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Chapter 13: Quantitatve Chapter 13: Quantitatve Methods in Health Care Methods in Health Care ManagementManagement
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Chapter 13.Project Management
Chapter 13.Project Management
Time in WeeksTime in Weeks
ActivitiesActivities 44 88 1212 1616 2020 2424 2828 3232 3636 4040 4444 4848 5252 5656 6060 6464
AA
BB
CC
DD
EE
FF
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HH
Chapter 13: Quantitatve Chapter 13: Quantitatve Methods in Health Care Methods in Health Care ManagementManagement
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OutlineOutline 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)
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The Characteristics of ProjectsThe Characteristics of ProjectsThe Characteristics of ProjectsThe 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 ProjectsThe Characteristics of ProjectsThe Characteristics of ProjectsThe 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
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The Project Manager. . .The Project Manager. . .The Project Manager. . .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 projectWorking for two bossesDynamic environment, thriving factorWorking with new people, team spirit
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ActivityActivity TimeTime
A. Land acquisitionA. Land acquisition 4 weeks4 weeks
B. Hire a radiation oncologistB. Hire a radiation oncologist 16 weeks16 weeks
C. Select contractor and develop a construction planC. Select contractor and develop a construction plan 8 weeks8 weeks
D. Build the facilityD. Build the facility 24 weeks24 weeks
E. Acquire equipmentE. Acquire equipment 28 weeks28 weeks
F. Hire technical staffF. Hire technical staff 4 weeks4 weeks
G. Purchase and set up information systems and softwareG. Purchase and set up information systems and software 8 weeks8 weeks
H. Testing of equipmentH. Testing of equipment 4 weeks4 weeks
Time in WeeksTime in Weeks
ActivitiesActivities 44 88 1212 1616 2020 2424 2828 3232 3636 4040 4444 4848 5252 5656 6060 6464
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BB
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Exhibit 13.1 Gantt Chart for Launching a New Radiation Oncology Service
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PERT/CPMPERT/CPMPERT/CPMPERT/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 activitiesAn estimate of how long the project will takeAn indication of which activities are the most critical to timely project completionAn indication of how long any activity can be delayed without lengthening the project.
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Activity Precedence RelationshipsActivity Precedence RelationshipsActivity Precedence RelationshipsActivity Precedence RelationshipsActivity Predecessor
A
B
C A,B
D C
E C
F D,E
G D,E
H F,G
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ARROW
NODE
The Network (precedence) Diagram
The network diagram is a diagram of project activities that shows the sequential relationships by use of arrows and nodes.
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Activity A
Activity B
Activity C
Activit
y A
Activity B
Dummy Activity
Activity C
Activity on Arc Activity on Node
A
B
C
Figure 13.1 Network Representations
a)
b) c)
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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 timeEvents. 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.
The Network Diagram, cont.A glossary of terms
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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.
The Network Diagram, cont.A glossary of terms
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ES LS
EF LF
Activity Name
Figure 13.3 Activity Start and Finish Times
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Figure 13.2 AON Network Diagram for Radiation Oncology
Start
A
B
C
D
E
F
G
H End
Critical Path Method (CPM)
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Critical Path Method (CPM)
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
Path Lengths for the Radiation Oncology Project
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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.
Time Estimates
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Beta Distribution
6
4 pmote
36
)( 22 op
Mean
Variance
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.
tpath = Σte
Path
2activitiespath
Mean
Standard Deviation
path =
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The Normal Distribution:The Normal Distribution:
DeviationStdPath
TimeExpectedTimeSpecifiedz
.
Probabilistic Time Estimates, cont..
path
es ttz
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Example 13.1In 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
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Table 13.4 Calculation of Expected Time and Standard Deviations on Each Path for the Radiation Oncology Project
Paths Activities o m p tpath = Σte Σσ2 σpath
1 A 2 4 8 4.33 1.00
C 4 8 16
8.67 4.00
D 12 24 36
24.00 46.00 16.00 24.22 4.92
F 2 4 12
5.00 2.78
H 2 4 6
4.00 0.44
2 A 2 4 8 4.33 1.00
C 4 8 16
8.67 4.00
D 12 24 36
24.00 49.00 16.00 23.22 4.82
G 4 8 12
8.00 1.78
H 2 4 6
4.00 0.44
6
4 pmote
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path
es ttz
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
Table 13.5 Path Completion Probabilities
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te ts
50%
84%
64 69Weeks (1σ = 5)
Figure 13.6 Project Completion Probabilities by the Specified Time
z0 1 2 2.5
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Completion time in weeks
5) BCDFH
8) BCEGH
7) BCEFH
6) BCDGH
.33.1
path
es ttz
.80.0
path
es ttz
.79.0
path
es ttz
.20.0
path
es ttz
p=.9082
p=.7881
p=.7852
p=.5793
Figure 13.5 Completion Probabilities for 65 Weeks
57.7
60.7
61
64
58 60 61 64 65
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Path Completion ProbabilitiesThe 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%.
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Table 13.6 Path Completion Probabilities
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
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Crash only those activities that are on the critical pathto obtain reduction on project completion time.
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.
Project Compression: Trade-Offs Between Reduced Project Time and Cost
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Overhead and indirect costs
Total cost (TC)
Cumulative (direct) cost of compression
Cos
t
MinimumTC
Minimum compression or normal finish time
Optimal solution
Figure 13.10 Project Duration and Compression (Crashing) Costs
Compression of time (crashing)
Maximum compression time
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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.
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A B
C
D
E
F
G
H
Figure 13.11 Project Compression
I
Start
Finish
NormalNormal CompressedCompressedDirect compression Direct compression
costscosts
ActivityActivity timetime timetime per week (in 000)per week (in 000)
AA 2020 1919 1111
BB 7575 7474 88
CC 4242 4040 66
DD 4545 4444 1010
EE 2828 2626 77
FF 2121 1818 2020
GG 4040 4040 00
HH 2020 1919 1818
II 2020 1919 2020
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SolutionWe apply the algorithm shown earlier to this example in successive iterations to find the solution for the optimal earlier project completion time.
Iteration 1Step 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.
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Iteration 1Step 2: Rank critical activities according to their costs.
Criticalactivities
Compressioncost Rank
A 11 3
B 8 2
E 7 1
G n/a n/a
H 18 4
I 20 5
Solution
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.
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SolutionIteration 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.
Paths Path time
ABCFHI 198
ABDFHI 201*
ABEGHI 201*
Step 2: Rank critical activities according to their costs.
Criticalactivities
CompressionCost Rank
Criticalactivities
Compressioncost
Rank
A 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
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Iteration 2Now 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.
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SolutionIteration 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.
Step 2: Rank critical activities according to their costs.
Paths Path time
ABCFHI 198
ABDFHI 200*
ABEGHI 200*
CriticalActivitie
sCompression
cost RankCritical
ActivitiesCompression
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.
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Figure 13.12 Total Cost of Compression
1625
1622 1622
1623
1624
1621.5
1622
1622.5
1623
1623.5
1624
1624.5
1625
1625.5
198.5 199 199.5 200 200.5 201 201.5 202 202.5 203 203.5
Project duration
Co
st Total Cost
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Project management SoftwareCA Super ProjectHarvard Total ManagerMS ProjectSure Track Project ManagerTime Line
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Advantages of PM SoftwareAdvantages of PM SoftwareImposes 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
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Clinical Health Applications (Clinical Paths)Clinical Health Applications (Clinical Paths)
Administrative ApplicationsAdministrative Applications
Applications
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The End