SUBDOMAIN 309.3 – QUANTITATIVE ANALYSIS
Competency 309.3.2: PERT/CPM Techniques – The graduate correctly applies PERT/CPM
techniques to project management tasks.
309.3.2-01: Determine the critical path identified by a given PERT/CPM analysis.
309.3.2-02: Utilize PERT analysis to determine the probability that a given project will
meet a specified deadline for completion.
309.3.2-03: Determine slack time for a given project activity.
309.3.2-04: Determine scheduled start time for a given project activity.
309.3.2-05: Determine scheduled completion time for a given project activity.
309.3.2-06: Use time-cost trade-offs to appropriately crash a project network.
This task requires candidates to prepare a program evaluation and review technique (PERT)
chart and apply critical path method (CPM) techniques.
Company A is installing a Web-based customer-feedback system to meet customer needs
for quick response when rolling out new products. A new product line is rolling out in 34
weeks and the customer-feedback system must be installed and running in time for the new
Table 1.1 in the attached spreadsheet “PERT/CPM Tables” shows three estimates of the time
it will take Company A to complete each of the activities and project tasks in the customer
feedback system project (optimistic, probable, pessimistic).
Company B is installing a similar feedback system to accompany a new product line and
originally had the same time line as Company A. Company B just announced that its new
product line is ahead of schedule and will be launched in 30 weeks instead of the initially
projected 34 weeks. Because the Web-based customer feedback system must be installed
and running in time for the revised date of the product launch, something must be done to
shorten implementation time required for the customer-feedback system project. Refer to
Table 1.2 in the attached worksheet “PERT/CPM Tables” that lists the expected time it will
take to complete the activities if shortened as much as possible (crash time), the cost to
complete the activity using normal resources (normal cost), and the cost of completing the
activity on an accelerated basis (crash cost).
A. Use the estimates for Company A in Table 1.1 to do each of the following:
1. Determine the expected completion time for each of the ten project activities,
entering all your answers in Table 1.1 and showing all your work.
a. Determine the variance for each project activity to two decimal places, entering
all your answers in Table 1.1 and showing all of your work.
2. Prepare a PERT chart (network diagram) and identify the critical path for project
completion, using your calculated values from part A.
Note: Any additional numbers included in the PERT chart will not be evaluated for
Note: If you don’t have software to build a PERT chart, use text boxes with lines or
arrows in a word processing program or Excel.
3. Determine each of the following, showing all of your work or reasoning:
Note: Referencing a value in the PERT chart is not considered showing work. Please
explain how the value was determined for each of the following.
a. Expected duration of the entire project
b. Slack for project task A
c. Slack for project task H
d. The week project task F is scheduled to start
e. The week project task I is scheduled to finish
4. Determine the probability of completing this project in time for the product launch in
34 weeks, showing all your work.
Note: You may want to use the complete cumulative normal table located at the back
of the book or at http://homes.cs.washington.edu/~jrl/normal_cdf.pdf.
B. Assume that Company B has the same expected completion times for project activities
as Company A. Use your results from part A1 to calculate the following information,
entering all answers in Table 1.2 and showing all of your work:
1. Maximum reduction in time
2. Crash cost per week
C. Identify the following by using your results from part B:
1. Activities to be crashed in order to complete the project within 30 weeks.
Note: All pathways must be within the 30 week deadline.
2. Number of weeks each of these activities should be crashed to meet the deadlinewith
the lowest possible increase in cost.
3. Additional crashing cost of the activities identified in part C1.
D. When you use sources, include all in-text citations and references in APA format.
Note: To reduce unnecessary matches select ignore “small matches <20 words” and
Note: When bulleted points are present in the task prompt, the level of detail or support
called for in the rubric refers to those bulleted points.
Note: For definitions of terms commonly used in the rubric, see the Rubric Terms web link
included in the Evaluation Procedures section.
Note: When using sources to support ideas and elements in a paper or project, the
submission MUST include APA formatted in-text citations with a corresponding reference list
for any direct quotes or paraphrasing. It is not necessary to list sources that were consulted
if they have not been quoted or paraphrased in the text of the paper or project.
Note: No more than a combined total of 30% of a submission can be directly quoted or
closely paraphrased from sources, even if cited correctly. For tips on using APA style, please
refer to the APA Handout web link included in the General Instructions section.
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