Although one-way carsharing systems allow users the flexibility to use the different pick-up and drop-off stations, these systems experience serious mismatches between vehicle supply and trip demands at stations during their operations. Therefore, vehicles are relocated among the stations to accommodate the spatial and temporal characteristics of the demand. As relocation operations require personnel involvement, having vehicles (and available parking spots) at the right place at the right time comes with a considerable cost. One other way to reduce the relocation activities and the associated cost with them is by giving incentives to the users to make alterations in their original trip requests and manage the spatio-temporal demand asymmetries.

In this paper, we introduce a reservation-decision framework that determines the offer (both incentives and route) made to the users at each request. The framework consists of a simulator and a mixed integer linear programming (MILP) model, which aims to maximize the expected profit while considering the acceptance probabilities of the offers. Due to the computational complexity of the proposed MILP, we present graph spanner-based heuristic algorithms that efficiently solve large-size problems. We have conducted a case study using real-life system data from Nice, France. The results suggest that incorporating user flexibility can significantly reduce the need for relocation and improve profitability.