Integrated optimization of train stopping plan and seat allocation scheme for railway systems under equilibrium travel choice and elastic demand

This paper examines the integrated optimization of train stopping plan and seat allocation scheme in railway systems, where equilibrium passenger travel choice under elastic demand is considered. The integrated optimization problem is formulated as a non-concave and non-linear mixed-integer mathematical model, where the objective is to maximize the system net benefit considering ticket revenue, consumer surplus, and cost associated with train stoppings. The integrated optimization model can be reformulated into a mixed-integer linear programming (MILP) model based on a series of linearization, relaxation, and outer-approximation techniques, which can then be solved by commercial MILP solvers (e.g., GUROBI). We also compare the integrated optimization approach with that when the train stopping plan and seat allocation are optimized separately and identify the potential benefits. Numerical studies have been conducted on a small-scale example, the Zhengzhou-Xi'an and Shanghai-Beijing high-speed railway corridors to illustrate the proposed model and solution approach.