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The paired mail carrier problem

Author

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  • Luo, Yuchen
  • Golden, Bruce
  • Poikonen, Stefan
  • Wasil, Edward
  • Zhang, Rui

Abstract

Often traditional mail carrier models assume that one carrier is assigned to each truck. This carrier drives the truck according to a delivery route, gets out of the truck at a stop, and services customers using a walking loop. We introduce the Paired Mail Carrier Problem (PMCP), which allows for two mail carriers per truck. If at least one carrier is in the truck, the truck may move forward. Given two mail carriers per truck, the objective is to minimize the time from the start to the end of the route while ensuring that each service stop is fully serviced and obeys all feasibility constraints. We develop a mixed integer programming (MIP) formulation and two fast heuristics for the PMCP. The MIP formulation obtains optimal solutions for smaller instances within reasonable running times. Furthermore, we demonstrate that, in addition to being very efficient (running time is on the order of milliseconds, even for large instances), our heuristics are near-optimal (within 5% of optimality) on instances up to 80 stops. More importantly, we evaluate the impact of the paired mail carrier (PMC) setting on both a one-truck situation and a fleet (multiple trucks) situation, relative to the single mail carrier (SMC) setting. Overall, the PMC setting not only can accomplish over 50% extra work within the same shift hours but also can lead to 22% cost savings. Finally, we discuss an extension where we can have three or more mail carriers per truck.

Suggested Citation

  • Luo, Yuchen & Golden, Bruce & Poikonen, Stefan & Wasil, Edward & Zhang, Rui, 2023. "The paired mail carrier problem," European Journal of Operational Research, Elsevier, vol. 308(2), pages 801-817.
    • Handle: RePEc:eee:ejores:v:308:y:2023:i:2:p:801-817
    DOI: 10.1016/j.ejor.2022.11.032
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    References listed on IDEAS

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    1. Coindreau, Marc-Antoine & Gallay, Olivier & Zufferey, Nicolas, 2019. "Vehicle routing with transportable resources: Using carpooling and walking for on-site services," European Journal of Operational Research, Elsevier, vol. 279(3), pages 996-1010.
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    3. Pureza, Vitória & Morabito, Reinaldo & Reimann, Marc, 2012. "Vehicle routing with multiple deliverymen: Modeling and heuristic approaches for the VRPTW," European Journal of Operational Research, Elsevier, vol. 218(3), pages 636-647.
    4. Sara Reed & Ann Melissa Campbell & Barrett W. Thomas, 2022. "The Value of Autonomous Vehicles for Last-Mile Deliveries in Urban Environments," Management Science, INFORMS, vol. 68(1), pages 280-299, January.
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