Planning and
Managing Projects
Chapter 8
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Activity
A
B
C
D
E
F
G
H
I
J
K
Description
Immediate
Predecessor(s)
Select administrative and medical staff.
—
Select site and do site survey.
—
Select equipment.
A
Prepare final construction plans and layout.
B
Bring utilities to the site.
B
Interview applicants and fill positions in
A
nursing, support staff, maintenance,
and security.
Purchase and take delivery of equipment.
C
Construct the hospital.
D
Develop an information system.
A
Install the equipment.
E,G,H
Train nurses and support staff.
F,I
Responsibility
Johnson
Taylor
Adams
Taylor
Burton
Johnson
Adams
Taylor
Simmons
Adams
Johnson
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Activity
AON Network
A
B
C
D
E
F
G
H
I
J
K
Description
I
Immediate
Predecessor(s)
Select administrative and medical staff.
—
Select site and do site survey.
—
Select equipment.
A
F
K A
Prepare final construction plans and layout.
B
Bring utilities to the site.
B
Interview applicants and fill positions in
A
nursing,
maintenance,
Startsupport staff, C
Finish
G
and security.
Purchase and take delivery of equipment.
C
Construct the hospital.
D
D
B
H
J A
Develop an information
system.
Install the equipment.
E,G,H
Train nurses and support staff.
F,I,J
Responsibility
Johnson
Taylor
Adams
Taylor
Burton
Johnson
Adams
Taylor
Simmons
Adams
Johnson
E
Figure 8.4
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Activity
Description
Completion Time
A
B
C
D
E
F
G
H
I
J
K
I
15
Immediate
Predecessor(s)
Select administrative and medical staff.
—
Select site and do site survey.
—
A
F
KA
Select equipment.
12
10
Prepare final construction
plans and layout. 6B
Bring utilities to the site.
B
Interview applicants and fill positions in
A
C
G
nursing,
Startsupport staff, maintenance,
Finish
10
35
and security.
Purchase and take delivery of equipment.
C
Construct the hospital.
B
D
H
JD
Develop an information
system.
9
10
40
4A
Install the equipment.
E,G,H
Train nurses and support staff.
F,I,J
Responsibility
Johnson
Taylor
Adams
Taylor
Burton
Johnson
Adams
Taylor
Simmons
Adams
Johnson
E
24
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Path
Expected Time (wks)
Activity
Immediate
Predecessor(s)
Description I
Completion
Time
A-F-K
28
15
A
Select administrative
and medical staff.
A-I-K
33
B
Select site and
A-C-G-J
61Ado site survey.
F
C
Select equipment.
12
10
B-D-H-J
D
Prepare final63
construction
plans and layout.
B-E-J
E
Bring utilities37
to the site.
F
G
H
I
J
K
Interview applicants and fill positions in
C
G
nursing,
Startsupport staff, maintenance,
10
35
and security.
Purchase and take delivery of equipment.
Construct the hospital.
B
D
H
Develop an information
system.
9
10
40
Install the equipment.
Train nurses and support staff.
—
—
KA
6
B
B
A
Responsibility
Johnson
Taylor
Adams
Taylor
Burton
Johnson
Finish
C
JD
4A
E,G,H
F,I,J
Adams
Taylor
Simmons
Adams
Johnson
E
24
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Path
Expected Time (wks)
Activity
Immediate
Predecessor(s)
Description I
Completion
Time
A-F-K
28
15
A
Select administrative
and medical staff.
A-I-K
33
B
Select site and
A-C-G-J
61Ado site survey.
F
C
Select equipment.
12
10
B-D-H-J
D
Prepare final63
construction
plans and layout.
B-E-J
E
Bring utilities37
to the site.
F
G
H
I
J
K
Interview applicants and fill positions in
C
G
nursing,
Startsupport staff, maintenance,
10
35
and security.
Purchase and take delivery of equipment.
Construct the hospital.
B
D
H
Develop an information
system.
9
10
40
Install the equipment.
Train nurses and support staff.
