  The advent of autonomous driving and electrification is enabling the
deployment of Electric Autonomous Mobility-on-Demand (E-AMoD) systems, whereby
electric autonomous vehicles provide on-demand mobility. Crucially, the design
of the individual vehicles and the fleet, and the operation of the system are
strongly coupled. Hence, to maximize the system-level performance, they must be
optimized in a joint fashion. To this end, this paper presents a framework to
jointly optimize the fleet design in terms of battery capacity and number of
vehicles, and the operational strategies of the E-AMoD system, with the aim of
maximizing the operator's total profit. Specifically, we first formulate this
joint optimization problem using directed acyclic graphs as a mixed integer
linear program, which can be solved using commercial solvers with optimality
guarantees. Second, to solve large instances of the problem, we propose a
solution algorithm that solves for randomly sampled sub-problems, providing a
more conservative solution of the full problem, and devise a heuristic approach
to tackle larger individual sub-problem instances. Finally, we showcase our
framework on a real-world case study in Manhattan, where we demonstrate the
interdependence between the number of vehicles, their battery size, and
operational and fixed costs. Our results indicate that to maximize a mobility
operator's profit, a fleet of small and light vehicles with battery capacity of
20 kWh only can strike the best trade-off in terms of battery degradation,
fixed costs and operational efficiency.
