The multicommodity, mixed fleet transportation problem to find minimum cost origin-destination flows for loaded and empty hopper barges such that all commodities are moved and flow conservation conditions at each port are satisfied is solved. A linear programming model of this problem is developed, and an efficient solution technique is presented. The model is used to derive optimal barge flows for an inland waterway system. The effect of this flow optimization on system operations is investigated, with the aid of an inland waterway simulation model.