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PROJECT MANAGEMENT:Computing Algorithm, Project Crashing, Risk Management

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Production and Operations Management ­MGT613
VU
Lesson 44
PROJECT MANAGEMENT
Learning Objectives
After learning about the network diagrams, the project life cycle and the responsibilities of project
manager. We will now learn the important concept of time estimates (which is based on computing
algorithms of Early Start, Early Finish, Late Start and Late Finish) and variances which are used to
control the project activities. We will consider important aspects like the forward and backward
path time estimates, Project Crashing, Time Cost Trade Offs, Project Management Software, Risk
Management and develop a project management based Operations Strategy.
Time Estimates
There are two common types of time estimates namely
1. Deterministic: Time estimates that are fairly certain
2. Probabilistic: Estimates of times that allow for variation
Example: Hospital
We take the same hospital example and now place the time dimension to it .
6 weeks
4
Order
Machine
Machines
Setup 3 weeks
2
8 weeks
Locate
Remodel
facilities
Operational
11 weeks
1
5
6
1 week
Interview
Hire and train
4 weeks
Medical Staff
9 weeks
3
The activities from locating the facility to making the hospital fully are represented in the form of a
network diagram. The student should try to write down the activities along with the activity
description then try to draw the network diagram using both the activity on node and activity on
arrow as practice.
Computing Algorithm
Network activities
1. ES: early start
2. EF: early finish
3. LS: late start
4. LF: late finish
Used to determine
1. Expected project duration
2. Slack time
3. Critical path
Probabilistic Time Estimates
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1. Optimistic time : Time required under optimal conditions
2. Pessimistic time: Time required under worst conditions
3. Most likely time: Most probable length of time that will be required
Probabilistic Estimates require two important parameters like Expected Time and
Variance represented by te and σ respectively.
t
t
t
to
Activity
Optimistic
Most Likely
Pessimistic
Time
Start
Time
Time
to + 4tm +tp
te
=
6
where
te = expected time
to = optimistic time
tm = most likely time
tp = pessimistic time
Variance
The word variance reflects the square of standard deviation of activities on a path and represented
by σ2. The size of variance reflects the degree of uncertainty associated with activity's time, the
larger the variance the larger the uncertainty.
(tp ­ to)2
2
σ
=
36
σ2 = variance
to = optimistic time
tp = pessimistic
time
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Example
Optimistic
Most likely
Pessimistic
Time
Time
Time
2-4-6
b
2-3-5
1-3-4
c
a
3-4-5
3-5-7
5-7-9
d
e
f
2-3-6
3-4-6
g
i
4-6-8
h
Path Probabilities
Specified time ­ Path
Z
mean
Z indicates how many standard deviations of the path distribution the specified tine
is beyond the expected path duration. If the value of "z" is +2.50 or more, treat the probability of
path completion by the specified time as 100 percent.
Time-cost Trade-offs: Crashing
Crash is the shortening activity duration
Procedure for crashing
Crash the project one period at a time
Only an activity on the critical path
Crash the least expensive activity
Multiple critical paths: find the sum of crashing the least expensive activity on each critical path
Project Crashing
Crashing a project involves paying more money to complete a project more quickly.
Since the critical path determines the length of a project, it makes sense to reduce the length of
activities on the critical path.
Critical Path activities should be reduced until the project is reduced to the desired length or you are
paying more per day than you save.
If you have multiple Critical Paths, they should be shortened simultaneously.
Time-Cost Trade-Offs: Crashing
Time-Cost Trade-Offs: Crashing
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Total
Cost
Expected Indirect
Shorte
CRAS
Cumulative
Cost of
Crashing
Shorte
Optimum
Example
The manager of a PHA is about to undertake a reforestation project throughout Pakistan. He is first
asked to carryout a pilot project. The project will involve the following six activities:
SR. ACTIVITY PRECEEDS
TIME ESITIMATES ( DAYS)
#
OPTIMISTIC MOST LIKELY" PESSIMISTIC
" a"
m"
" b"
START
U,V
U
W
35
50
65
V
W,X
28
40
52
W
Z
26
35
44
X
Y
28
40
52
Y
Z
26
29
38
Z
END
36
60
84
Solution: First of all, we construct network diagram based on Activity on Node followed by
calculating the probabilistic time "t" and standard deviation "σ" using the formulas given below and
then the ES,EF and LS, LF using the forward pass (progression) and backward pass (progression)
respectively.
t = (a+4m+b)/6
and
σ = (b-a)/6
The denominator of "6" reflects the concept of area under the curve that the range of data lies to + 3
Standard Deviations from mean also it shows the weighted average.
