This paper solves the problem of optimizing a surcharge-reward scheme and analyzes equilibrium properties incorporating commuters’ departure time choice to relieve crowding and queuing congestion in mass transit systems. The surcharge-reward scheme incentivizes commuters to switch departure times from a pre-specified central period to shoulder periods. We formulate a bilevel model to design and optimize the surcharge-reward scheme. The upper-level problem minimizes the total equilibrium costs by determining the refundable surcharges, the rewards, and the corresponding central charging period. The lower-level problem determines the equilibrium of commuters’ departure times with respect to generalized travel costs. Equilibrium properties are analyzed and a sequential iterative solution algorithm is developed. We found that the existence of an optimal solution depends on the scheme design and there exists a lower bound on the surcharge to achieve the system optimum. Numerical studies are conducted on a commuting rail line in Copenhagen. The proposed algorithm converges efficiently, and the fare incentive scheme can simultaneously reduce the individual trip costs, total crowding costs, and total queuing time costs. The performance of the scheme increases with the rewards and surcharges up to a point and beyond which it stays unchanged.

本文解决了优化附加费奖励方案的问题，并结合通勤者的出发时间选择来分析平衡特性，以缓解公交系统中的拥挤和排队拥堵情况。附加费奖励计划激励通勤者将出发时间从预先指定的中央时段切换为肩部时段。我们制定了一个双层模型来设计和优化附加费奖励方案。上层问题通过确定可退还的附加费，奖励和相应的中央收费期来最大程度地降低总均衡成本。下层问题决定了通勤者出发时间相对于一般旅行费用的平衡。分析了平衡性质，并开发了顺序迭代求解算法。我们发现最佳解决方案的存在取决于方案设计，并且附加费存在下限以实现系统优化。在哥本哈根的通勤铁路上进行了数值研究。所提出的算法有效地收敛，并且票价激励方案可以同时减少个人出行成本，总拥挤成本和总排队时间成本。该计划的绩效随着奖励和附加费的增加而提高，直至超出一定程度为止。总拥挤成本和总排队时间成本。该计划的绩效随着奖励和附加费的增加而提高，直至超出一定程度为止。总拥挤成本和总排队时间成本。该计划的绩效随着奖励和附加费的增加而提高，直至超出一定程度为止。