  Different types of formulations are proposed in the literature to model
vehicle routing problems. Currently, the most used ones can be fitted into two
classes, namely vehicle flow formulations and set partitioning formulations.
These types of formulations differ from each other not only due to their
variables and constraints but also due to their main features. Vehicle flow
formulations have the advantage of being compact models, so general-purpose
optimization packages can be used to straightforwardly solve them. However,
they typically show weak linear relaxations and have a large number of
constraints. Branch-and-cut methods based on specialized valid inequalities can
also be devised to solve these formulations, but they have not shown to be
effective for large-scale instances. On the other hand, set partitioning
formulations have stronger linear relaxations, but requires the implementation
of sophisticate techniques such as column generation and specialized
branch-and-price methods. Due to all these reasons, so far it is has been
recognized in the vehicle routing community that these two types of
formulations are rather different. In this paper, we show that they are
actually strongly related as they correspond to special cases of a generalized
formulation of vehicle routing problems.
