Abstract: This paper analyzes the fare schemes for different urban rail transitrider groups. Different rider groups include general groups and special groups (i.e., the elderly, the disabled, and students). Preferential fares and service frequency are analyzed to account for the heterogeneity of different groups. An optimization model is developed to determine the optimal fare discount rates and transit headways with the goal of maximizing the transportation equity for different groups. The method based on simulated annealing algorithm is designed to solve the proposed model considering the constrains of transit capacity, total subsidy, and fare discount rates. Taking the Metro Line No. 2 in Changsha city as an example, this paper analyzes and compares the fare discount rates for different rider groups and provides a feasible preferential fare scheme based on train operation plans. The results show an optimal fare scheme would beno discount for general groups, 40% discount for the disabled, 20% discount for the elderly, and 60% discount for students. The travel demand would increases by 1.06% for the disabled, 2.86% for the elderly, and 1.94% for students.When the government implements the subsidy policy, the subsidy amount can be determined by the preferential fare scheme of different groups and the service level of the operator.

Key words: urban traffic, fare discount rate, simulate dannealing algorithm, rail transit rider groups, social welfare; headway

摘要： 为研究不同群体，即一般群体和特殊群体(老年人、残疾人、学生)的票价方案和补贴问题，本文考虑不同群体的差异性，以各群体的票价折扣率和列车开行间隔为决策变量，构建基于群体差异化的运营补贴优化模型，以社会福利最大化为目标，优化各群体的票价折扣率、企业的服务水平及政府的补贴额度，确保各群体获得合适的补贴，实现公共交通出行的公平性。综合考虑城市轨道交通运输能力约束、政府财政约束及不同群体票价折扣率约束，设计了基于模拟退火算法的求解算法。以长沙地铁2号线为例，分析比较不同群体的票价折扣率，提出基于列车运行计划的福利票价方案。研究结果表明，一般群体不享受折扣，残疾人4折优惠，老年人2折优惠及学生6折优惠，交通特殊群体的出行比分别提升了1.06%，2.86%及1.94%。政府在实施补贴政策时，可以通过不同群体的票价福利措施和企业的服务水平确定补贴额度。

关键词: 城市交通, 票价折扣率, 模拟退火算法, 交通群体, 社会福利, 开行间隔