Outline
Operations Management
Global Company Profile: Bechtel Group The Importance of Project Management
Chapter 3 – Project Management
Project Planning The Project Manager
PowerPoint presentation to accompany Heizer/Render Principles of Operations Management, 7e Operations Management, 9e
Work Breakdown Structure
Project Scheduling
Some additions and deletions have been made by Ömer Yağız to this slide set. (revised February 2012) © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
Outline - Continued
Outline - Continued Determining the Project Schedule
Project Controlling
Forward Pass
Project Management Techniques: PERT and CPM
Backward Pass Calculating Slack Time and Identifying the Critical Path(s)
The Framework of PERT and CPM Network Diagrams and Approaches
Variability in Activity Times
Activity-on-Node Example
Three Time Estimates in PERT
Activity-on-Arrow Example
Probability of Project Completion
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© 2008 Prentice Hall, Inc.
Outline - Continued
3– 4
Learning Objectives
Cost-Time Trade-Offs and Project Crashing
When you complete this chapter you should be able to:
A Critique of PERT and CPM
1. Create a work breakdown structure
Using Microsoft Project to Manage Projects
© 2008 Prentice Hall, Inc.
3– 2
2. Draw AOA and AON networks
Creating a Project Schedule Using MS Project
3. Complete both forward and backward passes for a project
Tracking Progress and Managing Costs Using MS Project
4. Determine a critical path
3– 5
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1
Learning Objectives
Bechtel Projects
When you complete this chapter you should be able to:
Reconstruction projects in Iraq Building 26 massive distribution centers in just two years for the internet company Webvan Group ($1 billion) Constructing 30 high-security data centers worldwide for Equinix, Inc. ($1.2 billion) Building and running a rail line between London and the Channel Tunnel ($4.6 billion) Developing an oil pipeline from the Caspian Sea region to Russia ($850 million) Expanding the Dubai Airport in the UAE ($600 million), and the Miami Airport in Florida ($2 billion)
5. Calculate the variance of activity times 6. Crash a project 7. Use Microsoft Project software to create a project
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© 2008 Prentice Hall, Inc.
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Tepe Akfen Vie (TAV)
Bechtel Projects Building liquid natural gas plants in Yemen $2 billion) and in Trinidad, West Indies ($1 billion) Building a new subway for Athens, Greece ($2.6 billion) Constructing a natural gas pipeline in Thailand ($700 million) Building 30 plants for iMotors.com, a company that sells refurbished autos online ($300 million) Building a highway to link the north and south of Croatia ($303 million) Jubail and Yabu industrial cities in Saudi Arabia
İstanbul Atatürk airport Ankara Esenboğa airport İzmir Adnan Menderes airport Georgia Tbilisi & Batumi airports Tunisia Habib Bourgiba airport Macedonia (3 airports)
Have visited Jubail several times - ÖY © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
Strategic Importance of Project Management
Organizations for PM
Microsoft Windows Vista Project :
Project Management Institute
hundreds of programmers
http://www.pmi.org
millions of lines of code
Turkish chapter of PMI
hundreds of millions of dollars cost
http://www.pmi-tr.org/cms2/
Hard Rock Cafe Rockfest Annual Concert Project:
PMBOK – Project Management Book of Knowledge (excellent source)
100,000 + fans
planning began 9 months in advance
U2 Concert in İstanbul (Sept. 2010)
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2
What is a project?
Management of Projects
Project – series of related jobs usually directed toward some major output and requiring a significant period of time (and often funds) to perform.
1. Planning - goal setting, defining the project, team organization 2. Scheduling - relates people, money, machines and supplies to specific activities and activities to each other according to time dimension
Project Management – a series of activities (planning, scheduling, and controlling) in using resources (people, equipment, material) to meet the technical, cost, and time constraints of the project. – Project or Program? Apollo moon program; GAP program
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3. Controlling - monitors resources, costs, quality, and budgets; revises plans and shifts resources to meet time and cost demands 3 – 13
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Project Planning, Scheduling, and Controlling
Project Management Activities Planning
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Scheduling
Objectives
Project activities
Resources
Start & end times
Work break-down schedule
Network
Organization
Controlling
Figure 3.1
Monitor, compare, revise, action
Before project
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Project Planning, Scheduling, and Controlling
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During project 3 – 16
Project Planning, Scheduling, and Controlling
Figure 3.1 Before project
Start of project Timeline
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Figure 3.1 Start of project Timeline
During project
Before project 3 – 17
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Start of project Timeline
During project 3 – 18
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Project Planning, Scheduling, and Controlling
estimates Project Time/cost Planning, Budgets Engineering diagrams Scheduling, and Controlling Cash flow charts Material availability details
Budgets Delayed activities report Slack activities report CPM/PERT Gantt charts Milestone charts Cash flow schedules Figure 3.1
Figure 3.1
Before project
Start of project Timeline
During project
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Before project 3 – 19
Start of project Timeline
Project Planning
Often temporary structure Uses specialists from entire company Headed by project manager Coordinates activities Monitors schedule and costs
Permanent structure called ‗matrix organization‘
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A Sample Project Organization
Project 1
Project 2 Figure 3.2 © 2008 Prentice Hall, Inc.
