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Solution Algorithm for Combined Interregional Commodity Flow and Transportation Network Model with Link Capacity Constraints

A solution algorithm for the multicommodity combined freight distribution and assignment problem that computes the system optimum link flow pattern is introduced here. The distribution component of the model is based on an input-output materials balance formulation that satisfies each region’s intermediate and final demands for each commodity. An entropy term is included to capture cross-hauling and dispersion effects. The network links are assumed to be capacitated. This problem is formulated as a nonlinear program, with the nonlinear entropy term appearing in the objective function. This problem tends to be intractable even for small networks, so a Dantzig–Wolfe decomposition approach is introduced to make the problem computationally feasible. Wilson’s balancing technique is used to solve the nonlinear distribution subproblem. Test results demonstrate that realistic networks can be solved in a reasonable amount of time. The model is used to obtain insights into the trade-offs between dispersion coefficients and transportation costs on both capacitated and uncapacitated networks.