Real-time vehicle relocation, personnel dispatch and trip pricing for carsharing systems under supply and demand uncertainties

In one-way carsharing systems, striking a balance between vehicle supply and user demand across stations poses considerable operational challenges. While existing research on vehicle relocation, personnel dispatch, and trip pricing have shown effectiveness, they often struggle with the complexities of fluctuating and unpredictable demand and supply patterns in uncertain environments. This paper introduces a real-time relocation-dispatch-pricing (RDP) problem, within an evolving time-state-extended transportation network, to optimize vehicle relocation, personnel dispatch, and trip pricing in carsharing systems considering both demand and supply uncertainties. Furthermore, recognizing the critical role of future insights in real-time decision making and strategic adaptability, we propose a novel two-stage anticipatory-decision rolling horizon (ADRH) optimization framework where the first stage solves a real-time RDP problem to make actionable decisions with future supply and demand distributions, while also incorporating anticipatory guidance from the second stage. The proposed RDP problem under the ADRH framework is then formulated as a stochastic nonlinear programming (SNP) model. However, the state-of-the-art commercial solvers are inadequate for solving the proposed SNP model due to its solution complexity. Thus, we customize a hybrid parallel Lagrangian decomposition (HPLD) algorithm, which decomposes the RDP problem into manageable subproblems. Extensive numerical experiments using a real-world dataset demonstrate the computational efficiency of the HPLD algorithm and its ability to converge to a near-globally optimal solution. Sensitivity analyses are conducted focusing on parameters such as horizon length, fleet size, number of dispatchers, and demand elasticity. Numerical results show that the profits under the stochastic scenario are 18$\text{\%}$ higher than those under the deterministic scenario, indicating the significance of incorporating uncertain and future information into the operational decisions of carsharing systems.