—
—
KA
6
B
B
A
Responsibility
Johnson
Taylor
Adams
Taylor
Burton
Johnson
Finish
C
JD
4A
E,G,H
F,I,J
Adams
Taylor
Simmons
Adams
Johnson
E
24
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
I
15
A
F
K
12
10
6
C
G
Start
B
9
Earliest Start
and
Earliest Finish Times
Finish
10
35
D
H
J
10
40
4
E
24
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Earliest start time
12
I 27
Earliest finish time
15
0
A 12
12
12
Critical
path
0
B 9
9
Earliest Start
and
Earliest Finish Times
27 K 33
10
12
Start
F 22
C 22
6
22
10
9
D 19
10
G 57
Finish
35
19
H 59
40
59
J 63
4
9 E 33
24
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
12
I 27
15
0
A 12
12
27 K 33
10
12
12
Start
F 22
C 22
6
22
10
0
B 9
9
Latest Start
and
Latest Finish Times
9
D 19
10
G 57
Finish
35
19
H 59
40
59
J 63
4
Project
finish
Time = 63
9 E 33
24
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
12
I 27
15
0
A 12
12
27 K 33
63
63
10
12
12
Start
F 22
C 22
6
22
10
0
B 9
9
Latest Start
and
Latest Finish Times
9
D 19
10
9 E 33
G 57
Finish
35
19
H 59
40
Latest
finish
time
59
J 63
4 63
Latest
finish
time
24
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
12
I 27
15
0
A 12
12
10
12
12
Start
F 22
C 22
Latest
start
time
22
10
0
B 9
9
Latest Start
and
Latest Finish Times
9
D 19
10
9 E 33
27 K 33
57
63
6
G 57
Finish
35
19
H 59
40
Latest
finish
time
J
59
63
59 4 63
Latest start
time
24
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Earliest start time
Latest start time
A
0
12
2 12 14
I
12
27
42 15 57
Critical
path
0
0
B 9
9 9
Latest Start
and
Latest Finish Times
Latest finish time
F
27 K 33
57
63
12
22
47 10 57
C
Start
Earliest finish time
12
22
14 10 24
D
9
19
9 10 19
6
G
22
57
24 35 59
H
19
59
19 40 59
Finish
J
59
63
59 4 63
9 E 33
35 24 59
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
I
12
27
42 15 57
A
0
12
2 12 14
F
C
12
22
14 10 24
Start
0
0
Activity Slack
Analysis
B 9
9 9
27 K 33
57
63
12
22
47 10 57
D
9
19
9 10 19
6
G
22
57
24 35 59
H
19
59
19 40 59
Finish
J
59
63
59 4 63
9 E 33
35 24 59
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
Slack Hospital
St. Activity
Adolf’s
I
12
27
42 15 57
Slack = LS – ES
or
A
0
12
2 12 14
Slack = LF – EF
F
C
12
22
14 10 24
Start
0
0
Activity Slack
Analysis
B 9
9 9
27 K 33
57
63
12
22
47 10 57
D
9
19
9 10 19
6
G
22
57
24 35 59
H
19
59
19 40 59
Finish
J
59
63
59 4 63
9 E 33
35 24 59
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
Slack Hospital
St. Activity
Adolf’s
I
SlackK = 57 – 27 = 30
or
A
0
12
2 12 14
SlackK = 63 – 33 = 30
12
27
42 15 57
F
C
12
22
14 10 24
Start
0
0
Activity Slack
Analysis
B 9
9 9
27 K 33
57
63
12
22
47 10 57
D
9
19
9 10 19
6
G
22
57
24 35 59
H
19
59
19 40 59
Finish
J
59
63
59 4 63
9 E 33
35 24 59
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
Node Duration ES
LS
Slack
St.
