The multi-robot task allocation (MRTA) is an NP-hard problem whose viable solutions are usually found by heuristic algorithms. Considering the growing need for improvements in logistics, using robots to increase warehouse management’s efficiency is an essential demand. In smart warehouses, the main tasks involve 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 delivery stations. The complexity of multi-robot task allocation arises mainly due to: (i) environmental aspects, such as multi-delivery stations and dispersed robots; and (ii) fleet heterogeneity. Despite these properties having been widely researched in the literature, they are commonly investigated separately. Also, many algorithms are not scalable for problems with thousands of tasks and hundreds of robots as those currently found in logistic warehouses. This work presents a scalable and efficient task allocation algorithm for smart warehouses with multi-delivery stations and heterogeneous fleets, called Dynamic Domain Zone based Capacity and Priority constrained Task Allocator (DoNe-CPTA). Our strategy employs a novel cost estimator to create groups of dominant tasks and thus optimize task allocation and reduce execution time and number of robots. Experiments have compared our method with the state-of-the-art algorithm in a series of benchmarks that simulate the operation of smart warehouses with multiple delivery stations and heterogenous fleets. Results show that DoNe-CPTA generated routes with 33% lower cost, running 96% faster than the state-of-the-art algorithm. Experiments also check out settings with single-delivery stations and non-dispersed robots, where DoNe-CPTA reduced the number of robots by up to 18%, running 92% faster without increasing route costs.