  The last few years have seen the massive deployment of electric buses in many
existing transit networks. However, the planning and operation of an electric
bus system differ from that of a bus system with conventional vehicles, and
some key problems have not yet been studied in the literature. In this work, we
address the integrated operational control and charging scheduling problem for
a network of electric buses with a limited opportunity charging capacity. We
propose a hierarchical control framework to solve this problem, where the
charging and operational decisions are taken jointly by solving a mixed-integer
linear program in the high-level control layer. Since this optimization problem
might become very large as more bus lines are considered, we propose to apply
Lagrangian relaxation in such a way as to exploit the structure of the problem
and enable a decomposition into independent subproblems. A local search
heuristic is then deployed in order to generate good feasible solutions to the
original problem. This entire Lagrangian heuristic procedure is shown to scale
much better on transit networks with an increasing number of bus lines than
trying to solve the original problem with an off-the-shelf solver. The proposed
procedure is then tested in the high-fidelity microscopic traffic environment
Vissim on a bus network constructed from an openly available dataset of the
city of Chicago. The results show the benefits of combining the charging
scheduling decisions together with the real-time operational control of the
vehicles as the proposed control framework manages to achieve both a better
level of service and lower charging costs over control baselines with
predetermined charging schedules.
