CPM - Critical Path Method
CPM is a project management technique that analyzes what activities have the least amount of scheduling flexibility (i.e., are the most mission-critical) and then predicts project duration schedule based on the activities that fall along the "critical path." Activities that lie along the critical path cannot be delayed without delaying the finish time for the entire project. Projects planned with CPM typically are graphically represented in a diagram showing how each activity is related to the others (Precedence Diagramming Method).
CPM is for projects that are made up of a number of individual "activities." If some of the activities require other activities to finish before they can start, then the project becomes a complex web of activities. The mission of the critical path method is to determine how early can the project be completed and to identify the critical activities, namely the activities whose delays will cause a delay in the completion of the entire project.
ET[A] :=Earliest time that activity A can commence (given the precedence constraint and the duration of its predecessors)
LT[A] :=Latest time that activity A can be completed without causing a delay in the completion of the entire project.
TF[A] :=LT[A] - ET[A]) - t(A) (total float of activity A.) The total float of an activity is then the longest possible delay in the completion of this activity that will not cause a delay in the completion of the entire project. Thus: Critical activity := An activity whose total float is equal to zero (TF[A]=0)
One of the important ideas about the Precedence Diagramming Method is illustrated by the bar chart shown below. While the duration of each task is easily shown, the sequence between tasks can not be easily shown. If, for example, the start of Task C depends on both Activity B and Activity E, then any delay to Task E will also push Task C back.