A new type of forecasting model of great potential for predicting flows in complicated spatial transportation networks is illustrated through application to the forecasting of interregional coal flows by barge over the Mississippi River system. Changes in these flows are related to regional coal production and consumption levels and to the freight charges by barge and rail. The special feature of the model is the great saving on the data needed for its implementation made possible by assuming that transportation patterns will be efficient, i.e., least‐cost, for given regional imports and exports. This assumption is incorporated by using the linear programming transportation method to generate individual flows from regional barge imports and exports forecasts by a system of statistically fitted equations. Various applications are illustrate