Two-stage robust railway line-planning approach with passenger demand uncertainty

A railway line-planning problem is one of the fundamental problems in the strategic planning of railway operations. Operation zone, frequency, stop schedule, and passenger distribution for each train based on passenger demand are determined to minimize both the operation cost of the railway enterprise and the total travel cost to the passengers. However, passenger demand uncertainty makes balancing transport capacity and fluctuating demand challenging. Therefore, this paper proposes a two-stage robust optimization model wherein the nominal line plan is determined in the first stage (i.e., the case in which passenger demand has no fluctuation) and the rescheduled line plan based on the nominal line plan is determined according to the demand realization in the second stage. A Lagrangian relaxation algorithm and some strengthening techniques are designed. The model and algorithm are tested on real-world instances of the Wuhan–Guangzhou high-speed railway line under uncertain passenger demands. Computational results indicate that the proposed solution algorithm can yield a high-quality solution in 3600 s. In addition, the proposed two-stage robust solution can help minimize both operation and travel costs on average when compared with the nominal solution under uncertainty realization.