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A minimum-cost multicommodity network flow problem concerning imports and exports

This paper develops an algorithm for handling nonlinear minimum-cost multicommodity flow problems and applies it to a specific large-scale network. The commodities will be imports and exports; the cost functions will be quadratic and convex. The setting will be a Port Planning Model which will seek to find optimal simultaneous routings through the network while fulfilling requirements both at foreign ports and at domestic hinterlands. The computer program written solves such a problem. The algorithm involves linearizing the cost function and solving the resulting linear program, which is, in fact, a series of shortest route problems. Negative cycles are studied in depth.