AI 中文总结
本研究针对动态大容量拼车的联合定价与匹配问题，提出基于松弛的梯度下降引导搜索算法，考虑乘客选择不确定性，大幅提升计算速度，同时显著增加拼车收入与服务率。
AI 中文摘要
本研究探讨面向动态大容量拼车服务的感知不确定性联合定价与匹配问题，假设乘客具有价格弹性，会根据平台提供的 upfront 价格决定是否接受拼车邀约。我们将所研究问题建模为两阶段随机规划问题：第一阶段优化针对乘客的 upfront 价格决策，第二阶段的补救问题则基于乘客的不确定选择捕捉乘客与车辆的分配过程。为提升计算效率，我们提出一种新颖的基于松弛的梯度下降引导搜索算法，该算法利用问题的结构特性：算法首先通过松弛生成第一阶段问题的可行解，随后通过推导得到的梯度信息引导的搜索过程迭代改进解；特别地，在计算梯度时应用场景缩减以消除不必要的场景，从而降低整体计算负担。数值实验表明，与直接求解随机规划相比，所提算法可将计算速度提升数千倍，同时最优性间隙不超过1.1%。最后，我们通过两座大城市的真实数据集与道路网络开展大规模模拟，验证了考虑乘客选择不确定性的益处，结果显示，与基线方法相比，所提方法平均可将收入提升5.2%，服务率提升8.2%。本研究为交通网络公司设计拼车定价策略以提升服务效率与增加收入提供了有价值的参考。
英文摘要
This work investigates the uncertainty-aware joint pricing and matching problem for dynamic high-capacity ride-sharing services, where passengers are assumed to be price-elastic and decide whether to accept a ride-sharing offer based on the upfront prices provided by the platform. We formulate the studied problem as a two-stage stochastic program, where the first stage optimizes upfront price decisions for passengers, and the second-stage recourse problem captures passenger-vehicle assignment based on passengers' uncertain choices. To enhance computational efficiency, we introduce a novel relaxation-based gradient descent-guided search algorithm that leverages the problem's structural properties. Initially, the algorithm generates a feasible solution for the first-stage problem via relaxation. It then iteratively improves the solution via a search process guided by the derived gradient information. In particular, scenario reduction is applied to eliminate unnecessary scenarios when calculating the gradient, thereby reducing the overall computational burden. Numerical experiments demonstrate that, compared to solving the stochastic program directly, the proposed algorithm can accelerate computation speed by thousands of times while achieving optimality gaps of no more than 1.1%. Finally, we validate the benefits of considering passengers' choice uncertainty through large-scale simulation using real-world datasets and road networks over two large cities. The results demonstrate that, on average, the proposed method can increase the revenue by 5.2% and the service rate by 8.2% compared to the baseline approaches. This study provides a valuable reference for transportation network companies to design pricing strategies for ride-sharing to enhance service efficiency and improve revenue.
