Exact Algorithms for the Chance-Constrained Vehicle Routing Problem. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_8

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  • DOI: https://doi.org/10.1007/978-3-319-33461-5_8

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