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A Constraint Programming Approach to Electric Vehicle Routing with Time Windows

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11494))

Abstract

The Electric Vehicle Routing Problem with Time Windows (EVRPTW) extends traditional vehicle routing to address the recent development of electric vehicles (EVs). In addition to traditional VRP problem components, the problem includes consideration of vehicle battery levels, limited vehicle range due to battery capacity, and the presence of vehicle recharging stations. The problem is related to others in emissions-conscious routing such as the Green Vehicle Routing Problem (GVRP). We propose the first constraint programming (CP) approaches for modeling and solving the EVRPTW and compare them to an existing mixed-integer linear program (MILP). Our initial CP model follows the alternative resource approach previously applied to routing problems, while our second CP model utilizes a single resource transformation. Experimental results on various objectives demonstrate the superiority of the single resource transformation over the alternative resource model, for all problem classes, and over MILP, for the majority of medium-to-large problem classes. We also present a hybrid MILP-CP approach that outperforms the other techniques for distance minimization problems over long scheduling horizons, a class that CP struggles with on its own.

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Notes

  1. 1.

    Service must start within the time window.

  2. 2.

    There also exist VRP variants posed with multiple disjoint time windows [18].

  3. 3.

    In fact, the single resource model required significantly less memory for \(|V|=50\) problems than the alternative resource model did for \(|V|=25\) problems.

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Acknowledgment

We would like to thank the anonymous reviewers whose detailed feedback helped improve the paper.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, M5S 3G8, Canada

    Kyle E. C. Booth & J. Christopher Beck

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  1. Kyle E. C. Booth
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Correspondence to Kyle E. C. Booth .

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Editors and Affiliations

  1. Ecole Polytechnique de Montréal, Montréal, QC, Canada

    Louis-Martin Rousseau

  2. University of Western Macedonia, Kozani, Greece

    Kostas Stergiou

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Booth, K.E.C., Beck, J.C. (2019). A Constraint Programming Approach to Electric Vehicle Routing with Time Windows. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_9

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  • DOI: https://doi.org/10.1007/978-3-030-19212-9_9

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