A Two-Stage Iteration Method for Solving the Departure Time Choice Problem

We discuss the numerical solution of the departure time choice problem. The non–quasi-monotone of the travel cost vector function is first proved to address the study motivation. A two-stage iteration method is then proposed to effectively solve the problem in a single origin-destination (OD) pair network with parallel links, in which departure time and route choices of commuters are involved. We analytically reveal why the iteration method can solve the problem and theoretically prove the convergence, that is, the iteration process finally achieves at a user equilibrium (UE) state. The iteration method is then extended to a single link network with heterogeneous users in the values of travel time and schedule delay and the preferred arrival time. Furthermore, numerical analyses are conducted for the two networks to demonstrate the effectiveness of the iteration method for solving the departure time choice problem. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72288101, 72171007, and 72021001]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0599 .