  The task allocation problem in multi-robot systems (MRTA) is an NP-hard
problem whose viable solutions are usually found by heuristic algorithms.
Considering the increasing need of improvement on logistics, the use of robots
for increasing the efficiency of logistics warehouses is becoming a
requirement. In a smart warehouse the main tasks consist of employing a fleet
of automated picking and mobile robots that coordinate by picking up items from
a set of orders from the shelves and dropping them at the delivery stations.
Two aspects generally justify multi-robot task allocation complexity: (i)
environmental aspects, such as multi-delivery stations and dispersed robots
(since they remain in constant motion) and (ii) fleet heterogeneity, where
robots' traffic speed and capacity loads are different from each other. Despite
these properties have been widely researched in the literature, they usually
are investigated separately. This work proposes a scalable and efficient task
allocation algorithm for smart warehouses with multi-delivery stations and
heterogeneous fleets. Our strategy employs a novel cost estimator, which
computes costs as a function of the robots' variable characteristics and
capacity while they receive new tasks. For validating the strategy a series of
experiments is performed simulating the operation of smart warehouses with
multiple delivery stations and heteregenous fleets. The results show that our
strategy generates routes costing up to $33$\% less than the routes generated
by a state-of-the-art task allocation algorithm and $96$\% faster in test
instances representing our target scenario. Considering single-delivery
stations and non-dispersed robots, we reduced the number of robots by up to
$18$\%, allocating tasks $92$\% faster, and generating routes whose costs are
statistically similar to the routes generated by the state-of-the-art
algorithm.
