Chapter 13.
Project Management
Time in Weeks
Activities
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
A
B
C
D
E
F
G
H
Chapter 13: Quantitatve
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Yasar A. Ozcan
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Outline










The Characteristics of Projects
The Project Manager
Managing Teams and Relationships on
Projects
Planning and Scheduling with Gantt Charts
The Gantt Chart
Pert & CPM
The Network
Deterministic Approach- Critical Path Method
Probabilistic Approach
Project Compression (Crashing or time
reduction in project length)
Chapter 13: Quantitatve
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2
The Characteristics of Projects
Projects are unique and non-routine endeavors,
designed to accomplish a specified set of objectives
(to create new products and services) in a limited
time.
Typical examples of such non-routine projects are
moving a hospital to a new location by a certain date,
or renovating an outpatient facility to meet changing
demand patterns.
Projects like those have considerable costs. They
involve a large number of activities that must be
carefully planned and coordinated to achieve the
desired results, and may take a long time to
complete.
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The Characteristics of Projects
Life-cycle concept -- projects go through a series
of stages including, formulation and analysis,
planning, implementation, and termination.
Projects bring together personnel with diverse
knowledge and skills, as their contributions are
necessitated by the projects
Chapter 13: Quantitatve
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The Project Manager. . .
. . . Bears the ultimate responsibility for
completion of the project.
The pros and cons of working on projects
include:
The effect of expert full-time employees
assigned to a project
Working for two bosses
Dynamic environment, thriving factor
Working with new people, team spirit
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Exhibit 13.1 Gantt Chart for Launching a New Radiation Oncology Service
Activity
Time
A. Land acquisition
4 weeks
B. Hire a radiation oncologist
16 weeks
C. Select contractor and develop a construction plan
8 weeks
D. Build the facility
24 weeks
E. Acquire equipment
28 weeks
F. Hire technical staff
4 weeks
G. Purchase and set up information systems and software
8 weeks
H. Testing of equipment
4 weeks
Time in Weeks
Activities
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
A
B
C
D
E
F
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H
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PERT/CPM
Program Evaluation and Review Technique (PERT)
and the Critical Path Method (CPM) are tools for
planning and coordinating large projects
Using PERT/CPM managers can obtain:
A graphical display of project activities
An estimate of how long the project will take
An indication of which activities are the most
critical to timely project completion
An indication of how long any activity can be
delayed without lengthening the project.
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Activity Precedence Relationships
Activity
Predecessor
A
B
C
A,B
D
C
E
C
F
D,E
G
D,E
H
F,G
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The Network (precedence) Diagram
The network diagram is a diagram of project
activities that shows the sequential relationships
by use of arrows and nodes.
NODE
ARROW
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9
Figure 13.1 Network Representations
Activity A
a)
Activity C
Activity B
Activity on Arc
Activity on Node
A
c)
b)
Activity B
C
Activity C
B
Chapter 13: Quantitatve
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The Network Diagram, cont.
A glossary of terms
Activity-on-Arrow (A-O-A). Network convention in
which arrows designate activities.
Activity-on-Node (A-O-N). Network convention in
which nodes designate activities.
Activities. Project steps that consume resources
and/or time
Events. The starting and finishing of activities,
designated by nodes in the A-O-A convention.
Path. A sequence of activities that leads from the
starting node to the finishing node.
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The Network Diagram, cont.
A glossary of terms
Critical Path. The longest path equaling the
expected project duration.
Critical Activities. All the activities on the critical
path.
Slack. Allowable slippage (time) for a path; the
difference between the length of a path and the
length of the critical path.
ES, EF, LS, LF. E (earliest); L (latest); S (start); F
(finish) times of each activity.
