  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.
