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Fast Combinatorial Algorithms for Efficient Sortation

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Integer Programming and Combinatorial Optimization (IPCO 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14679))

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Abstract

Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate nodes in a typical hub-and-spoke fashion. In practice, such consolidation requires parcel sortation. In this work, we propose a mathematical model for the physical requirements, and limitations of parcel sortation. We then show that it is NP-hard to determine whether a feasible sortation plan exists. We discuss several settings, where (near-) feasibility of a given sortation instance can be determined efficiently. The algorithms we propose are fast and build on combinatorial witness set type lower bounds that are reminiscent and extend those used in earlier work on degree-bounded spanning trees and arborescences.

M. Van Dyk and J. Koenemann—This work was partially supported by the NSERC Discovery Grant Program, grant number RGPIN-03956-2017 and by an Amazon Post-Internship Fellowship. The work presented here does not relate to the authors’ positions at Amazon.

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Acknowledgements

We thank Sharat Ibrahimpur and Kostya Pashkovich for valuable discussions on lower bounds and the link to matroid intersection.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada

    Madison Van Dyk & Jochen Koenemann

  2. Faculty of Mathematics and Computer Science, University of Bremen, Bremen, Germany

    Kim Klause & Nicole Megow

  3. Modeling and Optimization, Amazon, Seattle, USA

    Jochen Koenemann

Authors
  1. Madison Van Dyk
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  2. Kim Klause
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  3. Jochen Koenemann
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  4. Nicole Megow
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Corresponding author

Correspondence to Madison Van Dyk .

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Editors and Affiliations

  1. University of Bonn, Bonn, Germany

    Jens Vygen

  2. University of Wrocław, Wrocław, Poland

    Jarosław Byrka

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Van Dyk, M., Klause, K., Koenemann, J., Megow, N. (2024). Fast Combinatorial Algorithms for Efficient Sortation. In: Vygen, J., Byrka, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2024. Lecture Notes in Computer Science, vol 14679. Springer, Cham. https://doi.org/10.1007/978-3-031-59835-7_31

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  • DOI: https://doi.org/10.1007/978-3-031-59835-7_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-59834-0

  • Online ISBN: 978-3-031-59835-7

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