The profit-oriented hub line location problem with elastic demand
研究了考虑旅行时间需求弹性的枢纽线选址问题，提出混合整数非线性模型以最大化总收益，并给出线性化方案，通过蒙特利尔真实数据验证了模型在公共交通规划中的价值。
This paper deals with an extension of the hub line location problem considering demand elasticity with respect to travel times. The proposed model aims to capture the impact the hub network topology has on demand. The objective is to maximize the total revenue generated by each unit of demand using the hub line. We propose mixed-integer nonlinear formulations to model this problem. We study some properties of the nonlinear objective function associated with these formulations. Due to the inherent complexity involved in solving these nonlinear formulations with state-of-the-art solvers, we also present alternative mixed-integer linear programming formulations. Computational results compare the proposed formulations and the benefits of the presented model using benchmark instances commonly used in hub location. Moreover, a sensitivity analysis study is carried out with real data from the city of Montreal, Canada, to demonstrate the added value of incorporating demand elasticity when using the proposed model for public transportation planning.