In this talk I will discuss the optimal transport problem with ``storage fees.'' This is a variant of the semi-discrete optimal transport (a.k.a. Monge-Kantorovich) problem, where instead of transporting an absolutely continuous measure to a fixed discrete measure and minimizing the transport cost, one must choose the weights of the target measure, and minimize the sum of the transport cost and some given ``storage fee function'' of the target weights. This problem arises in queue penalization and semi-supervised data clustering. I will discuss some basic theoretical questions, such as existence, uniqueness, a dual problem, and characterization of solutions. Then, I will present a numerical algorithm which has global linear and local superlinear convergence for a subcase of storage fee functions. \\ \\ All work in this talk is joint with M. Bansil (UCLA).