Adolf’s
Hospital
A
12
0
2
2
I
B
C
D
E
F
G
H
I
J
K
9
10
10
24
10
35
40
15
4
6
0
12
9
9
12
22
19
12
59
27
0
14
9
35
47
24
19
42
59
57
0
2
0
26
35
2
0
30
0
30
0
0
Critical Path
B 9
9 9
12
27
42 15 57
F
27 K 33
57
63
12
22
47 10 57
C
12
22
14 10 24
D
9
19
9 10 19
6
G
22
57
24 35 59
H
19
59
19 40 59
Finish
J
59
63
59 4 63
9 E 33
35 24 59
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Cost-Time Relationships in Cost Analysis
Direct cost (dollars)
8000 —
Crash cost (CC)
7000 —
Linear cost assumption
6000 —
5200
5000 —
Estimated costs for
a 2-week reduction,
from 10 weeks to
8 weeks
4000 —
3000 —
0—
Normal cost (NC)
|
5
|
6
(Crash time)
Figure 8.11
|
7
8
|
9
|
10
|
11
(Normal time)
Time (weeks)
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
TABLE 8.1
DIRECT COST AND TIME DATA FOR
THE ST. ADOLF’S HOSPITAL PROJECT
Activity
Normal
Time
(NT)
Normal
Cost
(NC)
A
B
C
D
E
F
G
H
I
J
K
12
9
10
10
24
10
35
40
15
4
6
$ 12,000
50,000
4,000
16,000
120,000
10,000
500,000
1,200,000
40,000
10,000
30,000
Totals
$1,992,000
Crash
Time
(CT)
11
7
5
8
14
6
25
35
10
1
5
Crash
Cost
(CC)
$ 13,000
64,000
7,000
20,000
200,000
16,000
530,000
1,260,000
52,500
13,000
34,000
Maximum
Time
Reduction
(wk)
1
2
5
2
10
4
10
5
5
2
1
Cost of
Crashing per
Week
$ 1,000
7,000
600
2,000
8,000
1,500
3,000
12,000
2,500
1,000
4,000
$2,209,000
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Modeling project schedule in Excel
Forward schedule (Earliest time)
ES = EF of predecessor, if only one predecessor
ES = Max(EF of predecessors), if more than one
EF = ES + Activity duration
Backward schedule (Latest time)
LF = LS of successor, if only one successor
ES = Min(LS of successors), if more than one
LS = LF - Activity duration
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Optimal crashing using Excel Solver
Target cell = Cost or project completion time
Changing cells = Crashing time
Constraints = Crashing time <= MTR
Options:
• Non-negative
• Tolerance
• Estimates, derivative, search
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Pert = Project Evaluation Review Technique
Finding probability for project completion time
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
Probability
Probabilistic Time Estimates
a
m
b
Time
Mean
Figure 8.12 (a) Beta Distribution
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Probabilistic
Time Estimates
I
A
F
K
Mean
a + 4m + b
te =
6
Variance
2 =
(
Start
B
C
G
D
H
Finish
J
E
b–a
6
2
)
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Probabilistic
Time Estimates
I
A
Activity B
Most
Optimistic Likely Pessimistic
(a)
(m)
(b)
7
8
15
Start
B
F
K
C
G
D
H
Finish
J
E
Example 8.6
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Probabilistic
Time Estimates
I
A
Activity B
Most
Optimistic Likely Pessimistic
(a)
(m)
(b)
7
8
15
7 + 4(8) + 15
te =
= 9 weeks
6
2 =
(
15 - 7
6
Start
B
F
K
C
G
D
H
Finish
J
E
2
) = 1.78
Example 8.6
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Time Estimates (wk)
Optimistic
Activity
(a)
A
B
C
D
E
F
G
H
I
J
K
11
7
5
8
14
6
25
35
10
1
5
Likely
(m)
Pessimistic
(b)
12
8
10
9
25
9
36
40
13
2
6
13
15
15
16
30
18
41
45
28
15
7
Activity Statistics
Expected Variance
Time (te )
( 2 )
12
9
10
10
24
10
35
40
15
4
6
0.11
1.78
2.78
1.78
7.11
4.00
7.11
2.78
9.00
5.44
0.11
Example 8.6
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
What is the probability the project will be
completed in 65 days?
Critical Path = B - D - H - J
TE = 9 + 10 + 40 + 4 = 63 days
2 =  (variances of critical path activities)
2 = 1.78 + 1.78 + 2.78 + 5.44 = 11.78
 = 11.78 = 3.432
Example 8.7
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Probabilities
Critical Path = B - D - H - J
T = 65 days TE = 63 days  = 3.432
z=
T – TE

=
65 – 63
3.432
= 0.58
From Normal table in page 807,
for z = 0.58, the table area = 0.7190
The probability that the project will be
Completed within 65 days is 71.9%
Example 8.7
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Normal distribution:
Mean = 63 weeks;
 = 3.432 weeks
Length of
critical path
Probability of
meeting the
schedule is
0.7190
Probability of
exceeding 65
weeks is 0.2810
63 65
Project duration (weeks)
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Expected project completion time with 98% probability
Critical Path = B - D - H - J
T = TE + z 
Normal table for 98%, z = 2.055
T = 63 + 2.055 (3.432) = 70.05 weeks
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
St. Adolf’s Hospital
Probabilities
Path = A - C - G – J Find probability for T = 65 days
TE = 12 + 10 + 35 + 4 = 61 days
2 =  (variances of activities)
2 = 0.11 + 2.78 + 7.11 + 5.44 = 15.44
z=
T – TE
2
From Appendix 2
65 – 61
z=
= 1.02
Pz = .8461
15.44
Example 8.7
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.