作为公共交通的一部分,DRT通常适用于低需求地区,或是在夜间传统公交车停止运营时提供服务,或为老年人和残疾人提供非盈利的服务。我们推荐读者去阅读 Ho et al.的论文(A survey of dial-a-ride problems: literature review and recent developments. Transportation Research Part B: Methodological, 2018. 111: 395–421.),该文献详细总结了34 个不同类型的需求响应式交通系统。文献中的一些研究讨论了在各种应用场景下设计和实现DRT系统的问题。在不同类型的DRT 系统中,电话预定一次乘车 dial-a-ride (DAR) 系统是一种较为自由的服务类型,可能存在有限或无限的空间结构。Daganzo首先提出了一个理论空间队列模型来研究 DAR 系统的调度策略和服务水平(An approximate analytic model of many-to-many demand responsive transportation systems. Transportation Research, 1978. 12: 325–333.)。后来的很多研究都集中在更结构化的DRT系统上;例如,Durvasula et al.设计并实施了一种动态偏移线路服务,使普通公交车能够在某些低需求条件下按需运行(Peninsula transportation district commission route deviation feasibility study. Transportation Research Council., Virginia, 1998.)。Fu提出了一个理论规划模型,用于设计一种基于点偏移的DRT系统(Planning and design of flex-route transit services. Transportation Research Record: Journal of the Transportation Research Board, 2002. 1791: 59–66.)。Aldaihani et al.建立了一个混合网格分析模型,将DRT服务与固定线路公交服务结合在一起(Network design for a grid hybrid transit service. Transportation Research, Part A: Policy and Practice, 2004. 38: 511–530.)。Quadrifoglio et al.研究了一种允许公交车辆偏离固定路径的系统(MAST)(Mobility allowance shuttle transit (MAST) services: MIP formulation and strengthening with logic constraints. European Journal of Operational Research, 2008. 185(2): 481-494.)。Quadrifoglio 和Li提出了一个模型以预测接驳DRT系统的需求密度(A methodology to derive the critical demand density for designing and operating feeder transit services. Transportation Research Part B: Methodological, 2009. 43: 922–935. )。Jung and Jayakrishnan专注于高覆盖率的点对点交通(HCPPT),可以减少乘客换乘次数(High-coverage point-to-point transit: study of path-based vehicle routing through multiple hubs. Transportation Research Record, 2011. 2218(1): 78-87.)。Nourbakhsh and Ouyang提出了一个"结构化"的灵活路线公交系统,将"公交管道"的理念融入到一个宏观的网络结构中(A structured flexible transit system for low demand areas.Transportation Research Part B: Methodological, 2012. 46: 204–216.)。Stiglic et al.推出了一种能够推荐乘客上下车站的拼车系统(The benefits of meeting points in ride-sharing systems. Transportation Research Part B: Methodological, 82, 36-53.)。
很大一部分研究将DRT系统的路径设计问题归类为车辆配送路径规划问题(VRPPD)的变形,现在已存在广泛的文献资料介绍相关问题的模型与解决方案。例如,Hachicha et al. 提出的多车覆盖路径问题是一类需要访问更靠近用户位置的服务(Heuristics for the multi-vehicle covering tour problem. Computers & Operations Research, 2000. 27: 29–42.)。Chao et al. 提出了某种团体指向问题,旨在选择有限的路线并最大化利润(The team orienteering problem. European Journal of Operational Research, 2007. 88: 464–474.)。Park 和 Kim总结了校车路径规划问题,旨在规划将学生从家里运送到指定学校的时刻表和路线(The school bus routing problem: a review. European Journal of Operational Research, 2010. 202: 311–319.)。解决这些问题的方法包括精确的混合整数规划方法、构造的启发式和元启发式方法。我们推荐读者研读 Vigo 和 Toth,其中详细讨论了一些解决方案和方法(Vehicle Routing: Problems, Methods, and Applications. Society for Industrial and Applied Mathematics and the Mathematical Optimization Society, Philadelphia, 2014.)。除了静态问题,Sayarshad and Chow还提出了一个基于价值函数近似的采用预期定价的动态dial-a-ride服务系统(A scalable non-myopic dynamic dial-a-ride and pricing problem. Transportation Research Part B: Methodological, 2015. 81: 539-554.)。Masoud and Jayakrishnan提出了一个灵活的拼车系统,实时解决动态的点对点乘车匹配问题(A real-time algorithm to solve the peer-to-peer ride-matching problem in a flexible ridesharing system. Transportation Research Part B: Methodological, 2017. 106: 218-236.)。
现实中的公交路线设计实施问题也存在广泛的讨论。Schittekat et al.提出了一种无参数的元启发式算法,解决了公交车站选择和公交路径规划的两阶段问题(A metaheuristic for the school bus routing problem with bus stop selection. European Journal of Operational Research, 2013. 229: 518–528.)。Li et al.开发了一种自适应大型邻域搜索算法,解决了带时间窗口、利润和预约请求的VRPPD问题(Adaptive large neighborhood search for the pickup and delivery problem with time windows, profits, and reserved requests. European Journal of Operational Research, 2015. 252: 27–38)。Souza Lima et al.使用五种元启发式算法来解决具有异质需求的混合负载容量公交路径规划问题(A mixed load capacitated rural school bus routing problem with heterogeneous fleet: algorithms for the Brazilian context. Expert Systems with Applications, 2016. 56: 320–334.)。Masmoudi et al.设计了三种元启发式算法,以解决异质性dial-a-ride系统中的多库场多行程路径规划问题(Three effective metaheuristics to solve the multi-depot multi-trip heterogeneous dial-a-ride problem. Transportation Research Part E: Logistics and Transportation Review, 2016. 96: 60–80.)。