Chapter 13. Project Management

Chapter 13: Quantitatve Chapter 13: Quantitatve Methods in Health Care Methods in Health Care ManagementManagement

Yasar A. OzcanYasar A. Ozcan 11

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

GG

HH



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)



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.



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



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



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

AA

BB

CC

DD

EE

FF

GG

HH

Exhibit 13.1 Gantt Chart for Launching a New Radiation Oncology Service



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.



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



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.



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)



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



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



ES LS

EF LF

Activity Name

Figure 13.3 Activity Start and Finish Times



Figure 13.2 AON Network Diagram for Radiation Oncology

Start

A

B

C

D

E

F

G

H End

Critical Path Method (CPM)



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



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



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 =



The Normal Distribution:The Normal Distribution:

DeviationStdPath

TimeExpectedTimeSpecifiedz

.

Probabilistic Time Estimates, cont..

path

es ttz



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



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



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



te ts

50%

84%

64 69Weeks (1σ = 5)

Figure 13.6 Project Completion Probabilities by the Specified Time

z0 1 2 2.5



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



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%.



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



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



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



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.



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



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.



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.



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



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.



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.



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



Project management SoftwareCA Super ProjectHarvard Total ManagerMS ProjectSure Track Project ManagerTime Line



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



Clinical Health Applications (Clinical Paths)Clinical Health Applications (Clinical Paths)

Administrative ApplicationsAdministrative Applications

Applications



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Chapter 13. Project Management