D. Anthony Chevers
SBCO 6240 – Production and Operations Management
Lecture 9 – Project Management |
Lecture #8 – Project Management
Definition Project Schedule
• PERT
• Exercises
Discussion Questions
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Lecture 9 – Project Management |
Project ManagementDr. Tom Johns
A project is an enterprise undertaken to achieve planned results within a time frame and at some cost of resource
Project management is the business of creating appropriate behaviors within the organization to fulfill the objectives of the enterprise in the face of all the risks and problems encountered on the way.
Success depends largely on carrying out the constituent tasks in a sensible sequence and deploying resources to best advantage, and project managers are appropriately empowered by the organization to orchestrate the project.
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Lecture 9 – Project Management |
Project Schedule
The process of scheduling forces determination, first, of the order in which events must occur, and second, of the time it will take to do them all
Schedules are also a fundamental basis for control
Scheduling a process of communication
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Lecture 9 – Project Management |
The Framework of PERT
Program Evaluation Review Technique (PERT) is a management tool used to manage and control large and complex projects.
• Define the project and prepare the WBS• Develop the relationships among the activities. Decide which
activities must precede and which must follow others• Draw the network connecting all the activities• Assign time and/or cost estimates to each activity• Compute the longest time path through the network. This is
called the critical path• Use the network to help plan, schedule, monitor and control
the project
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Lecture 9 – Project Management |
Importance: PERT When will the entire project be completed? What are the critical activities in the project – i.e., the ones that
will delay the entire project if they are late? Which are the non-critical activities – the ones that can run late
without delaying the whole project’s completion? What are the probabilities that the project will be completed by a
specific date? At any particular date, is the project on schedule, behind schedule
or ahead of schedule? On a given date, is the money spent equal to, less than or greater
than the budgeted amount? Are there enough resources available to finish the project on
time? If the project is to be finished in a shorter amount of time, what is
the best way to accomplish this goal at the least cost?
Source: Operations Management, Jay Heizer & Barry Render
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Lecture 9 – Project Management |
PERT Notation - AOL
7
41
2
3
StartA
D
C
B
End
ActivityEvent
Activity Immediate Predecessor
A -
B -
C A
D B
Assign each event a number
Solution:
1. An event is an instant time, usually a starting or ending date.
2. An activity is a task or certain amount of work required in the project.
PERT – Example #1Given the following information, develop a PERT Network.
Lecture 9 – Project Management |
All that is required to construct a network is the starting and ending event for each activity.
PERT – Example #2
8
41
2
35
6
Given the following table, develop a network
Specify activities by their starting and ending event.
Beginning Event Ending Event Activity1 2 1 -› 2
1 3 1 -› 3
2 4 2 -› 4
3 4 3 -› 4
3 5 3 -› 5
4 6 4 -› 6
5 6 5 -› 6
Lecture 9 – Project Management |
PERT – Example #3
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Activity Immediate Predecessor (s)
A ---
B ---
C A
D B
E C, D
F E
G E
H F
I G
A
D
C
B
Develop a network based on the following information:
Complete a network below
Lecture 9 – Project Management |
PERT Equations
1.1. Elapsed time (t) Elapsed time (t) = a+4m + b
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Where a is optimistic time for activity completion, m is mort likely completion time and b is pessimistic time for activity completion.
2.2. EF=ES+tEF=ES+twhere EF is earliest finish & ES is earliest start
3.3. LF=LS+tLF=LS+t where LF is latest finish & LS is latest start
4.4. S=LS-ESS=LS-ES where S is slack
5.5. Variance (v) Variance (v) = b-a 2
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i.e. The probability of success that the project will be completed within the specified time.
PERT and CPM are two widely used network techniques that have the ability to consider precedence relationships and interdependency of activities. Their objectives are the same and the analysis used in both techniques are the same.
The major differences is that PERT employs three times estimates for each activity with levels of probabilities while CPM makes the assumption that activity times are known with certainty.
