Demand responsive transit (DRT) services in suburban regions serve residents as the complements of the public transportation. Since suburban DRT service usually faces demand fluctuation in some special situations, such as terrible weather, DRT operators have recourse to temporal rental vehicles to satisfy all requests. There are two types of rental contracts. In the first case, the costs of rental vehicles are similar to the costs of owned vehicles, and the multi-trip vehicle routing problem is studied. In the second case, the costs of outbound trips are not covered by DRT companies, and the open vehicle routes are introduced. In this paper, a mixed integer linear programming formulation is proposed to model the route optimization problem of the suburban DRT service, in which the number of rental vehicles and two classes of routes should be decided simultaneously. To solve the proposed model, a branch-and-price algorithm is designed, which has two pricing subproblems to generate two classes of routes, respectively. From the results of experiments, it can be found that the service sequence is introduced, when open routes are involved. Renting vehicles can help DRT companies save operational costs even in daily operations.

中文翻译：

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租赁车辆的郊区需求响应过境服务

郊区的需求响应运输（DRT）服务为居民提供了公共交通的补充。由于郊区DRT服务通常在某些特殊情况下（例如恶劣天气）面临需求波动，因此DRT运营商不得不依靠临时租车来满足所有要求。有两种类型的租赁合同。在第一种情况下，租赁车辆的成本与自有车辆的成本相似，并且研究了多程车辆的路径问题。在第二种情况下，DRT公司不承担出境旅行的费用，并引入了开放的车辆路线。本文提出了一种混合整数线性规划公式，以对郊区DRT服务的路线优化问题进行建模，其中应同时确定租赁车辆的数量和两类路线。为了解决该模型，设计了一种分支定价算法，该算法具有两个定价子问题，分别生成两类路线。从实验结果可以发现，当涉及开放路径时，引入了服务序列。租用车辆可以帮助DRT公司甚至在日常运营中节省运营成本。