End
35
50
Start
U
W
Z
40
40
Y
40
X
V
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ACTIVITY TIME ESITIMATES
FORWARD BACKWARD
SLACK
( DAYS)
" a" " m"
" b"
t
σ
ES
EF
LS
LF
n
START
U
35
50
65
50
5
0  50
25
75
25
V
28
40
52
40
4
0  40
0
40
0
W
26
35
44
35
3
50 85
75
110
25
X
28
40
52
40
4
40 80
40
80
0
Y
26
29
38
30
2
80 110
80
110
0
Z
36
60
84
60
8
110 170
110
170
0
I.
Time "t" = (a+4m+b)/6
Activity U =
(35+4(50) +65)/6= (100+200)/6= 300/6= 50 days
Activity V  =
(28+4(40) +52)/6= (80+160)/6= 240/6= 40 days
Activity W =
(26+4(35) +44)/6= (70+140)/6= 210/6= 35 days
Activity X  =
(28+4(40) +52)/6= (80+160)/6= 240/6= 40 days
Activity Y  =
(26+4(29) +38)/6= (64+116)/6= 180/6= 30 days
Activity Z  =
(36+4(60) +84)/6= (120+240)/6= 360/6= 60 days
Standard Deviation "σ" = (b-a)/6
Activity U
=
(65-35)/6= (30)/6= 5 days
Activity V
=
(52-28)/6= (24)/6= 4 days
Activity W
=
(44-26)/6= (18)/6= 3 days
Activity X
=
(52-28)/6= (24)/6= 4 days
Activity Y
=
(38-26)/6= (12)/6= 2 days
Activity Z
=
(84-36)/6= (48)/6= 8 days
Critical Path
The critical path is the longest path taken for the project to complete.
From Start to End there are three possible paths as from the Network Diagram
Start ­U-W-Z-End = 50 + 35+60
= 145 days (logically incorrect)
Start-V-X-Y-Z-End= 40+40+30+60 = 170 days
Start-V-W-Z-End= 40+35+60
= 135 days (logically incorrect)
For the Critical Path, we also calculate the standard deviation of Project portfolio
Start-V-X-Y-Z-End=σ2= [(4)2+(4)2+(2)2+(8)2]= (16+16+4+64)= (100 )
Then σ = Square Root ( 100) = 10 days
Also individual sum of standard deviations = 4+4+2+8 = 18 days
Since portfolio project σ = 10 days is less than individual sum of 18 days, it shows our value of
portfolio σ is correct
Normal Distribution
"z" = (X-μ)/σ , now since X= 200 days  μ = 170 days,
σ= 10 days
μ = 170 days,
σ= 10 days
X= 200 days
Also Using the Normal Probability Curve
Z= (X ­ μ)/σ
= (200-170)/10= 30/10= 3.0
According to the standard normal table, the area at z = 3 is 0.4987. Adding 0.5 for left hand side of
the standard normal curve, we get 0.9987.
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Q.3: What is the estimated expected (mean) time for Project Completion?
135 days
145 days
170 days
180 days
255 days
The answer is 170 Days (Choice C)
Q.4: What is the estimated slack time for activity W?
0 days
25 days
35 days
45 days
85 days
The answer is 25 Days (Choice B)
Q.5: What is the probability that the critical path for this project will be completed with in 200
days?
0.8413
0.9544
0.9772
0.9974
0.9987
Based on the calculations of critical path "σ" above, the answer comes out to be 0.9987 (Choice E).
4
7
8
10
11
2
9
Given the portion of the network shown above, what is the earliest finish time for activity 10-11, if
the earliest start time of 8-10 is "12" and the earliest start time of 9-10 is "13"?
22
23
24
25
26
Q.1: What is the estimated expected (mean) time for activity Y?
30 days
29 days
38 days
26 days
35 days
The answer is 30 Days (Choice A)
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ACTIVITY
FORWARD
BACKWARD
SLACK
t
ES
EF
LS
LF
n
START
8 to 10
4
12
16
12
16
0
9 to 10
2
13
15
14
16
1
10 to 11
7
16
16
23
0
23
Q.2: What is the estimated standard deviation in the time for activity Z?
