Program Management Calculations
Calculations for PERT and CPM are not particularly difficult-they require no
more than simple arithmetic. They can get lengthy and sometimes
convoluted, especially since CPM requires frequent recalculation. So, while it
can be done with pencil and paper, frequently it is done with the aid of
computers-simple spreadsheets, or even dedicated application programs like
Microsoft Project.
When calculating PERT and CPM without a dedicated application program, it is
best to approach it in a stepwise process (Krueckeberg & Silvers, 1974, pp.
231-255).
PERT Analysis
- Define tasks to be performed
- Links tasks in sequence
- Estimate time to complete each task ("normal time")
- use 3 estimates: most optimistic (a), most pessimistic (b), and most
likely (m)
- weighting most likely time, determine expected ("average")time:
- Determine earliest expected date for completion of tasks and activity
- always assign the longest time-path to the completion date
- the "longest" path is the critical path
- For each task, determine the latest allowable time for moving to the next
task
- difference between latest time and expected time is slack time
- Determine probability of meeting the expected time
- use time range (b-a) to estimate standard deviation of time for each
activity (i.e., estimate of average deviation from expected time):
- add the estimated deviations along the critical path to determine the
probability of completing the project within a specified time:
- Read this formula as "Probability equals the square root of the sum of
the squared standard deviations for each activity on the critical path"
- In PERT, shift the allocation of resources from slack activities to
activities on the critical path, and revise time estimates and probability
estimates. Usually, you would not settle just for shifting based on time
saving, but would move at this point to CPM and consider time and money
in determining the optimal path.
A typical PERT table might have the following structure:
Activity |
Beginning |
Ending |
a |
m |
b |
expected |
sd |
Foundatn |
1 |
2 |
1 |
2 |
3 |
2 |
.33 |
Frame |
2 |
3 |
1 |
4 |
6 |
4 |
.83 |
CPM Analysis
- Develop time and cost data ("normal" and "crashed") for all tasks
- Develop cost-per-week for crashing (crashed costs divided by time saved)
- Develop project network (PERT)
- Crash the activity on the critical path with the lowest
cost-for-crashing
- Recalculate the project network (the critical path might change!)
- Repeat steps 4 & 5 until all the paths have been crashed.
- Ease up on all noncritical paths, just to the point that all paths are
critical
A typical CPM table might have the following structure:
Activty |
Beg. |
End |
Time-Crash |
Time-Norml |
Cost-Crash |
Cost-Norml |
Time Saved |
Cost Increas |
Cost / Week |
Fdn |
1 |
2 |
1 |
2 |
4000 |
3000 |
1 |
1000 |
1000 |
Frame |
2 |
3 |
1 |
4 |
8000 |
4000 |
3 |
4000 |
1333 |
In addition to tabular data, both CPM and PERT will generally include a
graphic presentation of the network of activities, usually with the length of
each activity (in time) indicated and the critical path marked distinctively.
© 1996 A.J.Filipovitch
Revised 4 October 96