Enabling low data losses and ensuring reliability are essential requirements to guarantee Quality of Service in Industrial Internet of Things (IIoT) applications. This can be achieved by the adoption of various architectures and standards, the most promising of which is IEEE 802.15.4 Time Slotted Channel Hopping mode. However, there are still several open issues, such as providing effective scheduling scheme in the standard. In this paper, we propose a novel auction based scheduling mechanism that uses a first-price sealed bids auction to solve the throughput maximizing scheduling problem. We considered a centralized IIoT network where the gateway makes frequency allocations and time slot assignment. Simulation results show that the proposed algorithm yields a very close throughput performance to the optimal one obtained through CPLEX with a much lower complexity.