  The travel demand forecasting model plays a crucial role in evaluating
large-scale infrastructure projects, such as the construction of new roads or
transit lines. While combined modeling approaches have been explored as a
solution to overcome the problem of input and output discrepancies in a
sequential four-step modeling process, previous attempts at combined models
have encountered challenges in real-world applications, primarily due to their
limited behavioral richness or computational tractability. In this study, we
propose a novel convex programming approach and present a key theorem
demonstrating that the optimal solution is the same as the one from solving the
hierarchical extended logit model. This model is specifically designed to
capture correlations existing in travelers' choices, including similarities
among transport modes and route overlaps. The convex property of our model
ensures the existence and uniqueness of solutions and offers computational
efficiency. The advantages of our proposed model are twofold. Firstly, it
provides a single unifying rationale (i.e., utility maximization) that is valid
across all steps. Secondly, its combined nature allows a systematic approach to
handling observed data, enabling a more realistic representation of reality. By
addressing the limited behavior richness of previous combined models, our
convex programming-based approach shows promise in enhancing the accuracy and
applicability of travel demand forecasting, thereby aiding in the planning and
decision-making processes for infrastructure projects.
