Property of the Free Float and its Application in Seeking the Secondary Critical Path in CPM Network

The secondary critical path plays a very important role in the project scheduling and time/cost trade-off problems. The property of the free float is studied in this paper, and the preceding main chain theorem and free float theorem are proposed. Based on these theorems, the paper presents a simple method to seek the secondary critical path in a CPM network using the free float. That is, seeking the non-critical activity with the minimum value of free float in all activities immediately preceding the critical nodes, and then connecting its preceding main chain and the critical path segment between the finish node of that non-critical activity and the termination node. Finally, this method is proved to be correct, and an example is given to describe the method.