Unit – 9

1. Unit – 9 PERT and CPM

2. Steps • Define the activities of the project, their precedence relationships and their time requirements. • Translate the project in network that shows the precedence relationships among the activities. • Network calculations. • Time schedule of the each activity.

3. Network representation • Each activity of the project is represented by an arc pointing in the directing of progress in the project. The nodes of the network establish the precedence relationships among the different activities of the project. • Two rules for constructing the network. • Each activity is represented by one and only one arc. • Each activity must be identified by two distinct end nodes. • No two activities can be identified by the same head and tail events.

4. Representation of dummy activity • Activities represented by arrow and identified by two events. • Event is represented by nodes. • Dummy activities normally depicted by a dashed arc, consumes no time or resources.

5. To maintain the correct precedence relationships, the following questions must be answered as each activity is added to the network. • What activities must immediately precede the current activity? • What activities must follows the current activity? • What activity must occur concurrently with the current activity?

6. Example • Activity C starts immediately after A and B have been completed. • Activity D starts after B only has completed.

7. CPM • The final step is to construct the time schedule for the project. To achieve this objectve a special computations required. • An activity is said to be critical if there is no ‘ float’ in determining its start and finish times. A non critical activity allows some scheduling slack, so that the start time of the activity may be advanced or delayed within limits without affecting the completion date of the entire project.

8. To carry out the necessary computations and event as a point in time at which activities are terminated and others are started. • Earliest occurrence of time of event i is represented by rectangular while latest occurrence time of an event is represented by triangle.

9. Forward and Backward Pass • Early start time of any activity can be find out by ESi = max ( ESi + Dij) • Backward Pass time calculate the late completion time.(LC) which is represented by triangle. • LCi = min (LCj – Dij)

10. Floats • Total Float • The total float of an acitivity represents the amount of time by which it can be delayed without delaying the project completeion date. In other words, it referes to the amount of free time associated with an acitivity which can be used before, during or after the performance of this acitivity. It is euql to the difference betweent he total time available for the performance of an activity and the time required for its performances. • Total Float (TF) = LCj – ESi – Dij • TF = BPj – FWi - Dij

11. Free Float • The free float is that part of the total float which can be used without affecting the float of the succeeding activities. Thus it is that value of the float which is consumable when the succeeding activities can be started at their earliest starting times. • FF = FPj – FPi – Dij