Program Management Calculations: Spreadsheet Version

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:

t=(a+4m+b)/6

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):

sd=(b-a)/6

add the estimated deviations along the critical path to determine the probability of completing the project within a specified time:

prob=SqRt(Sum[sd**2])

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.

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