Distributionally robust alternative service design responding to joint closures in multimodal transit systems

Despite their occurrence in practice and typically severe consequences, little attention has been given to joint disruptions in multimodal transit systems. To bridge this gap, we focus on joint closures of metro stations and urban roads, a common type of joint disruptions that simultaneously affects multiple metro lines and bus routes. The proposed approach integrates the optimizations of adaptive bus routes, service departure times, and passenger demand assignment to design alternative metro and bus services for passengers. The coordination of alternative services is ensured both within individual transit systems and across the entire multimodal transit system. Uncertainties in passenger demand and bus travel time are duly incorporated using finite stochastic scenarios. Given the partially known uncertainty information, we develop a distributionally robust optimization (DRO) model to address the problem. The worst-case mean-conditional value-at-risk criterion is utilized to balance operators’ risk-averse attitude against the expected total passenger and operation costs. Afterwards, we devise a polyhedral ambiguity set to obtain a computationally tractable form of the DRO model and propose a tailored adaptive large neighborhood search heuristic for model solving. Finally, we test our methodology with mid-scale and large-scale cases in Beijing. Numerical results show that the DRO approach produces more robust solutions with superior out-of-sample performance compared to stochastic programming, with minimal additional cost. Besides, the integrated optimization of alternative metro and bus services plays a critical role in reducing total cost and enhancing service quality for passengers. Based on these numerical results, we conclude several valuable managerial insights for real-world applications.