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).