Customarily, the project sclheduling problem is thought in the context of PERT and CPM. Although widely used and powerful, these techniques do not take into account a basic feature of the problem, that is resource limitations. The problem addressed in this study is to schedule the activities of a single project in order that all resource and precedence relationships constraints are satisfied with an objective of minimizing total of activity completion times. Our purpose is to make a computational comparison of some solution procedures for the problem. Firstly, the 0 - 1 formulation of the problem is introduced together with the underlying assumptions. Then, we describe the solution procedures tested in this study. In order to evaluate them, the random activity networks are generated. Finally, we provide the results and conclusions.