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Integrated Location-Routing-Scheduling for Multi-Trip Mobile Parcel Lockers with Time Windows (Short Paper)

Authors Salma Essouaied , Leandro C. Coelho , Christophe Wilbaut , Raca Todosijević

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Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Theory of computation → Integer programming
  • Mathematics of computing → Combinatorial optimization
Keywords
  • Mobile parcel lockers
  • City logistics
  • Routing and scheduling
  • Mixed-integer programming
  • Logic-based Benders decomposition

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Abstract

Mobile parcel lockers can reposition delivery capacity during the day, but this flexibility requires decisions that are tightly linked: where lockers stop, which customers are assigned to each stop, how lockers move, and when service takes place. We introduce the multi-trip mobile parcel locker problem with time windows (MT-MPLP-TW), which integrates locker deployment, customer assignment, parking selection, routing, scheduling, parking capacity, walking limits, and depot replenishment. We present a compact mixed-integer programming formulation and a logic-based Benders decomposition (LBBD) that separates route-and-assignment decisions from detailed time-expanded certification. Computational results on generated instances and on the single-trip mobile parcel locker benchmark show that the compact formulation is effective on small and medium instances, while LBBD gives stronger performance on larger and more constrained cases.

Cite As Get BibTex

Salma Essouaied, Leandro C. Coelho, Christophe Wilbaut, and Raca Todosijević. Integrated Location-Routing-Scheduling for Multi-Trip Mobile Parcel Lockers with Time Windows (Short Paper). In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 17:1-17:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/OASIcs.ATMOS.2026.17

Author Details

Salma Essouaied
  • CIRRELT and Faculté des Sciences de l'Administration, Université Laval, Québec, Canada
  • Univ. Polytechnique Hauts-de-France, LAMIH, CNRS, UMR 8201, Valenciennes F-59313, France
  • INSA Hauts-de-France, Valenciennes F-59313, France
Leandro C. Coelho
  • CIRRELT and Faculté des Sciences de l'Administration, Université Laval, Québec, Canada
  • Canada Research Chair in Integrated Logistics, Université Laval, Québec, Canada
Christophe Wilbaut
  • Univ. Polytechnique Hauts-de-France, LAMIH, CNRS, UMR 8201, Valenciennes F-59313, France
  • INSA Hauts-de-France, Valenciennes F-59313, France
Raca Todosijević
  • Univ. Polytechnique Hauts-de-France, LAMIH, CNRS, UMR 8201, Valenciennes F-59313, France
  • INSA Hauts-de-France, Valenciennes F-59313, France

References

  1. Jacques F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1):238-252, 1962. URL: https://doi.org/10.1007/BF01386316.
  2. John N. Hooker. Logic-based methods for optimization: combining optimization and constraint satisfaction. John Wiley & Sons, 2011. Google Scholar
  3. John N. Hooker and Greger Ottosson. Logic-based benders decomposition. Mathematical Programming, 96(1):33-60, 2003. URL: https://doi.org/10.1007/s10107-003-0375-9.
  4. Stefan Schwerdfeger and Nils Boysen. Who moves the locker? A benchmark study of alternative mobile parcel locker concepts. Transportation Research Part C: Emerging Technologies, 142:103780, 2022. URL: https://doi.org/10.1016/j.trc.2022.103780.
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