A method includes forecasting demand for media content items of a media distribution system based on historical demand information to generate forecasted demand. The method includes generating 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. The method includes performing a Lagrangian relaxation operation using the mixed integer program model. The method includes determining values of a cost function based on a result of the Lagrangian relaxation operation. The method includes assigning each of the media content items to a corresponding distribution node of the plurality of distribution nodes based on the cost function and the forecasted demand.