Distributionally Robust Chance-Constrained Line Planning for Railway Systems Under Passenger Demand Uncertainty

In a railway network, making a line plan is a critical optimization problem that determines the daily transportation capacity of the network, aiming at aligning it with passenger demand while minimizing the operational cost. However, the inherent uncertainty in passenger demand often makes the determined line plan infeasible to cover. Meanwhile, additional adjustments to the line plan due to fluctuating demand in the complex railway system can cause unexpected costs. To obtain a robust line plan, we propose a distributionally robust chance-constrained (DRCC) line planning model based on a type- $\infty $ Wasserstein ambiguity set, aiming to generate a line plan that remains feasible with a pre-specified probability while accommodating a given distribution deviation tolerance. We present an equivalent tractable reformulation for the proposed DRCC model by explicitly characterizing the worst-case probability distribution. Furthermore, we develop valid inequalities and a warm start strategy tailored to this model to enhance computational efficiency. The proposed model and solution method are validated through numerical experiments conducted on the Wuhan-Guangzhou high-speed railway corridor. Results demonstrate the effectiveness of the solution acceleration techniques and underscore the advantage of the DRCC model over the robust optimization model and conventional chance-constrained model in reducing operational costs. Note to Practitioners—The motivation for this paper stems from the need to provide a daily line plan for the railway to meet the uncertain passenger demand with a pre-specified probability. We assume that an estimated probability distribution of the demand is available and characterized by finite scenarios with weights, but we do not need the estimation to be perfect/accurate. We propose a distributionally robust chance-constrained line planning model to maintain robustness under the deviation/inaccurate probability distribution. To solve the model efficiently, we develop a warm start method to quickly find a partial initial solution and design valid inequalities where adding them as constraints can shorten the solving procedure by reducing the feasible region of the model’s continuous relaxation. The produced line plan requires less operational cost than the robust optimization model to cover the same amount of demand by the benefits of leveraging the distributional information.