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Lecture 9 – Project Management |
PERT & Time Estimates For each activity in PERT techniques, we use three time estimates to
calculate an expected completion time & variance for each activity. Equations:
• t = (a + 4m + b)/6• V = [(b – a)/6]2
• Where a is optimistic time for activity completion• Where b is pessimistic time for activity completion• Where m is most likely time for activity completion• Where t is expected time for activity completion• Where v is variance of activity (the probability of success the project will be
completed within the specified time
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Example #5Example #5Activity a m b
1-2 3 4 51-3 1 3 52-4 5 6 73-4 6 7 8 [Solution below]
Activity (a+4m+b) t (b-a)/6 Var1-2 24 4 2/6 4/361-3 18 3 4/6 16/362-4 36 6 2/6 4/363-4 42 7 2/6 4/36
Lecture 9 – Project Management |
PERT NetworkBuilding a Church
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1 2 3 4 5 9 10 11 12
7 8
6
[Duration in Weeks]
EndStart
Buy material
Secure [3]men
Men arrive
erect install
Project to build a Church
Describe the Critical Path?Describe the Critical Path?Explain the importance of the Critical Path. DiscussExplain the importance of the Critical Path. Discuss
[2]
[2]
[5] [16]
[4]
[1]
[8] [2][3][3][2]
Planapprv
drawplan
furnibldg
Build found
DelivermaterialBill of
mtls
[Duration in Weeks]
negolandowner
Buyland$
[4]
Lecture 9 – Project Management |
Project Completion Time & Critical Path
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Path # Designation Duration
1 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 9 -> 10 -> 11 -> 12 27 weeks
2 1 -> 2 -> 3 -> 4 -> 5 -> 9 -> 10 -> 11 -> 12 44 weeks
3 1 -> 2 -> 3 -> 4 -> 7 -> 8 -> 9 -> 10 -> 11 -> 12 30 weeks
Inference: Project Completion Time = 44 weeks Critical Path = 1->2->3->4->5->9->10->11->12
Lecture 9 – Project Management |
Milwaukee Paper Manufacturing’s Activities, Predecessors & Times
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ActivityActivity DescriptionDescription Immediate Immediate PredecessorsPredecessors
Time Time (weeks)(weeks)
AA Build internal componentsBuild internal components —— 22
BB Modify roof and floorModify roof and floor —— 33
CC Construct collection stackConstruct collection stack AA 22
DD Pour concrete and install Pour concrete and install frameframe
A, BA, B 44
EE Build high-temperature burnerBuild high-temperature burner CC 44
FF Install pollution control Install pollution control systemsystem
CC 33
GG Install air pollution deviceInstall air pollution device D, ED, E 55
HH Inspect and testInspect and test F, GF, G 22
Total time (weeks)Total time (weeks) 2525
Lecture 9 – Project Management |
Exercise(a) Draw the AON network for Milwaukee Paper
Company
(b) Determine the project completion time
(c) Determine the critical path
(d) Calculate the Earliest start, Latest start, Earliest finish & Latest finish
(e) Calculate slack for each activity
(f) Calculate variances
(g) What is the probability of completing the project in 1q6 weeks?
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Lecture 9 – Project Management |
Notation Used in Nodes for Forward and Backward Pass
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A
Activity Name or Symbol
Earliest Start
ESEarliest FinishEF
Latest Start
LS Latest Finish
LF
Activity Duration
2
Lecture 9 – Project Management | 17
Earliest Start and Earliest Finish Times for Milwaukee Paper
[Completion Time = 15 weeks & Critical Path = A – C – E – G – H]
Lecture 9 – Project Management | 18
Lecture 9 – Project Management |
Earliest Start for Activity D
We now come to activity D. Both activities A and B are immediate predecessors for B. Whereas A has an EF of 2, activity B has an EF of 3. Using the earliest finish time rule, we compute the ES of activity D as follows:
ES of D ES of D = Max (EF of A, EF of B) = Max (2, 3) = 3
The EF of DEF of D equals 7 (= 3 + 4).
Next, both activities E and F have activity C as their only immediate predecessor.
Therefore, the ES for both E and F equals 4 (= EF of C). The EF of E is 8 (= 4 + 4), and the EF of F is 7 (= 4 + 3).
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Lecture 9 – Project Management |
Activity G has both activities D and E as predecessors. Using the earliest start time rule, its ES is therefore the maximum of EF of D and EF of E. Hence, the ES of activity G equals 8 (= maximum of 7 and 8), and its EF equals 13 (= 8 + 5)
Finally, we come to activity H. Since it also has two predecessors, F and G, the ES of H is the maximum EF of these two activities. That is, the ES of H equals 13 (= maximum of 13 and 7). This implies that the EF of H is 15 (= 13 + 2). Since H is the last activity in the project, this also implies that the earliest time in which the entire project can be completed is 15 weeks (the expected completion time of the project).
