This paper aims to address the integrated routing and appointment scheduling (RAS) problem for a single service provider. The RAS problem is an operational challenge faced by operators that provide services requiring home attendance, such as grocery delivery, home healthcare, or maintenance services. While considering the inherently random nature of service and travel times, the goal is to minimize a weighted sum of the operator’s travel times and idle time, and the client’s waiting times. To handle the complex search space of routing and appointment scheduling decisions, we propose a queueing-based approach to effectively deal with the appointment scheduling decisions. We use two well-known approximations from queueing theory: first, we use an approach based on phase-type distributions to accurately approximate the objective function, and second, we use an heavy-traffic approximation to derive an efficient procedure to obtain good appointment schedules. Combining these two approaches results in a fast and sufficiently accurate hybrid approximation, thus essentially reducing RAS to a routing problem. Moreover, we propose the use of a simple yet effective large neighborhood search metaheuristic to explore the space of routing decisions. The effectiveness of our proposed methodology is tested on benchmark instances with up to 40 clients, demonstrating an efficient and accurate methodology for integrated routing and appointment scheduling.

中文翻译：

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基于排队的集成路由和预约安排方法


本文旨在解决单个服务提供商的集成路由和预约调度（RAS）问题。 RAS 问题是提供需要上门服务的运营商面临的运营挑战，例如杂货配送、家庭医疗保健或维护服务。在考虑服务和出行时间固有的随机性的同时，目标是最小化运营商的出行时间和空闲时间以及客户的等待时间的加权总和。为了处理路由和预约调度决策的复杂搜索空间，我们提出了一种基于队列的方法来有效地处理预约调度决策。我们使用排队论中的两个著名的近似：首先，我们使用基于阶段型分布的方法来精确地近似目标函数，其次，我们使用大流量近似来推导出有效的程序来获得良好的预约时间表。结合这两种方法可以产生快速且足够准确的混合近似，从而从本质上将 RAS 简化为路由问题。此外，我们建议使用简单而有效的大邻域搜索元启发式来探索路由决策的空间。我们提出的方法的有效性在多达 40 个客户端的基准实例上进行了测试，展示了集成路由和预约安排的高效且准确的方法。