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The Stop Number Minimization Problem: Complexity and Polyhedral Analysis

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Combinatorial Optimization (ISCO 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10856))

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Abstract

The Stop Number Minimization Problem arises in the management of a dial-a-ride system with small autonomous electric vehicles. In such a system, clients request for a ride from an origin point to a destination point, and a fleet of capacitated vehicles must satisfy all requests. The goal is to minimize the number of pick-up/drop-off operations. In [18], a special case was conjectured to be NP-Hard. In this paper we give a positive answer to this conjecture for any fixed capacity greater than or equal to 2. Moreover, we introduce a set of non-trivial instances that can be solved in polynomial time for capacity equal to 2, but is NP-Hard for higher capacities. We also present a new family of valid inequalities that are facet-defining for a large set of instances. Based on these inequalities, we derive a new efficient branch-and-cut algorithm.

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Acknowledgements

We want to thank the laboratory of excellence IMobS3 for its financial support.

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Authors and Affiliations

  1. CNRS and Université Clermont Auvergne, Clermont-Ferrand, France

    Mourad Baïou, Rafael Colares & Hervé Kerivin

Authors
  1. Mourad Baïou
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  2. Rafael Colares
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  3. Hervé Kerivin
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Corresponding author

Correspondence to Rafael Colares .

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Editors and Affiliations

  1. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA

    Jon Lee

  2. Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” (IASI), CNR, Rome, Italy

    Giovanni Rinaldi

  3. LAMSADE, Université Paris-Dauphine, Paris, France

    A. Ridha Mahjoub

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Baïou, M., Colares, R., Kerivin, H. (2018). The Stop Number Minimization Problem: Complexity and Polyhedral Analysis. In: Lee, J., Rinaldi, G., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2018. Lecture Notes in Computer Science(), vol 10856. Springer, Cham. https://doi.org/10.1007/978-3-319-96151-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-96151-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96150-7

  • Online ISBN: 978-3-319-96151-4

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