Fog computing-based radio access network (Fog-RAN) leveraging the software-defined networking (SDN) and network function virtualization (NFV) is the most promising solution to offer real-time support for the massive number of connected devices in the industrial Internet of Things (IIoT) networks. However, designing an optimal dynamic radio resource allocation to handle the fluctuating traffic loads is critical. In this article, a novel architectural design of an SDN-based virtual Fog-RAN is proposed, in which we jointly study radio resource allocation and transmit beamforming to improve resource utilization and IIoT users’ satisfaction, by minimizing the network power consumption (NPC) and maximizing the achievable sum-rate (ASR), simultaneously. To this end, we first formulate a mixed-integer nonlinear problem to optimize the physical resource block allocation, the assignment of user equipments, and radio unit, and the downlink transmit beamforming, by considering imperfect channel state information. To solve the ntractable MINLP, we exploit the successive convex approximation approach. Then, we formulate a multiple knapsack problem (MKP) to optimize the assignment between RUs and virtual baseband units, by exploiting the set of active RUs minimized in the previous problem. We solve the formulated MKP by decomposing the dual problems and solving them through the dual descent method. Through performance analysis, we show the proposed approach provides a high users’ satisfaction rate, maximizes the ASR and minimizes the NPC, and provides better savings, in terms of the number of radio and baseband resources utilized, than its counterparts.