3 days
2 days
4 days
8 days
5 days
The answer is 8 Days (Choice D)
10
6
b
a
2
f
5
9
4
d
SOLVED EXAMPLES
You have been hired as the Chief Project Manager, by your city's Kabbadi Association for construction,
renovation and repairs of the city Kabbadi Stadium. The Kabbadi Associations President had in the past
hired an Indian Consultant to help him carry out the task of expanding and improving the hockey
stadium. The Indian Consultant left the work after collecting the time (in days) associated with the
activities and developing the forward path network diagrams.
TIME ESTIMATES
ACTIVITY OPTIMISTIC MOST LIKELY PESSIMISTIC IMMEDIATE PREDECESSOR
A
1
4
7
-
B
2
6
7
-
C
3
3
6
B
D
6
13
14
A
E
3
6
12
A,C
F
6
8
16
B
G
1
5
6
E,F
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D
E
Finish
A
Start
C
B
G
F
The Association President has asked you to calculate the following:
a. Calculate the expected time and variance for each activity.
b. Calculate the activity slacks and determine critical path using expected activity times?
c. What is the probability of completing the project with in 550 days?
Solution
We first of all calculate the Expected times and variances for each activity using the formulae
respectively
te= (a+4m+b)/6
σ2= ((b-a)/6)2
The results are presented in the form of the table
ACTIVITY EXPECTED TIME
VARIANCE
4.00
1.00
A
5.50
0.69
B
3.50
0.25
C
12.00
1.78
D
6.50
2.25
E
9.00
2.78
F
4.50
0.69
G
f.
We need to calculate the Earliest Start, Latest Start, Earliest Finish, Latest Finish represented by
the symbols ES, LS, EF and LF respectively. We use the forward path network diagram as
provided by the hockey association's president.
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ACTIVITY
ES
EF
t
0.00
4.00
4.00
A
0.00
5.50
5.50
B
5.50
9.00
3.50
C
4.00
16.00
12.00
D
9.00
15.50
6.50
E
5.50
14.50
9.00
F
15.50
20.00
4.50
G
As we can see from the table above the earliest time by which Activity G would finish is 20 days and
requires 4.5 days of time to complete. We need to know calculate values of Latest Start and Latest
Finish using the backward path. Please refer to the backward path diagram below, the direction of
arrows have been reversed indicating that we are actually back tracing the activities with the same times
as calculated above using forward path.
BACKWARD PATH
D
E
Finish
A
Start
C
B
G
F
ACTIVITY
LS
LF
t
G
15.50
20.00
4.50
F
6.50
15.50
9.00
E
9.00
15.50
6.50
D
8.00
20.00
12.00
C
5.50
9.00
3.50
B
0.00
5.50
5.50
A
4.00
8.00
4.00
Start
Finish
ACTIVITY
ES
LS
EF
LF
SLACK
CRITICAL PATH
0.00
4.00
4.00
8.00
4.00
NO
A
0.00
0.00
5.50
5.50
0.00
YES
B
5.50
5.50
9.00
9.00
0.00
YES
C
4.00
8.00
16.00
20.00
4.00
NO
D
9.00
9.00
15.50
15.50
0.00
YES
E
5.50
13.00
14.50
15.50
1.00
NO
F
15.50
15.50
20.00
20.00
0.00
YES
G
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PATH
EXPECTED TIME
VARIANCE
A-D
16.00
2.78
A-E-G
15.00
3.94
B-C-E-G
20.00
3.89
B-F-G
19.00
4.17
The critical path is B-C-E-G with total expected time of 20 days.
c.
We first calculate the z value
(t-te)/√σ2
Z
=
=
(23-20)/3.89
=
3/1.972
=
1.5210
Using the Normal Distribution table, we calculate the probability of completing the project in 23 days to
be 0.9357.
Project Management Software Tools
1. Computer aided design (CAD)
2. Groupware (Lotus Notes)
3. Project management software
a. CA Super Project
b. Harvard Total Manager
c. MS Project
d. Sure Track Project Manager
e. Time Line
Advantages of PM Software
1. Imposes a methodology
2. Provides logical planning structure
3. Enhances team communication
4. Flag constraint violations
5. Automatic report formats
6. Multiple levels of reports
7. Enables what-if scenarios
8. Generates various chart types
Project Risk Management
Risk: occurrence of events that have undesirable consequences
1. Delays
2. Increased costs
3. Inability to meet specifications
4. Project termination
Risk Management
1. Identify potential risks
2. Analyze and assess risks
3. Work to minimize occurrence of risk
4. Establish contingency plans
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Operations Strategy
1. Many Organizations have setup a separate Project Management department or cell to administer
unique and non repetitive activities.
