Flexible scheduling of customized bus for green mega-events: A distributionally robust optimization approach

Mega-events such as the Olympics and the World Championships face significant challenges in evacuating large numbers of attendees after the events conclude, which consume substantial transportation resources. Under the global pressure to reduce carbon emissions, energy conservation and emission reduction are increasingly becoming top priorities. This paper focuses on the efficient scheduling of customized buses (CB) after green mega-events, incorporating skip-stop operations and coordinated bus services to minimize energy consumption, fixed and transportation costs, and facilitate the evacuation of attendees, while accounting for practical constraints such as the availability of customized buses, vehicle capacity, time windows, and flow balance. A distributionally robust optimization (DRO) model is developed, using a novel ambiguity set to model uncertain demand via parametric interval-valued fuzzy variables. To ensure computational tractability, the model is reformulated as an integer linear programming model. To address the computational challenges of large-scale instances, an improved variable neighborhood search heuristic is designed by incorporating the reinforcement learning techniques, including the KL-UCB algorithm and a sliding window mechanism. Extensive numerical experiments are conducted to verify the performance of the proposed heuristic. Computational results demonstrate that the proposed DRO model effectively handles uncertainty, offering robust and adaptable solutions. Compared to existing heuristics, the proposed heuristic improves performance by 6.51% on average, and incorporating reinforcement learning into VNS enhances computational efficiency by 4.88% on average. A real-life case study further validates the model, demonstrating that the skip-stop strategy significantly reduces vehicle travel time and enhances overall operational efficiency.