SBCO 6240 Project Management HB Student

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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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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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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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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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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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.


All that is required to construct a network is the starting and ending event for each activity.

PERT – Example #2

8

41

2

35

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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


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


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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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


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]


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


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


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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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]


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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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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Computing Latest Start and Finish Times


Latest Start and Latest Finish Times for Milwaukee Paper

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Progression on Measures


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

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Milwaukee Paper’s Schedule and Slack Times

(Slack = LS – ES or LF – EF)


AON Network for AON Network for Milwaukee PaperMilwaukee Paper

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G

E

F

H

CA

Start

DB

Arrows Show Precedence

Relationships


Critical Path and Slack Times for Milwaukee Paper


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


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


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)]


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.


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


Normal Curve Areas [Z = 0.57; Probability = 0.71566 = 71.57% chance that the project can be

completed in 16 wks or less]


Normal Curve Areas


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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Project Management

CASEThe Pert Studebaker

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NEXT MEETING:Group Presentations

D. Anthony Chevers

[email protected], Room #28

SBCO 6240 Project Management HB Student

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