Optimal pricing and seat allocation schemes in passenger railway systems

This paper examines optimal pricing and seat allocation schemes in passenger railway systems, where ticket pricing and seat allocation (or capacity allocation) are both Origin-Destination specific. We consider that the demand is sensitive to the ticket price, and a non-concave and non-linear mixed integer optimization model is then formulated for the ticket pricing and seat allocation problem to maximize the railway ticket revenue. To find the optimal solution of the ticket revenue maximization problem effectively, the proposed non-concave and non-linear model is reformulated such that the objective function and constraints are linear with respect to the decision variables or the logarithms of the decision variables. The linearized model is then further relaxed as a mixed-integer programing problem (MILP). Based on the above linearization and relaxation techniques, a globally optimal solution can be obtained by iteratively solving the relaxed MILP and adopting the range reduction scheme. Two numerical examples are presented for illustration.