Seat allocation optimization for railway systems with equity considerations

Abstract

This paper investigates a railway seat allocation problem with a focus on equity. We aim to distribute the railway capacity more fairly among passengers from different Origin-Destination (OD) pairs while enhancing profitability. We first develop a Mixed Integer Linear Programming (MILP) model for scenarios with deterministic demand. We then further extend our study by formulating Stochastic Programming (SP) and Distributionally Robust Optimization (DRO) models for scenarios with demand uncertainty. Additionally, we derive the deterministic equivalent of the DRO model using a box ambiguity set. Furthermore, we explore the relationships between the proposed DRO and SP models, both of which can be efficiently solved by common MILP solvers like GUROBI. To validate our approach, we perform numerical studies on a small-scale example and the Zhengzhou-Xi’an high-speed railway corridor. The results demonstrate that the proposed optimization methods improve equity across OD pairs, where the DRO model can yield high-quality solutions.