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12
Figure 13.3 Activity Start and Finish Times
ES
LS
Activity Name
LF
EF
Chapter 13: Quantitatve
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13
Critical Path Method (CPM)
Figure 13.2 AON Network Diagram for Radiation Oncology
A
Start
D
F
C
B
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E
End
G
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Critical Path Method (CPM)
Path Lengths for the Radiation Oncology Project
Paths and activities
Path time length
1) A-C-D-F-H
4 + 8 + 24 + 4 + 4 = 44 weeks
2) A-C-D-G-H
4 + 8 + 24 + 8 + 4 = 48 weeks
3) A-C-E-F-H
4 + 8 + 28 + 4 + 4 = 48 weeks
4) A-C-E-G-H
4 + 8 + 28 + 8 + 4 = 52 weeks
5) B-C-D-F-H
16 + 8 + 24 + 4 + 4 = 56 weeks
6) B-C-D-G-H
16 + 8 + 24 + 8 + 4 = 60 weeks
7) B-C-E-F-H
16 + 8 + 28 + 4 + 4 = 60 weeks
8) B-C-E-G-H
16 + 8 + 28 + 8 + 4 = 64 weeks
Chapter 13: Quantitatve
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Time Estimates
Deterministic Time Estimates-- estimates for each
activity are fairly certain.
Probabilistic Time Estimates-- estimates for each
activity are subject to variation.
Optimistic Estimate-- Length of time required
under optimum conditions (o).
Pessimistic Estimate-- length of time required
under worst conditions (p).
Most likely time estimate-- the most probable
length of time required (m).
Beta Distribution-- A distribution which describes
the inherent variability in the time estimates.
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Beta Distribution
Mean
o  4m  p
te 
6
Variance
Path
2
(
p

o
)
2 
36
Standard Deviation
Mean
tpath = Σte
path =
2

 path activities
Assumption: path duration times are independent of each
other; requiring that activity times be independent, and that
each activity is on only one path.
Invoke Central Limit Theorem to use normal distribution.
Chapter 13: Quantitatve
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Probabilistic Time Estimates, cont.
The Normal Distribution:
Specified Time  Expected Time
z
Path Std. Deviation
z
Chapter 13: Quantitatve
Methods in Health Care
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t s  te
 path
Yasar A. Ozcan
18
Example 13.1
In planning for a new radiation oncology clinic, project
managers determined that due to the nature of some of the
activities, time estimates vary. After consulting with experts in
each of the activity areas, they have calculated the optimistic,
pessimistic and most likely time estimates, in weeks, as shown
in Table below:
Activity
Optimistic
(o)
Most Likely
(m)
Pessimistic
(p)
A
2
4
8
B
8
16
24
C
4
8
16
D
12
24
36
E
16
28
36
F
2
4
12
G
4
8
12
H
2
4
6
Chapter 13: Quantitatve
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Management
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19
Table 13.4 Calculation of Expected Time and Standard Deviations
on Each Path for the Radiation Oncology Project
Paths
Activities
o
m
p
1
A
2
4
8
C
4
8
16
D
F
H
2
12
2
2
24
4
4
36
4
8
C
4
8
16
G
H
4
2
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8
4
tpath = Σte
4.33
1.00
8.67
4.00
24.00
46.00
16.00
σpat
h
24.22
4.92
5.00
2.78
4.00
0.44
4.33
1.00
8.67
4.00
23.22
4.82
6
2
12
Σσ2
12
A
D
o  4m  p
te 
6
36
24.00
49.00
16.00
12
8.00
1.78
4.00
0.44
6
Yasar A. Ozcan
20
Table 13.5 Path Completion Probabilities
t s  te
Path
tpath
σpath
1) ACDFH
46.00
4.92
3.86
2) ACDGH
49.00
4.82
3.32
3) ACEFH
49.33
4.40
3.56
4) ACEGH
52.33
4.28
2.96
5) BCDFH
57.67
5.51
1.33
6) BCDGH
60.67
5.42
0.80
7) BCEFH
61.00
5.04
0.79
8) BCEGH
64.00
4.94
0.20
Chapter 13: Quantitatve
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Yasar A. Ozcan
z
 path
21
Figure 13.6 Project Completion Probabilities by the Specified Time
84%
50%
Weeks
te
ts
64
(1σ = 5) 69
z
Chapter 13: Quantitatve
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0
Yasar A. Ozcan
1
2
2.5
22
Figure 13.5 Completion Probabilities for 65 Weeks
z
5) BCDFH
p=.9082
t s  te
 path
 1.33.
