Joint pricing and matching for dynamic high-capacity ride-sharing considering passengers'choice uncertainty
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.