Cloud computing is a new and rapidly emerging computing paradigm where applications,data and IT services are provided over the Internet.The task-resource management is the key role in cloud computing systems.Task-resource scheduling problems are premier which relate to the efficiency of the whole cloud computing facilities.Task-resource scheduling problem is NPcomplete.In this paper,we consider an approach to solve this problem optimally.This approach is based on constructing a logical model for the problem.Using this model,we can apply algorithms for the satisfiability problem(SAT) to solve the task-resource scheduling problem.Also,this model allows us to create a testbed for particle swarm optimization algorithms for scheduling workflows. Cloud computing is a new and rapidly emerging computing paradigm where applications, data and IT services are provided over the Internet. The task-resource management is the key role in cloud computing systems. Task-resource scheduling problems are premier which relate to the efficiency of the whole cloud computing facilities.Task-resource scheduling problem is NPcomplete.In this paper, we consider an approach to solve this problem optimally. This approach is based on constructing a logical model for the problem. Use this model, we can apply algorithms for the satisfiability problem (SAT) to solve the task-resource scheduling problem.Also, this model allows us to create a testbed for particle swarm optimization algorithms for scheduling workflows.