  An electric car equipped with a battery of a finite capacity travels on a
road network with an infrastructure of charging stations. Each charging station
has a possibly different cost per unit of energy. Traversing a given road
segment requires a specified amount of energy that may be positive, zero or
negative. The car can only traverse a road segment if it has enough charge to
do so (the charge cannot drop below zero), and it cannot charge its battery
beyond its capacity.
  To travel from one point to another the car needs to choose a \emph{travel
plan} consisting of a path in the network and a recharging schedule that
specifies how much energy to charge at each charging station on the path,
making sure of having enough energy to reach the next charging station or the
destination. The cost of the plan is the total charging cost along the chosen
path. We reduce the problem of computing plans between every two junctions of
the network to two problems: Finding optimal energetic paths when no charging
is allowed and finding standard shortest paths. When there are no negative
cycles in the network, we obtain an $O(n^3)$-time algorithm for computing
all-pairs travel plans, where~$n$ is the number of junctions in the network. We
obtain slightly faster algorithms under some further assumptions. We also
consider the case in which a bound is placed on the number of rechargings
allowed.
