Robust optimization models for integrated train stop planning and timetabling with passenger demand uncertainty

In this work, we consider the problem of scheduling a set of trains (i.e., determining their departure and arrival times at the visited stations) and simultaneously deciding their stopping patterns (i.e., determining at which stations the trains should stop) with constraints on passenger demand, given as the number of passengers that travel between an origin station and a destination station. In particular, we face the setting in which demand can be uncertain, and propose Mixed Integer Linear Programming (MILP) models to derive robust solutions in planning, i.e., several months before operations. These models are based on the technique of Light Robustness, in which uncertainty is handled by inserting a desired protection level, and solution efficiency is guaranteed by limiting the worsening of the nominal objective value (i.e., the objective value of the problem in which uncertainty is neglected). In our case, the protection is against a potential increased passenger demand, and the solution efficiency is obtained by limiting the train travel time and the number of train stops. The goal is to determine robust solutions in planning so as to reduce the passenger inconvenience that may occur in real-time due to additional passenger demand. The proposed models differ in the way of inserting the protection, and show different levels of detail on the required information about passenger demand. They are tested on real-life data of the Wuhan–Guangzhou high-speed railway line under different demand scenarios, and the obtained results are compared with those found by solving the nominal problem. The comparison shows that robust solutions can handle uncertain passenger demand in a considerably more effective way.