The Industrial Internet of Things (IIoT) has become a critical technology to accelerate the process of digital and intelligent transformation of industries. As the cooperative relationship between smart devices in IIoT becomes more complex, getting deterministic responses of IIoT periodic time-critical computing tasks becomes a crucial and nontrivial problem. However, few current works in cloud/edge/fog computing focus on this problem. This paper is a pioneer to explore the deterministic scheduling and network structural optimization problems for IIoT periodic time-critical computing tasks. We first formulate the two problems and derive theorems to help quickly identify computation and network resource sharing conflicts. Based on this, we propose a deterministic scheduling algorithm, IIoTBroker, which realizes deterministic response for each IIoT task by optimizing the fine-grained computation and network resources allocations, and a network optimization algorithm, IIoTDeployer, providing a cost-effective structural upgrade solution for existing IIoT networks. Our methods are illustrated to be cost-friendly, scalable, and deterministic response guaranteed with low computation cost from our simulation results.