  We introduce the electric vehicle sharing problem (EVSP), a problem that
arises from the planning and operation of electric car-sharing systems which
allow one-way rental of vehicles. The problem aims at finding the maximum total
daily rental time in which customers' demands are assigned to the existing
fleet. In addition, either all of the customer's demands are completely
fulfilled or the customer does not use the system at all. We show that the EVSP
is NP-hard, and we provide four mixed-integer linear programming formulations
based on space-time network flow models, along with some theoretical results.
We perform a comprehensive computational study of the behavior of the proposed
formulations using two benchmark sets, one of which is based on real-world data
from an electric car-sharing system located in Fortaleza, Brazil. The results
show that our best formulation is effective in solving instances where each
customer has only one demand. In general, we were able to optimally solve at
least 55% of the instances within the time limit of one hour.
