This research studies the most complex travel demand forecasting combined model that casts trip generation, trip distribution, mode choice, traffic assignment as well as variable demand functions into a unified framework. By way of a supernetwork representation, this variable demand combined model can be explained as an extended traffic assignment problem. The "B" algorithm is adopted to solve the problem and demonstrated with a small network. Further comparisons among the three selected algorithms (i.e., "B", Frank-Wolfe and Gradient Projection) are made for three test networks. The results show that the "B" algorithm is superior to the Gradient Projection and Frank-Wolfe algorithms in terms of computational time.