# SCM 302

## Operations Management / Supply Chain Management

### Module 02.03 Key Concept: Impact of Activity Time Variation and link to PERT Approach

The Critical Path Method assumes a fixed time estimate for each activity and assumes there is no variation in activity times.  This makes the analysis straight forward but does not recognize that there is usually variation evident across the lifetime of a project.

Program Evaluation and Review Technique (PERT) uses a probability distribution for activity times to allow for variability.  Three time estimates are required:

• Optimistic Time – if everything goes according to plan
• Pessimistic Time – assumes very unfavorable conditions
• Most Likely Time – most realistic estimate.

PERT assumes that total project completion times follow a normal probability distribution and that activity times are statistically independent.  Application of probabilities for activities is shown in the text.

Project variance is computed by summing the variances of critical activities (on the Critical Path)

This data can be used to calculate the probability that a project can be completed at a specific time.

Variability of times for activities on noncritical paths must be considered when finding the probability of finishing in a specified time as variation in noncritical activity may cause a change in the Critical path.

It is not uncommon with any project to face problems / changes.  For example, the project can be behind schedule and / or specified completion times can be moved forward.  This may require the shortening of a project – a process called “Crashing.”

There are several things that should be considered related to the process.  The amount by which and activity is crashed must be feasible / permissible.  The resultant shortened activity durations should be expected to enable completion of the project by the due date.  The total cost of Crashing is as small as possible.  The following steps are followed in the Crashing of a project:

• Compute the crash cost per time period.  If crash costs are linear over time: Crash Cost / Period = ((Crash Cost – Normal Cost) / (Normal time – Crash Time))
• Using current activity times, find the critical path and identify the critical activities.
• If there is only one critical path, then select the activity on this critical path that (a) can still be crashed, and (b) has the smallest crash cost per period.  If there is more than one critical path, then select one activity from each critical path such that (a) each selected activity can still be crashed, and (b) the total crash cost of all selected activities is the smallest. Note that the same activity may be common to more than one critical path.
• Update all activity times. If the desired due date has been reached, stop. If not, return to Step 2.

An example of the calculations is shown in the text.

In general, PERT is a straightforward concept and is not mathematically complex.  It is especially useful when scheduling and controlling large projects.  Graphical networks help highlight relationships among project activities.   Critical Path and Slack Time analyses help pinpoint activities that need to be closely watched.  Project documentation and graphics point out who iw responsible for various activities.  Thus, PERT is applicable to a wide variety of projects and is useful in monitoring costs as well as schedules.

On the other hand, PERT has several disadvantages.

• Project activities have to be clearly defined, independent, and stable in their relationships
• Precedence relationships must be specified and networked together
• Time estimates tend to be subjective and are subject to fudging by managers
• There is an inherent danger of too much emphasis being placed on the longest, or critical, path