Automating the execution of workflows (or business processes) on computer resources has been the subject of much research. However, many workflow scenarios still require human involvement, which introduces additional authorization concerns. Role-Based Authorization Control (RBAC), under which the users are assigned to certain roles while the roles are associated with prescribed permissions, is a popular authorisation control scheme. When we allocate resources for workloads and plan system capacities, it is often assumed that when a task is allocated to a resource, the resource will accept the task and start the execution once the processor becomes available. However, the authorization policies impose further constraints on task executions, and therefore may incur performance penalty and affect both application- and system-oriented performance. This paper investigates the issue of allocating resources for running workflows under the role-based authorization control. The resource allocation strategies are developed in this paper for both human resources and computing resources. The allocation strategy for human resources takes into account the authorization constraints and establishes the optimization equation subject to the constraint of the budget available to hire human resources. Then the optimization equation is solved to obtain the number of human resources allocated to each authorization role. The allocation strategy for computing resources also takes into account authorization constraints, calculating not only the number of computing resources, but also the proportion of processing capacity in each resource allocated to serve the tasks assuming each role. The simulation experiments have been conducted to verify the effectiveness of the developed allocation strategies. The experimental results show that the allocation strategy developed in this paper outperforms the traditional allocation strategies, which do not consider authorization constraints, in terms of both average response time and resource utilization.