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The last-mile vehicle routing problem with delivery options

Author

Listed:
  • Christian Tilk

    (Johannes Gutenberg University Mainz)

  • Katharina Olkis

    (Johannes Gutenberg University Mainz)

  • Stefan Irnich

    (Johannes Gutenberg University Mainz)

Abstract

The ongoing rise in e-commerce comes along with an increasing number of first-time delivery failures due to the absence of the customer at the delivery location. Failed deliveries result in rework which in turn has a large impact on the carriers’ delivery cost. In the classical vehicle routing problem (VRP) with time windows, each customer request has only one location and one time window describing where and when shipments need to be delivered. In contrast, we introduce and analyze the vehicle routing problem with delivery options (VRPDO), in which some requests can be shipped to alternative locations with possibly different time windows. Furthermore, customers may prefer some delivery options. The carrier must then select, for each request, one delivery option such that the carriers’ overall cost is minimized and a given service level regarding customer preferences is achieved. Moreover, when delivery options share a common location, e.g., a locker, capacities must be respected when assigning shipments. To solve the VRPDO exactly, we present a new branch-price-and-cut algorithm. The associated pricing subproblem is a shortest-path problem with resource constraints that we solve with a bidirectional labeling algorithm on an auxiliary network. We focus on the comparison of two alternative modeling approaches for the auxiliary network and present optimal solutions for instances with up to 100 delivery options. Moreover, we provide 17 new optimal solutions for the benchmark set for the VRP with roaming delivery locations.

Suggested Citation

  • Christian Tilk & Katharina Olkis & Stefan Irnich, 2021. "The last-mile vehicle routing problem with delivery options," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 877-904, December.
    • Handle: RePEc:spr:orspec:v:43:y:2021:i:4:d:10.1007_s00291-021-00633-0
    DOI: 10.1007/s00291-021-00633-0
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    3. Archetti, C. & Carrabs, F. & Cerulli, R. & Laureana, F., 2024. "A new formulation and a branch-and-cut algorithm for the set orienteering problem," European Journal of Operational Research, Elsevier, vol. 314(2), pages 446-465.
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    5. Alexander Jungwirth & Guy Desaulniers & Markus Frey & Rainer Kolisch, 2022. "Exact Branch-Price-and-Cut for a Hospital Therapist Scheduling Problem with Flexible Service Locations and Time-Dependent Location Capacity," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1157-1175, March.

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