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