  In ride-hailing systems, en-route time refers to the time that elapses from
the moment a car is dispatched to pick up a rider until the rider is picked up.
A fundamental phenomenon in ride-hailing systems is that there is a trade-off
between en-route time and the time that a car waits for a dispatch. In short,
if cars spend little time idle waiting for a dispatch, then few cars are
available when a rider makes a request, and thus the mean distance between a
rider and the closest available car is long, which means that en-route time is
long. This phenomenon is of great importance in ride-hailing, because en-route
time increases rapidly as the number of idle cars decreases, and every minute
that a car spends en-route is one minute less that the car can transport
riders. In spite of this, the existing literature on price optimization for
ride-hailing, and on repositioning optimization for ride-hailing, ignores
en-route time. Initial attempts to take this trade-off for the mean en-route
time into account when considering price optimization or repositioning
optimization all resulted in intractable optimization problems. Then we found a
way to reformulate a simultaneous price and repositioning optimization problem,
that takes this trade-off for the distribution of en-route time into account,
as a tractable convex optimization problem. We show how the optimal solution
can be used to construct policies that perform much better in simulations than
the policies proposed in previous papers.
