1. A method comprising: forecasting, by a computer, demand for media content items available to a media distribution system based on historical demand information to generate forecasted demand; generating, by the computer, a mixed integer program model based on storage constraints of a plurality of distribution nodes of the media distribution system, bandwidth constraints of the media distribution system, and the forecasted demand, wherein each distribution node of the plurality of distribution nodes is associated with a corresponding set of a plurality of endpoints, wherein the bandwidth constraints include a particular bandwidth constraint for a link between a first distribution node of the plurality of distribution nodes and a second distribution node of the plurality of distribution nodes, the first distribution node associated with a first set of the plurality of endpoints and the second distribution node associated with a second set of the plurality of endpoints, the second set of the plurality of endpoints distinct from the first set of the plurality of endpoints; performing, by the computer, a Lagrangian relaxation operation using the mixed integer program model; determining, by the computer, values of a cost function, wherein the cost function is associated with an amount of bandwidth for the media distribution system to provide the media content items to each of the plurality of endpoints of the media distribution system, and wherein the values of the cost function are based on a result of the Lagrangian relaxation operation; and causing, by the computer, each of the media content items to be stored at a corresponding distribution node of the plurality of distribution nodes based on the cost function and the forecasted demand.