The vehicle routing problem with partial outsourcing

Annelieke C. Baller, Said Dabia, Wout E.H. Dullaert, Daniele Vigo

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This paper introduces the vehicle routing problem with partial outsourcing (VRPPO) in which a customer can be served by a single private vehicle, by a common carrier, or by both a single private vehicle and a common carrier. As such, it is a variant of the vehicle routing problem with private fleet and common carrier (VRPPC). The objective of the VRPPO is to minimize fixed and variable costs of the private fleet plus the outsourcing cost. We propose two different path-based formulations for the VRPPO and solve these with a branch-and-price-and-cut solution method. For each path-based formulation, two different pricing procedures are designed and used when solving the linear relaxations by column generation. To assess the quality of the solution methods and gain insight in potential cost improvements compared with the VRPPC, we perform tests on two instance sets with up to 100 customers from the literature.

Original languageEnglish
Pages (from-to)1034-1052
Number of pages19
JournalTransportation Science
Issue number4
Early online date17 Jun 2020
Publication statusPublished - Aug 2020


  • Exact algorithms
  • Outsourcing
  • Private fleet and common carrier
  • Split delivery
  • Vehicle routing problem


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