  Joint parcel delivery by trucks and drones has enjoyed significant attention
for some time, as the advantages of one delivery method offset the
disadvantages of the other. This paper focuses on the vehicle routing problem
with drones and drone speed selection (VRPD-DSS), which considers
speed-dependent energy consumption and drone-charging in detail. For this
purpose, we formulate a comprehensive mixed-integer problem that aims to
minimize the operational costs consisting of fuel consumption costs of the
trucks, labor costs for the drivers, and energy costs of the drones. The speed
at which a drone performs a flight must be selected from a discrete set. We
introduce preprocessing steps to eliminate dominated speeds for a flight to
reduce the problem size and use valid inequalities to accelerate the solution
process. The consideration of speed-dependent energy consumption leads to the
fact that it is advisable to perform different flights at different speeds and
not to consistently operate a drone at maximum speed. Instead, drone speed
should be selected to balance drone range and speed of delivery. Our extensive
computational study of a rural real-world setting shows that, by modeling
energy consumption realistically, the savings in operational costs compared to
truck-only delivery are significant but smaller than those identified in
previously published work. Our analysis further reveals that the greatest
savings stem from the fact that overall delivery time decreases compared to
truck-only delivery, allowing costly truck-driver time to be reduced. The
additional energy costs of the drone, however, are largely negligible.