57.7
6) BCDGH
z
t s  te
 0.80.
z
t s  te
 0.79.
z
t s  te
 0.20.
 path
p=.7881
60.7
7) BCEFH
 path
p=.7852
61
8) BCEGH
 path
p=.5793
64
Chapter 13: Quantitatve
Methods in Health Care
Management
Completion time in weeks
58
60 61 Yasar
64A.65Ozcan
23
Path Completion Probabilities
The last step in the analysis is the computation of joint
probability, that is, we are interested in the joint effect
of all the paths on the completion of the project. This is
a simple multiplication of the completion probabilities of
the significant paths (paths 5 through 8).
The probability of completion of this project within 65
weeks is:
P (completion by 65th week) = .9082 * .7881 * .7852 * .5793
= .3255 or 32.5%.
Similarly, one can compute the probability of completion for other
target days such as 66, 67 and 70 weeks.
P (completion by 66th week) = .9345 * .8365 * .8389 * .6700
= .4394 or 43.9%.
P (completion by 67th week) = .9545 * .8770 * .8830 * .7486
=.5533 or 55.3%.
P (completion by 70th week) = .9871 * .9573 * .9625 * .8869
=.8066 or 80.7%.
Chapter 13: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
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Table 13.6 Path Completion Probabilities
Chapter 13: Quantitatve
Methods in Health Care
Management
Desired
completion
time in weeks
Critical Path
Probability
64
B-C-E-G-H
0.5000
65
B-C-E-G-H
0.5801
66
B-C-E-G-H
0.6571
67
B-C-E-G-H
0.7280
68
B-C-E-G-H
0.7908
69
B-C-E-G-H
0.8441
70
B-C-E-G-H
0.8876
71
B-C-E-G-H
0.9216
72
B-C-E-G-H
0.9472
73
B-C-E-G-H
0.9656
74
B-C-E-G-H
0.9784
75
B-C-E-G-H
0.9869
76
B-C-E-G-H
0.9924
Yasar A. Ozcan
25
Project Compression: Trade-Offs Between
Reduced Project Time and Cost
In order to crash, need information on:
Regular time and crash time estimates for
each activity.
Regular costs and crash cost estimates for
each activity.
A list of activities that are on the critical path.
Crash only those activities that are on the critical path
to obtain reduction on project completion time.
Chapter 13: Quantitatve
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Figure 13.10 Project Duration and Compression (Crashing) Costs
Total cost (TC)
Cost
Minimum
TC
Overhead and indirect costs
Cumulative (direct) cost of compression
Compression of time (crashing)
Maximum compression time
Chapter 13: Quantitatve
Methods in Health Care
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Optimal solution
Yasar A. Ozcan
Minimum compression or
normal finish time
27
Example 13.2:
The indirect costs for design and implementation of a
new health information system project are $8,000 per
week.
The project activities (A through I), their normal
durations and compressed durations, and also the direct
compression, or crashing, costs are shown in Figure 13.7.
Find optimal earlier project completion time.
Chapter 13: Quantitatve
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Yasar A. Ozcan
28
Figure 13.11 Project Compression
C
D
Star
t
A
F
B
I
E
Chapter 13: Quantitatve
Methods in Health Care
Management
Finis
h
H
G
Normal
Compressed
Direct compression
costs
Activity
time
time
per week (in 000)
A
20
19
11
B
75
74
8
C
42
40
6
D
45
44
10
E
28
26
7
F
21
18
20
G
40
40
0
H
20
19
18
I
20
19
20
Yasar A. Ozcan
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Solution
We apply the algorithm shown earlier to this example in successive iterations
to find the solution for the optimal earlier project completion time.
Iteration 1
Step 1: There are three paths. Adding the times of the activities, we obtain
the path times. Since ABEGHI is the longest time path, with 203 days, it is
the critical path.
Paths
Path time
ABCFHI
198
ABDFHI
201
ABEGHI
203*
Since activity G is not available for compression, it is not shown in
the rankings. Among the remaining activities on the critical path,
activity E has the lowest compression cost, and thus it is selected
for time reduction.
Chapter 13: Quantitatve
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30
Solution
Iteration 1
Step 2: Rank critical activities according to their costs.
Critical
activities
Compression
cost
A
11
3
B
8
2
E
7
1
G
n/a
n/a
H
18
4
I
20
5
Rank
Step 3: Since we can reduce this activity by two days, the new completion time
considered for the project becomes (203-2 = 201) 201 days.