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Lecture 9 – Project Management | 21
Computing Latest Start and Finish Times
Lecture 9 – Project Management |
Latest Start and Latest Finish Times for Milwaukee Paper
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Lecture 9 – Project Management | 23
Progression on Measures
Lecture 9 – Project Management |
Gradual Progression on Measures
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ES EF
A C F2 2 3
ES EF Slack = 0 Slack = 0 Slack = 6 End
0 0
E H0 0 4 2
LS LF Slack = 0 Slack = 0
B D G3 4 5
Slack = 1 Slack = 1 Slack = 0
Activity
Duration
Activity
Name
Start
0
0
0
2
3
4
4
8
13
2
3 7
4
8
13
7
15
13
10
8
4
2
41
0 2
4
4
8
8
13
13
15
Lecture 9 – Project Management | 25
Milwaukee Paper’s Schedule and Slack Times
(Slack = LS – ES or LF – EF)
Lecture 9 – Project Management |
AON Network for AON Network for Milwaukee PaperMilwaukee Paper
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G
E
F
H
CA
Start
DB
Arrows Show Precedence
Relationships
Lecture 9 – Project Management | 27
Critical Path and Slack Times for Milwaukee Paper
Lecture 9 – Project Management |
Beta Probability Distribution with 3 Time Estimates
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Probability of 1 in 100 of > b occurring
Probability of 1 in 100 of < a occurring
Pro
bab
ility
Optimistic Time (a)
Most Likely Time (m)
Pessimistic Time (b)
Activity Time
To compute the dispersion or variance of activity completion time, we use the
formula; Variance = [(b-a)/6]Variance = [(b-a)/6]22
Lecture 9 – Project Management |
Expected Times and Variances
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[Critical Path = A C E G H = 15 weeks]
[Variance along critical path = 0.11+0.11+1.00+1.78+0.11 = 3.11; Std Dev = √ 3.11 =
1.76
Lecture 9 – Project Management |
Probability Distribution forProject Completion Times
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Standard deviation = 1.76 weeks
15 Weeks
(Expected Completion Time)
Milwaukee Paper
[Where Standard Deviation = ѵ var (square root of variance)]
Lecture 9 – Project Management |
Probability that Milwaukee Paper will meet the 16-Week Deadline
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Time
Probability(T ≤ 16 weeks)is 71.57%
0.57 Standard deviationsTime
15 16Weeks Weeks
[Probability of Project completed 1 week later than the expected duration?]
Joni Steinberg would like to find the probability that her project will be finished on or before the 16-week deadline.To do so, she needs to determine the appropriate area under the normal curve. The standard normal equation can be applied as follows:
ZZ == –– //pp
= = (16 (16 wkswks – 15 – 15 wkswks)/ 1.76 )/ 1.76 = = 0.570.57
duedue expected date expected datedatedate of completion of completion
Where Z is the number of standard deviations the due date lies from the
mean or expected date.
Lecture 9 – Project Management |
Z-Value for 99% Probability of Project Completion at Milwaukee Paper
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Probability of 0.01
Z
Probability of 0.99
2.33 Standard deviations
0 2.33
Joni Steinberg wants to find the due date under which her company’s project has a 99% chance of completion. She first needs to compute the Z-value corresponding to 99% shown in Figure 3.17
Lecture 9 – Project Management | 33
Normal Curve Areas [Z = 0.57; Probability = 0.71566 = 71.57% chance that the project can be
completed in 16 wks or less]
Lecture 9 – Project Management | 34
Normal Curve Areas
Lecture 9 – Project Management |
Discussion Questions One of your colleagues comments that software is the
ultimate key to project management success. How would you respond?
When a large project is mismanaged, it makes news. Form a discussion group and identify penalties associated with a mismanaged project in your experience or in recent headlines. Identify the cause of the problem, such as inaccurate time estimates, changed scope, unplanned or improperly sequenced activities, inadequate resources or poor management –labor relations.
Describe a project in which you participated. What activities were involved and how were they interrelated? How would you rate the project manager? What is the basis of your evaluation?
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Lecture 9 – Project Management |
Project Management
CASEThe Pert Studebaker
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