Solving transportation network equilibrium models with the Dantzig-Wolfe decomposition method

Four step (sequential) procedures are traditionally used in forecasting travel on an urban transportation network. A typical transportation network consists of different trip purposes, user classes, and transportation modes. Due to the inconsistency results from the four step procedures, some research works proposed to combine these four step procedures. The resulting transportation model becomes a quite general supply-demand equilibrium problem which is a class of variational inequalities with a small number of asymmetric functions (also called combined model). Hence, we propose that Dantzig-Wolfe decomposition method should be used to divide the model into a small-scale equilibrium problem (variational inequalities) with the asymmetric functions and a large-scale symmetric transportation model (a nonlinear programming) with all of the details of network structure and trip demand.