The problem of moving a commodity with a given initial mass distribution to a pre-specified target mass distribution so that the total work is minimized can be traced back at least to Monge’s work from 1781. Here, we consider a version of this problem aiming to minimize a combination of road construction and transportation cost by determining, at each point, the local direction of transportation. This paper covers the modeling of the problem, highlights how it can be formulated as a material distribution topology optimization problem, and shows some results.