Car rental logistics: a metaheuristic and a matheuristic for the vehicle-reservation assignment problem

Car rental companies face a critical problem related to the empty reposition of their vehicles, which comprise significant and avoidable costs and increase their environmental impact due to the fuel consumption and CO2 emission. Especially when dealing with special types of vehicles whose number of units is small, the company is forced to empty transfer them between rental stations in order to meet reservation requirements concerning available time and location. This dissertation describes and structures this problem, considering it within the operational vehicle-reservation assignment framework. The main objective is to develop a tool that assigns reservations to special vehicles, maximizing the company’s profit whilst minimizing the impacts of these empty transfers. A metaheuristic and a matheuristic were developed to tackle this problem. The metaheuristic developed is based on a GRASP algorithm. The greediness of the randomized constructive heuristic is based on several criteria with different importance degrees, such as reservation profit and time proximity, and vehicle idle time. Two local search procedures were developed. The move that defines the neighbourhood structure is in both cases based on the swap of pairs of allocated reservations, yet the approach to the selection of the new incumbent solution differs. Real instances were used to test this method. Furthermore, this problem was formulated as a network-flow model. As the exact solution of real-sized instances is generally deemed impractical due to the processing time required, a matheuristic was developed to solve it. It comprises a relax-and-fix-based heuristic procedure, which includes a mechanism that enables and controls the changes between consecutive iterations, based on the local branching paradigm. Random instances based on real data were generated to test this method. Both approaches were able to improve the company’s profit and reduce the empty transfer time and consequent environmental impact, when comparing with the current procedures. The matheuristic was able to achieve significantly better results and tackle larger instances while the metaheuristic was able to allocate more reservations than the company’s current procedure. Another major advantage of the utilization of these tools is the re-allocation of two qualified and experienced employees to other value-adding tasks.