  We consider optimal transport problems where the cost for transporting a
given probability measure $\mu_0$ to another one $\mu_1$ consists of two parts:
the first one measures the transportation from $\mu_0$ to an intermediate
(pivot) measure $\mu$ to be determined (and subject to various constraints),
and the second one measures the transportation from $\mu$ to $\mu_1$. This
leads to Wasserstein interpolation problems under constraints for which we
establish various properties of the optimal pivot measures $\mu$. Considering
the more general situation where only some part of the mass uses the
intermediate stop leads to a mathematical model for the optimal location of a
parking region around a city. Numerical simulations, based on entropic
regularization, are presented both for the optimal parking regions and for
Wasserstein constrained interpolation problems.
