# QUANTITATIVE ANALYSIS 4

Introduction:

This task requires candidates to prepare a program evaluation and review technique (PERT) chart and apply critical path method (CPM) techniques.

Given:

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 product launch.

Table 1.1 in the attached worksheet “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, showing all your work.

a. Determine the variance for each project activity, showing all your work.

2. Prepare a PERT chart (network diagram) to identify the critical path for project completion.

Note: If you don’t have software to build a PERT chart, use text boxes with lines or arrows in a word processing program.

3. Determine each of the following, showing all of your work or reasoning:

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.

B. Assume that Company B has the same expected completion times for project activities as Company A. Use your results from part A1 and the data in Table 1.2 to determine the following, showing all 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

2. Number of weeks each of these activities should be crashed to meet the deadline with the lowest possible increase in cost

3. Additional crashing cost of the activities identified in part C1.

2

>Table 1.1

RT/

PM

nalysis

etail Table 1.1

(weeks)

A START 2

START

C A 3 4

D B

E C 4 5 6

B 8 10

F 4 6 11

8 10

G 3 6 12

2 3

P

E C A
Preceding Activity Optimistic Time to Complete
(weeks)
Probable Time to Complete
(weeks)
Pessimistic Time to Complete
(weeks)
Expected Time to Complete Variance
(weeks)
START
3 4
B 5 6 13
8
10 11 15
F 12
G
H D,E 18
I
J H,I 7
END

## Table 1.2

Task Expected Time to Complete

START

A 2

B 5

C 3

D 7

E 3

F 6

\$ 24,000

G 5

\$ 28,000

H 8

I

J 3

\$ 36,000

END

 PERT/CPM Analysis Task Detail Table 1.2 Normal Cost Crash Cost Maximum Reduction in Time Crash Cost per week Normal (weeks) Crash (weeks) \$ 8,400 \$ 11,200 \$ 28,000 \$ 40,000 \$ 18,000 \$ 24,000 \$ 36,800 \$ 44,800 \$ 14,000 \$ 16,800 \$ 20,000 \$ 18,200 \$ 44,000 \$ 64,000 4.5 \$ 26,000 \$ 36,000 \$ 21,000

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QAT1 – 309.3.2-01-06

Levels

Criteria

Unacceptable Needs
Revision

Meets
Standard

Exemplary Score/Level

Articulation of
Response (clarity,
organization, word
usage, ease of
understandability)

There is no
evidence of
response to the
prompts.

The articulation
of the response
is weak.

The articulation
of the response

The articulation of
the response is
skillful.

Accuracy of Mechanics
(grammar,
punctuation, spelling)

The work includes
several major errors
that disrupt the
meaning or flow of
the response.

The work
includes a few
major errors
and/or many
minor errors that
interfere with the
clarity of the
response.

The work
includes a few
minor errors but
detectable major
errors.

The work includes
detectable major
or minor errors.

A1. Expected
Completion Time

The candidate
correctly determines
the expected
completion time,
showing all work,
for 0-7 project
activities.

The candidate
correctly
determines the
expected
completion time,
showing all work,
for 8-9 project
activities.

Not applicable. The candidate
correctly
determines the
expected
completion time,
showing all work,
for 10 project
activities.

A1a. Variance The candidate
correctly determines
the variance,
showing all work,
for 0-7 project
activities.

The candidate
correctly
determines the
variance,
showing all work,
for 8-9 project
activities.

Not applicable. The candidate
correctly
determines the
variance, showing
all work, for 10
project activities.

A2. PERT Chart The candidate does
not prepare a PERT
chart that correctly
identifies the critical
path for project
completion.

Not applicable. Not applicable. The candidate
prepares a PERT
chart that
correctly identifies
the critical path
for project
completion.

A3a. Expected
Duration

The candidate does
not correctly
determine the
expected duration
of the entire project
or does not show all
work or

reasoning.

The candidate
does not
correctly
determine the
expected
duration of the
entire project but
shows all work or
reasoning.

Not applicable. The candidate
correctly
determines the
expected duration
of the entire
project and shows
all work or
reasoning.

A3b. Slack for Project

The candidate does
not correctly
determine the slack
for project task A or
does not show all
work or reasoning.

The candidate
does not
correctly
determine the
slack for project
task A but shows
all work or

Not applicable. The candidate
correctly
determines the
slack for project
task A and shows
all work or
reasoning.

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reasoning.

A3c. Slack for Project

The candidate does
not correctly
determine the slack
for project task H or
does not show all
work or reasoning.

The candidate
does not
correctly
determine the
slack for project
task H but shows
all work or
reasoning.

Not applicable. The candidate
correctly
determines the
slack for project
task H and shows
all work or
reasoning.

A3d. Scheduled Start
for Project Task F

The candidate does
not correctly
determine the week
project task F is
scheduled to start
or does not show all
work or reasoning.

The candidate
does not
correctly
determine the
week project
scheduled to
start but shows
all work or
reasoning.

Not applicable. The candidate
correctly
determines the
F is scheduled to
start and shows
all work or
reasoning.

A3e. Scheduled Finish
for Project Task I

The candidate does
not correctly
determine the week
project task I is
scheduled to finish
or does not show all
work or reasoning.

The candidate
does not
correctly
determine the
week project
scheduled to
finish but shows
all work or
reasoning.

Not applicable. The candidate
correctly
determines the
I is scheduled to
finish and shows
all work or
reasoning.

A4. Probability of
Completing on Time

The candidate does
not correctly
determine the
probability of
completing this
project in time for
the product launch
in 34 weeks or does
not show all work.

The candidate
does not
correctly
determine the
probability of
completing this
project in time
for the product
launch in 34
weeks but shows
all work.

Not applicable. The candidate
correctly
determines the
probability of
completing this
project in time for
the product launch
in 34 weeks and
shows all work.

B1. Maximum Time
Reduction

The candidate does
not correctly
determine the
maximum reduction
in time or does not
show all work.

The candidate
does not
correctly
determine the
maximum
reduction in time
but shows all
work.

Not applicable. The candidate
correctly
determines the
maximum
reduction in time
and shows all
work.

B2. Crash Cost Per
Week

The candidate does
not correctly
determine the crash
cost per week or
does not show all
work.

The candidate
does not
correctly
determine the
crash cost per
week but shows
all work.

Not applicable. The candidate
correctly
determines the
crash cost per
week and shows
all work.

C1. Activities to Be
Crashed

The candidate does
not correctly
identify activities to
be crashed in order
to complete the
project within 30
weeks.

Not applicable. Not applicable. The candidate
correctly identifies
activities to be
crashed in order
to complete the
project within 30
weeks.

C2. Number of Weeks The candidate does Not applicable. Not applicable. The candidate

to Crash not correctly
identify the number
of weeks identified
activities from part
C1 should be
crashed to meet the
lowest possible
increase in cost.

correctly identifies
the number of
weeks identified
activities from
part C1 should be
crashed to meet
the lowest
possible increase
in cost.

Crashing Cost

The candidate does
not correctly
identify the
cost of the activities
identified in part C1.

Not applicable. Not applicable. The candidate
correctly identifies
crashing cost of
the activities
identified in part
C1.

D. Sources If the candidate
uses sources, the
candidate does not
provide in-text
citations and/or
references for each
source used.

If the candidate
uses sources, the
candidate
provides
appropriate in-
text citations
and/or
references with
major deviations
from APA style.

If the candidate
uses sources, the
candidate
provides
appropriate in-
text citations
and/or
references with
minor deviations
from APA style.

If the candidate
uses sources, the
candidate
provides
appropriate in-
text citations
and/or references