Many production processes require the cooperation of various resources. Especially when using expensive machines, their utilization plays a decisive role in efficient production. In agricultural production or civil construction processes, e.g., harvesting or road building, the machines are typically mobile, and synchronization of different machine types is required to perform operations. In addition, the productivity of one type often depends on the availability of another type. In this paper, we consider two types of vehicles, called primary and support vehicles. Primary vehicles perform operations and are assisted by at least one support vehicle, with more support vehicles resulting in faster service times for primary vehicles. We call this practical problem the vehicle routing and scheduling problem with support vehicle-dependent service times and introduce two mixed-integer linear programming models. The first represents each support vehicle individually with binary decision variables, while the second considers the cumulative flow of support vehicles with integer decision variables. Furthermore, the models are defined on a graph that allows easy transformation into multiple variants. These variants are based on allowing or prohibiting switching support vehicles between primary vehicles and splitting services among primary vehicles. We show in our extensive computational experiments that: i) the integer representation of support vehicles is superior to the binary representation, ii) the benefit of additional vehicles is subject to saturation effects and depends on the ratio of support and primary vehicles, and iii) switching and splitting lead to problems that are more difficult to solve, but also result in better solutions with higher primary vehicle utilization.

翻译：许多生产过程需要多种资源的协同配合。特别是在使用昂贵设备时，其利用率对高效生产起着决定性作用。在农业生产或土木工程流程（如收割或道路建设）中，设备通常具有移动性，需要同步不同设备类型才能执行操作。此外，某类设备的产能往往依赖于另一类设备的可用性。本文考虑两种车辆类型：主车辆与辅助车辆。主车辆执行操作，并需至少一辆辅助车辆协助，辅助车辆数量越多，主车辆的服务时间越短。我们将这一实际问题称为"辅助车辆相关服务时间的车辆路径与调度问题"，并提出两个混合整数线性规划模型。第一个模型对每辆辅助车辆采用二元决策变量独立表示，第二个模型则利用整数决策变量考虑辅助车辆的累积流量。此外，这些模型定义在便于转化为多种变体的图结构上。这些变体基于是否允许在主车辆间切换辅助车辆、以及是否允许在主车辆间拆分服务。通过大量计算实验表明：i) 辅助车辆的整数表示优于二元表示，ii) 新增车辆的效益存在饱和效应，且取决于辅助车辆与主车辆的比例，iii) 切换与拆分操作虽增加了问题的求解难度，但能获得更优解，从而提升主车辆利用率。