A new progress in the theory of PERT

This paper put forward the concept of “quasi-critical path” and related four theorems. We proved that each activity has a quasi-critical path related with it. By “activity dependent quasi-critical path” we mean that for this activity, there must be a path preceding it and for all activities in the path their free slacks are zeros. Similarly, there must be a path succeeding it and for all activities in the path, their backward free slacks (a new concept!) are zeros. The difference between a “critical path” and an “activity dependent quasi-critical path” is: For the “critical path”, there are no time slacks. For the “activity dependent quasi-critical path”, there are no free slacks in the activities preceding this activity and no backward free slacks in the activities succeeding this activity. For important activities with uncertain time we need to calculate their “activity dependent quasi-critical path” to guarantee enough time for them.