This study is inspired by a challenging dynamic Dial-a-Ride Problem (DARP) encountered in a mobility service operated by the company Padam.¹ . Customers ask for a transportation service either in advance or in real-time and get an immediate answer about whether their requests are accepted or rejected. The main goal is to maximize the number of accepted requests during the service while respecting maximum capacity of limited number of vehicles. In this study, we propose novel methods based on reinsertion techniques to improve Padam's online system. The proposed reinsertion techniques aim to exploit the neighborhood of a solution and must be run in real-time whenever a request is rejected by an online system. Three main online reinsertion heuristics based on different neighborhoods are proposed. The first heuristic called HDR uses destruction and repair operators, the second heuristic called GH (graph heuristic) uses the ejection chain concept, and allow modeling the reinsertion problem as a constrained shortest path problem on directed graph built from a current solution, and the third heuristic called IGH (improved graph heuristic) based on GH with intensive exploration of the neighborhood. Our proposed approaches were extensively tested on real and hard instances provided by Padam. These instances contain up to 1011 requests and 14 vehicles and with very tight time windows. The obtained results revealed the performance of the proposed reinsertion methods compared to the online heuristic, where the number of served requests is increased and the number of vehicles is reduced while maintaining operating costs close to those of the online system. The results confirm the interest of using reinsertion techniques in the dynamic DARP service.

这项研究的灵感来自Padam公司运营的移动服务中遇到的具有挑战性的动态“乘车问题”（DARP）。¹。客户要求提前或实时提供运输服务，并立即获得有关其请求是否被接受的答复。主要目标是在服务期间最大化接受的请求数量，同时尊重有限数量的车辆的最大容量。在这项研究中，我们提出了基于重新插入技术的新方法来改善Padam的在线系统。提出的重新插入技术旨在利用解决方案的邻域，并且每当在线系统拒绝请求时，都必须实时运行。提出了基于不同邻域的三种主要的在线重新插入试探法。第一个称为HDR的启发式算法使用破坏和修复运算符，第二个称为GH（图形启发式）的启发式算法使用弹出链概念，并允许将重新插入问题建模为根据当前解决方案构建的有向图上的约束最短路径问题，第三个启发式算法称为GH（改进的图形启发式算法），基于GH并深入研究了邻域。我们建议的方法已在Padam提供的真实和困难实例上进行了广泛的测试。这些实例包含多达1011个请求和14辆车，并且时间窗口非常紧凑。与在线启发式方法相比，所获得的结果揭示了所提出的重新插入方法的性能，在在线启发式方法中，服务请求的数量增加了，而车辆的数量减少了，同时保持了接近在线系统的运营成本。结果证实了在动态DARP服务中使用重新插入技术的兴趣。