The Edge Set Cost of the Vehicle Routing Problem with Time Windows

Line Reinhardt*, Mads Kehlet Jepsen, David Pisinger

*Corresponding author

Research output: Contribution to journalJournal articleResearchpeer-review


We consider an important generalization of the vehicle routing problem with time windows in which a fixed cost must be paid for accessing a set of edges. This fixed cost could reflect payment for toll roads, investment in new facilities, the need for certifications, and other costly investments. The certifications and investments impose a cost for the company while they also give unlimited usage of a set of roads to all vehicles belonging to the company.

This violates the traditional assumption that the path between two destinations is well defined and independent of other choices. Different versions for defining the edge sets are discussed and formulated. Both the multigraph case and the direct path case are described, and mixed-integer-programming formulations of the problem are presented for both cases. A solution method based on branch-price-and-cut is applied to the direct path case. The computational results show that instances with up to 40 customers can be solved in a reasonable time, and that the branch-cut-and-price algorithm generally outperforms CPLEX.
Original languageEnglish
JournalTransportation Science
Issue number2
Pages (from-to)363-761
Number of pages15
Publication statusPublished - 2016
Externally publishedYes

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