In this paper, a combined model of auto-transit assignment is introduced based on two complementarity formulations in the literature. The model accounts for interactions between the auto and transit modes through non-separable asymmetric demand and cost functions. A path-based solution algorithm is presented based on the three ideas of decomposition, column generation, and linearization, which have proved to be effective in tackling large-size networks. Numerical results over the Chicago Sketch network suggest that the algorithm converges quickly within the first iterations, but is less effective as the solution gets closer to neighbourhood of the equilibrium solution. The sluggish convergence behavior is attributed to the difficulty of searching the space of strategy-based transit assignment model.
