  In this article we study the problem of jointly deciding carsharing prices
and vehicle relocations. We consider carsharing services operating in the
context of multi-modal urban transportation systems. Pricing decisions take
into account the availability of alternative transport modes, and customer
preferences with respect to these. In order to account for the inherent
uncertainty in customer preferences, the problem is formulated as a
mixed-integer two-stage stochastic program with integer decision variables at
both stages. We propose an exact solution method for the problem based on the
integer L-Shaped method which exploits an efficient exact algorithm for the
solution of the subproblems. Tests on artificial instances based on the city of
Milan illustrate that the method can solve, or find good solutions to,
moderately sized instances for which a commercial solver fails. Furthermore,
our results suggest that, by adjusting prices between different zones of the
city, the operator can attract significantly more demand than with a fixed
pricing scheme and that such a pricing scheme, coupled with a sufficiently
large fleet, significantly reduces the relevance of staff-based relocations. A
number of issues, that remain to be addressed in future research, are pointed
out in our conclusions.
