INF3708 DRAWING A CPM DIAGRAM (ACTIVITY-ON-ARROW)

EXAMPLE 1: Consider the list of tasks with dependencies and estimated durations (in weeks) in the table below: 1. Draw a CPM network for the list of tasks in the table above to illustrate the interaction of activities. 2. Identify the critical path and its duration. 3. After carefully considering the problem again, the project team decides that an alternative to the original plan would be to extend the duration of activity C to four weeks. This would allow activity E to drop to three weeks. Identify what the resulting critical activities are. Do these changes affect the total duration of the project? A few aspects to bear in mind when drawing a CPM network:  make sure that you understand and can apply the rules on pages 128-131 of the textbook;  the forward pass calculates the earliest date each event may start and the earliest date on which it may be completed;  the backward pass calculates the latest date when each event may be started and the latest date when it can be achieved or finished;  event dates are recorded on the diagram and activity dates on the activity table. In this example both processes D and C have to be finished and serve as input to process E, but process D and I also serve as input to process J. Thus a dummy activity was created, namely process 4a, to illustrate the duality. SOLUTION: 1. The diagram is given below: Task Precedents Duration (weeks) A None 1 B A 2 C B 2 D A 5 E C, D 5 F E 2 G A 4 H G 4 I F, H 1 J D, I 2 A=1 B=2 C=2 E=5 G=4 H=4 F=2 A=1 A=1 I=1 J=2 INF3708 2 2. In order to determine the critical path, we first of all list all of the different paths: path 1 A, D, E, F, I, J = 16 weeks path 2 A, B, C, E, F, I, J = 15 weeks path 3 A, G, H, I, J = 12 weeks path 4 A, D, J = 8 weeks Path 1 is thus the critical path. 3. Path 1 drops to 14 weeks and path 2 to15 weeks. Now the critical path will be path 2: A, B, C, E, F, I, J. The minimum duration drops to 15 weeks.