Critical Path
Critical Path Procedure 1. Develop a list of the activities that make up the project. 2. Determine the immediate predecessor(s) for each activity in the project. 3. Estimate the completion time for each activity. For example:
Activity Immediate Predecessor Time A - 3 B - 1 C - 2 D A, B, C 4 E C, D 5 F A 3 G D, F 6 H E 4
4. Draw a project network with nodes and arcs depicting the activities and immediate predecessors listed in steps 1 and 2. Please see problem 4, 7, and 8 below for an example of a network with arcs. 5. Prepare the outline of the activity schedule with column and row titles as shown below. 6. Use the project network and the activity times to determine the earliest start and then the earliest finish time for each activity by making a forward pass through the network. 7. The earliest start time for the first activity(s) in a network is zero (0). The earliest finish time for the first activity(s) in a network is the activity time for that activity. 8. The earliest start time for an activity with one predecessor is the earliest finish time for the predecessor. The earliest finish time for this activity is the earliest start time plus the activity time for the activity. 9. The earliest start time for an activity with two or more predecessors is the maximum of the earliest finish times for all of the predecessors for that activity. 10. The earliest finish time for the last activity in the project identifies the project completion time.
Activity Schedule | Activity | Earliest | Earliest | Latest | Latest | | Critical | Activity | Time | Start | Finish | Finish | Start | Slack | Path | A | 4 | 0 | 4 | 4 | 0 | 0 | X | B | 6 | 0 | 6 | 7 | 1 | 1 | | C | 2 | 4 | 6 | 7 | 5 |
Activity Immediate Predecessor Time A - 3 B - 1 C - 2 D A, B, C 4 E C, D 5 F A 3 G D, F 6 H E 4
4. Draw a project network with nodes and arcs depicting the activities and immediate predecessors listed in steps 1 and 2. Please see problem 4, 7, and 8 below for an example of a network with arcs. 5. Prepare the outline of the activity schedule with column and row titles as shown below. 6. Use the project network and the activity times to determine the earliest start and then the earliest finish time for each activity by making a forward pass through the network. 7. The earliest start time for the first activity(s) in a network is zero (0). The earliest finish time for the first activity(s) in a network is the activity time for that activity. 8. The earliest start time for an activity with one predecessor is the earliest finish time for the predecessor. The earliest finish time for this activity is the earliest start time plus the activity time for the activity. 9. The earliest start time for an activity with two or more predecessors is the maximum of the earliest finish times for all of the predecessors for that activity. 10. The earliest finish time for the last activity in the project identifies the project completion time.
Activity Schedule | Activity | Earliest | Earliest | Latest | Latest | | Critical | Activity | Time | Start | Finish | Finish | Start | Slack | Path | A | 4 | 0 | 4 | 4 | 0 | 0 | X | B | 6 | 0 | 6 | 7 | 1 | 1 | | C | 2 | 4 | 6 | 7 | 5 |