Solutions to Chapter 12 Exercises

1
Solutions to Chapter 12 Exercises

2
Exercise 1

• There are four paths
• A-C-I (7 days)
• A-D-G-J (13 days)
• B-E-G-J (11 days)
• B-F-H-J (10 days)
• Thus, the critical path is A-D-G-J and these are
  the activities that should be monitored
  most closely because if they slip, the entire
  project will be delayed.

3
Exercise 1 concluded

• The time to complete the four paths is now
• A-C-I (5.5 days)
• A-D-G-J (11.5 days)
• B-E-G-J (12.5 days)
• B-F-H-J (11.5 days)
• The critical path is now B-E-G-J and the project
  completion is expected to be 12.5 days.
• Activities G and J remain as critical activities
  while A and D are no longer critical.

4
Exercise 2
5
Exercise 2 Path Slacks

• Path A-C-I Slack 6
• Path A-D-G-J Slack 0
• Path B-E-G-J Slack 2
• Path B-F-H-J Slack 10

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Exercise 3 Network Diagram
2
6
1
3
7
4
5
7
Exercise 3 Activity Expected Times, Variances
and Standard Deviations
8
Exercise 3 Path Expected Times, Variances, and
Standard Deviations
9
Exercise 3 Probability Project Finishes within
17 Weeks
All paths must be considered since they all have
a reasonable chance of taking longer than 17
weeks. Thus, there is a very small chance (i.e.,
.005) that the project can be completed in 17
weeks or less.
10
Exercise 3 Probability Project Finishes within
24 Weeks
Only paths 1-2-6-7 and 1-3-5-7 need be considered.
However, all paths can be easily included by
simply changing cell B1 from 17 to 24. With all
paths considered, there is a over an 86 chance
of completing the project in 24 weeks.
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Exercise 3 Should the Project be Pursued?

• Using the spreadsheet it can be easily determined
  that the probability of finishing within 18 weeks
  is .176 and the probability of the project
  taking 22 weeks or longer is 48.321.
• The expected value of the project is thus
• (.176 ? 10,000) (48.321 ? -5,000)
  -2398.40
• Given the negative expected value, the firm
  should not bid.

12
Exercise 4
The path with the longest expected time is
a-b-dummy-f-h-i 16.
e 3
b 5
i 1
a 3
0
h 3
c 3
g 2
d 1
f 4
13
Exercise 5
14
Exercise 5a continued
15
Exercise 5b continued
16
Exercise 5c concluded
17
Exercise 6
1
6
4
5
9
7
3
2
8
18
Exercise 6 continued
19
Exercise 6 concluded
Path 2-3-4-5-7-8-9 has the longest expected time.
Thus, the project would be expected to take
66.33.
20
Exercise 7
(000)
Plan
Plan
Progress,
40
30
Actual
35
24
20
17
55 70
55 70
Time, Days
Time, Days
21
Exercise 7 concluded

• Spending variance EC - AC 17,000 - 30,000
  -13,000. This indicates a cost overrun of
  13,000.
• Schedule variance EC - SC 17,000 - 24,000
  -7,000 indicating the project is behind.
• Time variance TE - TA 55 -70 -15 days
  indicating a 15 day delay.

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Exercise 8
(000)
Plan
84
Value
81
Actual
78
1 TE 2 3
Time, Months
23
Exercise 8 concluded

• Spending variance EC - AC 81,000 - 78,000
  3,000.
• Schedule variance EC - SC 81,000 - 84,000
  -3,000.
• TE can be estimated from chart by determining how
  much time should have elapsed according to the
  plan to achieve the current value completed. In
  this case TE is approximately 1.5 months.
• Thus, the spending variance TE - TA 1.5 - 2
  -0.5 month.

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Exercise 9

• Spending variance EC - AC 39,000 - 34,000
  5,000.
• Schedule variance EC - SC 39,000 - 42,000
  -3,000.

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Exercise 10a
26
Exercise 10a (concluded)
27
Exercise 10b

• From the above spreadsheet, the average project
  completion time is 90.33 days with a standard
  deviation of 5.16 days.
• Across the 100 replications of the simulation
  model, the project finished as quickly as 78.85
  days and took as long as 103.51 days.

28
Exercise 10c
29
Exercise 10d

• Path A-C-F has an expected duration of 88.8 days
  with a standard deviation of 4.81 days. Based on
  this, the probability that it is completed in 80
  days or less can be calculated as
• From the z table in the Appendix A, the
  probability of the path being completed in 80
  days or less is 3.51. Alternatively, this can
  be found using Excel as follows
  normdist(80,88.8,4.81,true) 3.37.
  Incidentally, the value found using Excel is
  actually more accurate since rounding the value
  of z was not required.
• Path B-D-F has an expected duration of 85.2 days
  and standard deviation of 7.31 days. Using Excel
  the probability it is completed in 80 days or
  less is found as normdist(80,85.2,7.31,true)
  23.84.
• Path B-E has an expected duration of 59.0 days
  and standard deviation of 6.93 days. Using Excel
  the probability it is completed in 80 days or
  less is found as normdist(80,59,6.93,true)
  99.88.
• The probability the entire project is completed
  in 80 days or less is calculated as
  (.0337)(.2384)(.9988) 0.80

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Exercise 10e

• The results shown in the spreadsheet to part a
  are consistent with the probability calculated in
  part d.
• In only one of the 100 replications was the
  project completed in 80 days or less (i.e., rep
  number 14).
• One percent of the replications is quite close
  to the 0.8 calculated in part d.