On determining optimal fleet size and vehicle transfer policy for a car rental company

This paper considers how to determine the optimal fleet size and vehicle transfer policy for a rental-car company that serves two cities. In each city, there are single-trip and round-trip customers, where the former is given a higher priority. Because of the single-trip traffic, the number of cars at these two cities may become unbalanced. Hence, the central planner in each day needs to decide whether to transfer any cars from one city to the other. We develop a two-stage dynamic programming model, in which we determine the vehicle transfer policy in the second stage and the optimal fleet size in the first stage. Although the objective function could be neither concave nor quasi-concave due to lost sales, we can find the optimal fleet size and vehicle transfer policy by solving a series of linear programming problems. We propose a heuristic solution, which is based on a special case analysis, for the fleet size problem. A numerical study reveals that our heuristic solution for the fleet size performs well. However, if the corresponding vehicle transfer policy is not appropriate, the overall performance can drastically deteriorate even with the optimal fleet size. Several extensions of our basic model are also analyzed.