Optimizing Fleet Size in Point-to-Point Shared Demand Responsive Transportation Service: A Network Decomposition Approach

With increasing urbanization and the demand for efficient, flexible transportation solutions, demand-responsive transportation services (DTRS) has emerged as a viable alternative to traditional public transit. However, determining the optimal fleet size to balance the investment and operational revenue remains a significant challenge for service providers. In this article, we address the optimization of fleet size in point-to-point shared demand DRTS, which widely operates within many cities. To capture the uncertain passenger demands in the future when planning the fleet size currently, we model this problem with a framework of two-stage stochastic programming with recourse. Fleet sizing decisions are made in the first stage before the uncertain demands are revealed. After the uncertainty is revealed, the second stage involves making additional decisions to maximize operational revenue. The objective is to optimize the total revenue of the first-stage decisions and the expected revenue of the recourse actions. To solve this practical problem, we resort to the Model Predictive Control method (MPC) and propose a network decomposition approach that first converts the transportation network to a nodal tree structure and then develops a Nodal Tree Recourse with Dependent Arc Capacities (NTRDAC) algorithm to obtain the exact value of the expected recourse functions. In the experiments, NTRDAC is able to produce results within seconds for transportation networks with over 30 nodes. In contrast, a commercial solver is only capable of solving networks with up to five nodes. The stability tests show that NTRDAC remains robust as the problem size varies. Lastly, the value of the stochastic solution (VSS) was evaluated, and the results indicate that it consistently outperforms the expected value solutions. Numerical experiments show that the performance of the NTRDAC algorithm is quite encouraging and fit for large-scale practical problems.