A Ranking-Based Optimization Algorithm for the Vehicle Relocation Problem in Car Sharing Services

The paper addresses the Vehicle Relocation Problem in free-floating car-sharing services by presenting a solution focused on strategies for repositioning vehicles and transferring personnel with the use of scooters. Our method begins by dividing the service area into zones that group regions with similar temporal patterns of vehicle presence and service demand, allowing the application of discrete optimization methods. In the next stage, we propose a fast ranking-based algorithm that makes its decisions on the basis of the number of cars available in each zone, the projected probability density of demand, and estimated trip durations. The experiments were carried out on the basis of real-world data originating from a major car-sharing service operator in Poland. The results of this algorithm are evaluated against scenarios without optimization that constitute a baseline and compared with the results of an exact algorithm to solve the Mixed Integer Programming (MIP) model. As performance metrics, the total travel time was used. Under identical conditions (number of vehicles, staff, and demand distribution), the average improvements with respect to the baseline of our algorithm and MIP solver were equal to 8.44\% and 19.6\% correspondingly. However, it should be noted that the MIP model also mimicked decisions on trip selection, which are excluded by current services business rules. The analysis of results suggests that, depending on the size of the workforce, the application of the proposed solution allows for improving performance metrics by roughly 3%-10%.