2. The scope of the project decides whether to use a project management software tool or not.
3. Project teams normally operate as a matrix team with employees from different functional
departments working with the project team. In such situations the organizations device a
strategy that project manger should lead the team as he or she is more aware of the situation
being faced by the whole organization as well as the constituent functional departments.
Summary
1.
Projects are unique set of activities established to given set of objectives in a limited time span.
2.
PERT and CPM two commonly used techniques for developing and monitoring projects.
3.
Two slightly different conventions can be used for constructing a network diagram.
4.
The task of developing and updating project networks quickly becomes projects of even
moderate size or PC applications.
5. A deterministic approach is useful for estimating the duration of the project, when activity times
can be fairly well established.
6. In some instances, it may be possible to shorten or crash the length of a project by shortening
one or more of the project activities.
7. Often Projects are shortened to the point where the cost of additional reduction would exceed
the benefit of additional reduction to a specified time.
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Table of Contents:
  1. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT
  2. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Decision Making
  3. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Strategy
  4. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Service Delivery System
  5. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Productivity
  6. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:The Decision Process
  7. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Demand Management
  8. Roadmap to the Lecture:Fundamental Types of Forecasts, Finer Classification of Forecasts
  9. Time Series Forecasts:Techniques for Averaging, Simple Moving Average Solution
  10. The formula for the moving average is:Exponential Smoothing Model, Common Nonlinear Trends
  11. The formula for the moving average is:Major factors in design strategy
  12. The formula for the moving average is:Standardization, Mass Customization
  13. The formula for the moving average is:DESIGN STRATEGIES
  14. The formula for the moving average is:Measuring Reliability, AVAILABILITY
  15. The formula for the moving average is:Learning Objectives, Capacity Planning
  16. The formula for the moving average is:Efficiency and Utilization, Evaluating Alternatives
  17. The formula for the moving average is:Evaluating Alternatives, Financial Analysis
  18. PROCESS SELECTION:Types of Operation, Intermittent Processing
  19. PROCESS SELECTION:Basic Layout Types, Advantages of Product Layout
  20. PROCESS SELECTION:Cellular Layouts, Facilities Layouts, Importance of Layout Decisions
  21. DESIGN OF WORK SYSTEMS:Job Design, Specialization, Methods Analysis
  22. LOCATION PLANNING AND ANALYSIS:MANAGING GLOBAL OPERATIONS, Regional Factors
  23. MANAGEMENT OF QUALITY:Dimensions of Quality, Examples of Service Quality
  24. SERVICE QUALITY:Moments of Truth, Perceived Service Quality, Service Gap Analysis
  25. TOTAL QUALITY MANAGEMENT:Determinants of Quality, Responsibility for Quality
  26. TQM QUALITY:Six Sigma Team, PROCESS IMPROVEMENT
  27. QUALITY CONTROL & QUALITY ASSURANCE:INSPECTION, Control Chart
  28. ACCEPTANCE SAMPLING:CHOOSING A PLAN, CONSUMER’S AND PRODUCER’S RISK
  29. AGGREGATE PLANNING:Demand and Capacity Options
  30. AGGREGATE PLANNING:Aggregate Planning Relationships, Master Scheduling
  31. INVENTORY MANAGEMENT:Objective of Inventory Control, Inventory Counting Systems
  32. INVENTORY MANAGEMENT:ABC Classification System, Cycle Counting
  33. INVENTORY MANAGEMENT:Economic Production Quantity Assumptions
  34. INVENTORY MANAGEMENT:Independent and Dependent Demand
  35. INVENTORY MANAGEMENT:Capacity Planning, Manufacturing Resource Planning
  36. JUST IN TIME PRODUCTION SYSTEMS:Organizational and Operational Strategies
  37. JUST IN TIME PRODUCTION SYSTEMS:Operational Benefits, Kanban Formula
  38. JUST IN TIME PRODUCTION SYSTEMS:Secondary Goals, Tiered Supplier Network
  39. SUPPLY CHAIN MANAGEMENT:Logistics, Distribution Requirements Planning
  40. SUPPLY CHAIN MANAGEMENT:Supply Chain Benefits and Drawbacks
  41. SCHEDULING:High-Volume Systems, Load Chart, Hungarian Method
  42. SEQUENCING:Assumptions to Priority Rules, Scheduling Service Operations
  43. PROJECT MANAGEMENT:Project Life Cycle, Work Breakdown Structure
  44. PROJECT MANAGEMENT:Computing Algorithm, Project Crashing, Risk Management
  45. Waiting Lines:Queuing Analysis, System Characteristics, Priority Model