# SCM 302

## Operations Management / Supply Chain Management

### Module 02.02 Key Concept: Critical Path Method and Examples

Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM) are described as “network” techniques.  The relevance will become evident from subsequent illustrations.  These techniques were developed in the 1950 and used initially for chemical plant and military operations.  Both go beyond the simple Gantt Chart approach to include precedence relationships and inter-dependencies as well as to offer different estimates of activity times.  This brings in the realization that there is variation / uncertainty in everything.

There are six steps involved in each process:

• Define the project and prepare work breakdown structure
• Develop relationships among the activities – decide which activities must precede and which must follow others
• Draw the network connecting all of the activities
• Assign time and/or cost estimates to each activity
• Compute the longest time path through the network – this is called the critical path
• Use the network to help plan, schedule, monitor, and control the project

Use of PERT and CPM provides Project Management teams the answers to the following questions:

• When will the entire project be completed?
• What are the critical activities or tasks in the project?
• Which are the noncritical activities?
• What is the probability the project will be completed by a specific date?
• Is the project on schedule, behind schedule, or ahead of schedule?
• Is the money spent equal to, less than, or greater than the budget?
• Are there enough resources available to finish the project on time?
• If the project must be finished in a shorter time, what is the way to accomplish this at least cost?

The authors of the text provide two different approaches to construction of diagrams for use in PERT and CPM.  One is called Activity on Node (AON) and the other is called Activity on Arrow.  For the purpose of this course we will only focus on the AON approach.

The construction of an Activity on Node network diagram is illustrated in the text with reference to a high level process at Milwaukee Paper.  You should invest significant time going through the examples presented.  This will help you with Homework Problems in MYOMLab.

This information can be used to construct an AON Network diagram that easily shows the inter-relationship between activities.

From a scheduling perspective we must now link time requirements to each specific activity.  The Critical Path is the longest path through the network.  It is also the shortest time in which the project can be completed.  Any delay in the Critical Path activities delays the project.  By definition, Critical Path activities have no slack time.

Information from the planning table presented in the text can be linked with the AON Diagram to provide the foundation for a Critical Path analysis.  The overall approach is to identify Start and Finish Times for each activity from a Start-to-Finish (forward pass) and from a Finish-to-Start (backward pass) perspective.  This approach is illustrated nicely in your text with full description of the process and the use of overlays to show the building of steps through the process.  They following are established during the process:

• Earliest start (ES) = earliest time at which an activity can start, assuming all predecessors have been completed
•  Earliest finish (EF) = earliest time at which an activity can be finished
•  Latest start (LS) = latest time at which an activity can start so as to not delay the completion time of the entire project
•  Latest finish (LF) = latest time by which an activity has to be finished so as to not delay the completion time of the entire project

In employing the Critical Path Approach the Network Diagram is expanded by showing the Activity, Duration, Earliest Start, Earliest Finish, Latest Start and Latest Finish for each “Node”.

To determine the earliest start and finish times for the project you complete a Forward Pass analysis through the network.

• If an activity has only a single immediate predecessor, it’s Earliest Start time equals the Earliest Finish time of the predecessor.
• If an activity has multiple immediate predecessors, its Earliest Start is the maximum of the Earliest Finish of its predecessors.
• The Earliest Finish time of an activity is the sum of its Earliest Start time and its Activity time.

The text shows the extension of the Network Diagram for Milwaukee Paper with addition of data from the Forward Path Analysis.

To determine the latest start and finish times for the project you complete a Backward Pass analysis through the network.

• If an activity is an immediate predecessor for just a single activity, it’s Latest Finish time equals the Latest Start of the activity that immediately follows it.
• If an activity is an immediate predecessor to more than one activity, its Latest Finish time is the minimum of all Latest Start values of all activities that immediately follow it.
• The Latest Start time of an activity is the difference of its Latest Finish time and its Activity time.

Note that you always perform the Forward Pass before the Backward Pass

After computing the Earliest Start, Earliest Finish, Latest Start and Latest Finish times for all activities, compute the Slack (Free Time) for each activity.  Slack is the length of time an activity can be delayed without delaying the entire project.  If there is no slack for a particular activity then, by convention, it lies on the Critical Path of the Project.  Any delay in any activity on the Critical Path will result in a delay of the entire project.  This is illustrated quite nicely for the Milwaukee Paper example in the text.

The Critical Path analysis can be converted to Gantt Charts with Earliest Start and Finish vs. Latest Start and Finish.