Large-scale network distribution of pooled empty freight cars over time, with limited substitution and equitable benefits

A set of models and procedures is described for finding the optimal distribution of empty freight cars owned by the railroads participating in a pooling agreement. A distinction is drawn between a system focus, in which the emphasis is on minimizing total cost, and a company focus, in which the benefits of the agreement to the individual railroads are emphasized. Limited car substitution is accounted for by combining interchange costs with distribution costs, and incorporating interchange possibilities and prohibitions into the network structure. Temporal variations in car supply and demand levels are also taken into account. A large-scale network algorithm is used in conjunction with decomposition to obtain solutions which show for a given time horizon how much equity can be achieved in the balance of savings among the railroads involved and at what cost. Results using actual operating data are reported.