  In this paper, we study the optimal transport problem induced by separable
cost functions. In this framework, transportation can be expressed as the
composition of two lower-dimensional movements. Through this reformulation, we
prove that the random variable inducing the optimal transportation plan enjoys
a conditional independence property. We conclude the paper by focusing on some
significant settings. In particular, we study the problem in the Euclidean
space endowed with the squared Euclidean distance. In this instance, we
retrieve an explicit formula for the optimal transportation plan between any
couple of measures as long as one of them is supported on a straight line.
