Critical Path

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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:

ActivityImmediate PredecessorTime
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| 1| |
D| 6| 4| 10| 10| 4| 0| X|
E| 3| 6| 9| 10| 7| 1| |
F| 3| 6| 9| 15| 12| 6| |
G| 5| 10| 15| 15| 10| 0| X|

11. Use the project completion time identified in step 10 as the latest finish time for the last activity and make a backward pass through the network to identify the latest start and latest finish time for each activity. 12. The latest finish time for an activity that has one succeeding activity is the latest start time for that succeeding activity. 13. The latest finish time for an activity that has two or more succeeding activities is the minimum of the latest start times for all of the succeeding activities. 14. Use the difference between the latest start time and the earliest start time for each activity to determine the slack time for each activity (i.e., slack time = latest start time – earliest start time). 15. Find the activities with zero slack; these are the activities on the critical path. 16. Prepare the formulas to calculate the earliest start, earliest finish, latest finish, latest start, slack, and critical activity cells. With these formulas in place, you can change any of the activity times and the related cells will reflect the change. Critical Path Problems

1. Construct a project network for the following project. The project is completed when activities F and G are both complete.

Immediate Predecessor--AA C,B C,B D,E

Assume that the project has the following activity times (in months):


a. Draw a project network.
b. Develop the activity schedule for the project.
c. Can the project be completed in 1.5 years?

2. Embassy Club Condominium, located on the west coast of Florida, is undertaking a summer renovation of its main building. The project is scheduled to begin May 1, and a September 1 (17-week) completion date is desired. The condominium manager...
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