Step 4: The cost of compression for two days for activity E is 2 * $7,000 = $14,000.
The indirect project cost for 201 days @ $8,000 per day amounts to $1,608,000
(201*8,000 = $1,608,000).
The total cost for 201 days then is equivalent to $1,622,000 (14,000 + 1,608,000).
Step 5: Without compressing the project, we would incur only the indirect costs,
which would be for 203 days without the time reduction.
The total cost for 203 days then would be $1,624,000 (203 * $8,000). Comparing
that to the total cost for 201 days (see step 4): $1,624,000 to $1,622,000, we observe
a decrease. Thus we can continue compressing the project.
Chapter 13: Quantitatve
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31
Solution
Iteration 2
Step 1: After compression of two days in iteration 1, among the
three paths we now have two paths with equivalent path times.
Both ABDFHI and ABEGHI are the longest paths, with 201 days;
thus both are critical paths.
Step 2: Rank critical activities
according to their costs.
Critical
activities
Compression
Cost
A
Paths
Path time
ABCFHI
198
ABDFHI
201*
ABEGHI
201*
Compression
cost
Rank
Rank
Critical
activities
11
2
A
11
3
B
8
1
B
8
1
E
7
n/a
D
10
2
G
n/a
n/a
F
20
5
H
18
3
H
18
4
I
20
4
I
20
5
Chapter 13: Quantitatve
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32
Iteration 2
Now we are considering critical activities from both paths simultaneously.
In the ABEGHI path, we have exhausted compression time for activity E;
hence it is no longer available for compression and is not shown in the
rankings. Among the remaining activities on both critical paths, the activity
B has the lowest compression cost, so it is selected for time reduction.
Step 3: Since we can reduce activity B by only one day, the new completion
time to consider for the project becomes 200 (201-1) days.
Step 4: The cost of compression for activity B for one day is 1 * $8,000 =
$8,000. The indirect cost for the project for 200 days @ $8,000 per day
amounts to $1,600,000 (200*8,000 = $1,600,000).
The total cost for 200 days, then, is equivalent to $1,622,000 (14,000 +
8,000+ 1,600,000). Please note that the direct compression costs should be
added in cumulatively; that is, for all 3 days of compression the project
incurred $22,000 (14,000 + 8,000).
Step 5: From iteration 1, the total cost for 201 days was $1,622,000.
Comparing that to the total cost for 200 days (see step 4): $1,622,000 to
$1,622,000, we observe no change. Thus we can still continue compressing
the project.
Chapter 13: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
33
Solution
Iteration 3
Step 1: After compression by one day in iteration 2, of the three
paths we still have two paths, ABDFHI and ABEGHI, with 200 days
each; both are critical paths. Step 1: After compression by one day
in iteration 2, of the three paths we still have two paths, ABDFHI
and ABEGHI, with 200 days each; both are critical paths.
Paths
Path time
ABCFHI
198
ABDFHI
200*
ABEGHI
200*
Step 2: Rank critical activities according to their costs.
Critical
Activitie
s
Compression
cost
Rank
Critical
Activities
Compression
cost
Rank
A
11
1
A
11
2
B
8
n/a
B
8
n/a
E
7
n/a
D
10
1
G
n/a
n/a
F
20
4
H
18
2
H
18
3
I
20
3
I
20
4
Step 5: cost is $1,625,000; hence stop compression.
Chapter 13: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
34
Figure 13.12 Total Cost of Compression
1625.5
1625
1625
1624.5
Cost
1624
1624
1623.5
Total Cost
1623
1623
1622.5
1622
1621.5
198.5
1622
199
199.5
200
1622
200.5
201
201.5
202
202.5
203
203.5
Project duration
Chapter 13: Quantitatve
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Management
Yasar A. Ozcan
35
Project management Software
CA Super Project
Harvard Total Manager
MS Project
Sure Track Project Manager
Time Line
Chapter 13: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
36
Advantages of PM Software
Imposes a methodology
Provides logical planning structure
Enhances team communication
Flag constraint violations
Automatic report formats
Multiple levels of reports
Enables what-if scenarios
Generates various chart types
Chapter 13: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
37
Applications
Clinical Health Applications (Clinical Paths)
Administrative Applications
Chapter 13: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
38
The End
Chapter 13: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
39