We consider a vehicle routing problem which seeks to minimize cost subject to time window and synchronization constraints. In this problem, the fleet of vehicles is categorized into regular and special vehicles. Some customers require both vehicles' services, whose starting service times at the customer are synchronized. Despite its important real-world application, this problem has rarely been studied in the literature. To solve the problem, we propose a Constraint Programming (CP) model and an Adaptive Large Neighborhood Search (ALNS) in which the design of insertion operators is based on solving linear programming (LP) models to check the insertion feasibility. A number of acceleration techniques is also proposed to significantly reduce the computational time. The computational experiments show that our new CP model finds better solutions than an existing CP-based ANLS, when used on small instances with 25 customers and with a much shorter running time. Our LP-based ALNS dominates the cp-ALNS, in terms of solution quality, when it provides solutions with better objective values, on average, for all instance classes. This demonstrates the advantage of using linear programming instead of constraint programming when dealing with a variant of vehicle routing problems with relatively tight constraints, which is often considered to be more favorable for CP-based methods.

中文翻译：

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具有同步约束的车辆路径问题的新约束规划模型和基于线性规划的自适应大邻域搜索

我们考虑一个车辆路径问题，该问题寻求在时间窗口和同步约束下最小化成本。在这个问题中，车队分为普通车辆和特种车辆。一些客户需要两种车辆的服务，其在客户处的开始服务时间是同步的。尽管它在现实世界中具有重要的应用，但在文献中很少研究这个问题。为了解决这个问题，我们提出了约束规划 (CP) 模型和自适应大邻域搜索 (ALNS)，其中插入算子的设计基于求解线性规划 (LP) 模型来检查插入的可行性。还提出了许多加速技术来显着减少计算时间。计算实验表明，当在拥有 25 个客户且运行时间更短的小型实例上使用时，我们的新 CP 模型找到了比现有的基于 CP 的 ANLS 更好的解决方案。我们基于 LP 的 ALNS 在解决方案质量方面优于 cp-ALNS，当它为所有实例类提供具有更好目标值的解决方案时。这证明了在处理具有相对严格约束的车辆路径问题的变体时使用线性规划而不是约束规划的优势，这通常被认为对基于 CP 的方法更有利。平均而言，对于所有实例类。这证明了在处理具有相对严格约束的车辆路径问题的变体时使用线性规划而不是约束规划的优势，这通常被认为对基于 CP 的方法更有利。平均而言，对于所有实例类。这证明了在处理具有相对严格约束的车辆路径问题的变体时使用线性规划而不是约束规划的优势，这通常被认为对基于 CP 的方法更有利。