The point of departure of this paper is the planning and scheduling of a project by using the critical path method for a block diagram. The network is represented as a graph, and the task of scheduling the time is formulatod as a potential problem. Considering available resource levels in realizing a project, the graph is extended and several constraints are formed for a flow in the extended graph. These constraints and the potential problem lead to an integer linear programming problem with the object of minimizing the time. Finally, by using an example the structure of the linear programming problem is displayed and an algorithm for solving the problem is mentioned.