A mixed-equilibrium model of individual and household activity–travel choices in multimodal transportation networks

This paper develops a novel household-oriented activity-based mixed-equilibrium model for estimating individual and household activity–travel choices in multimodal transportation networks with interactions between private car and public transit modes. In the novel model, household members with heterogeneous errors of perception on the time-dependent utility of different activity types make daily joint/solo activity–travel choices in a mixed-equilibrium manner, which maximizes either perceived household utility or perceived individual utility. A logit-based stochastic choice model is developed to capture the mixed equilibrium with heterogeneous errors of perception and used to predict the choices of alternative joint activity–travel paths (JATPs) on a supernetwork platform. Based on this stochastic JATP choice model, the mixed-equilibrium model is formulated as an equivalent variational inequality (VI) problem and solved using a modified diagonalization method. This converts the time-dependent activity–travel scheduling problem into an equivalent static traffic assignment problem on JATPs. The conditions required for the existence and uniqueness of a solution to the equivalent VI problem in terms of a JATP flow pattern are also identified. Numerical examples are provided to illustrate the model's merits and its applications for examining the effect of the coronavirus disease 2019 (COVID-19) pandemic.