  Given a set of customers, the Flying Sidekick Traveling Salesman Problem
(FSTSP) consists of using one truck and one drone to perform deliveries to
them. The drone is limited to delivering to one customer at a time, after which
it returns to the truck, from where it can be launched again. The goal is to
minimize the time required to service all customers and return both vehicles to
the depot. In the literature, we can find heuristics for this problem that
follow the order-first split-second approach: find a Hamiltonian cycle h with
all customers, and then remove some customers to be handled by the drone while
deciding from where the drone will be launched and where it will be retrieved.
Indeed, they optimally solve the h-FSTSP, which is a variation that consists of
solving the FSTSP while respecting a given initial cycle h. We present the Lazy
Drone Property, which guarantees that only some combinations of nodes for
launch and retrieval of the drone need to be considered by algorithms for the
h-FSTSP. We also present an algorithm that uses the property, and we show
experimental results which corroborate its effectiveness in decreasing the
running time of such algorithms. Our algorithm was shown to be more than 84
times faster than the previously best-known ones over the literature benchmark.
Moreover, on average, it considered a number of launch and retrieval pairs that
is linear on the number of customers, indicating that the algorithm's
performance should be sustainable for larger instances.