Finance
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Project Organization Works Best When
President
Marketing
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Project Organization
Establishing objectives Defining project Creating work breakdown structure Determining resources Forming organization
Human Resources
During project
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Design
Quality Mgt
Production
Mechanical Engineer
Test Engineer
Technician
Electrical Engineer
Computer Engineer
Technician
1. Work can be defined with a specific goal and deadline 2. The job is unique or somewhat unfamiliar to the existing organization 3. The work contains complex interrelated tasks requiring specialized skills 4. The project is temporary but critical to the organization 5. The project cuts across organizational lines
Project Manager
Project Manager
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4
The Role of the Project Manager
Matrix Organization Marketing
Operations
Engineering
Finance
Highly visible Responsible for making sure that:
Project 1
All necessary activities are finished in order and on time
Project 2
The project comes in (i.e. completed) within budget
Project 3
The project meets quality goals Project 4
The people assigned to the project receive motivation, direction, and information
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Ethical Issues in PM
The Role of the Project Manager
Bid rigging – divulging confidential information to give some bidders an unfair advantage very common in Turkey (ihaleye fesat karıştırmak)
Highly visible Responsible for making sure that: should be: Project managers
―Low balling‖ contractors – try to ―buy‖ the project by bidding low and hope to renegotiate or cut corners
Good coaches All necessary activities are finished in order Good communicators and on time to organize The project comesinAble within budget activities from a variety of disciplines The project meets quality goals
İlk defa duymuyorsunuz herhalde! Bribery – particularly on international projects Remember Lockheed scandal; it was investigated in every country except guess which? (hep bir ağızdan …. Türkiye…)
The people assigned to the project receive motivation, direction, and information © 2008 Prentice Hall, Inc.
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Ethical Issues
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Statement of Work (SOW)
Mercedes Benz bribery scandal in 22 countries. (http://www.hurriyet.com.tr/ekonomi/14208149 .asp)
A project starts with a statement of work (SOW). (Proje Tanımı) – description of the objectives to be achieved
Expense account padding
– brief statement of the work to be done
Use of substandard materials Compromising health and safety standards
– proposed schedule with start and completion dates
Withholding needed information
– performance measures in terms of budget
Failure to admit project failure at close
– completion steps (milestones) (önemli aşamalar) – written progress reports (gelişme raporları) to be submitted
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5
Work Breakdown Structure MS Vista
Work Breakdown Structure(WBS) Level
1. Project 2. 3. 4.
Level ID Number
Activity
1
1.0
Develop/launch Windows Vista OS
2
1.1
Development of GUIs
2
1.2
Ensure compatibility with earlier Windows versions
3
1.21
Compatibility with Windows ME
3
1.22
Compatibility with Windows XP
3
1.23
Compatibility with Windows 2000
4
1.231
Ensure ability to import files
Level
Major tasks in the project Subtasks in the major tasks Activities (or work packages) to be completed
Figure 3.3 © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
Another way to look at WBS Level
1
2
Project Scheduling Identifying precedence (öncelik) relationships Sequencing activities Determining activity times & costs Estimating material & worker requirements Determining critical activities
Program
Project
1
Project
Task 1.1
2
Task 1.2
3
Subtask 1.1.1
4
Work Package 1.1.1.1
Subtask 1.1.2
Work Package 1.1.1.2
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Purposes of Project Scheduling
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Scheduling Techniques 1. Ensure that all activities are planned for 2. Their order of performance is accounted for 3. The activity time estimates are recorded 4. The overall project time is developed
1. Shows the relationship of each activity to others and to the whole project 2. Identifies the precedence relationships among activities 3. Encourages the setting of realistic time and cost estimates for each activity 4. Helps make better use of people, money, and material resources by identifying critical bottlenecks in the project © 2008 Prentice Hall, Inc.
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6
Project Management Techniques
A Simple Gantt Chart
Gantt chart Critical Path Method (CPM) Program Evaluation and Review Technique (PERT)
J
F
M
A
Time M J
J
A
S
Design
Prototype Test Revise Production
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© 2008 Prentice Hall, Inc.
Service For A Delta Jet Passengers Baggage Fueling Cargo and mail Galley servicing Lavatory servicing Drinking water Cabin cleaning Cargo and mail Flight services Operating crew Baggage Passengers
Figure 3.4
Project Control Reports
Deplaning Baggage claim Container offload Pumping Engine injection water Container offload Main cabin door Aft cabin door Aft, center, forward Loading First-class section Economy section Container/bulk loading Galley/cabin check Receive passengers Aircraft check Loading Boarding
Detailed cost breakdowns for each task Total program labor curves
Cost distribution tables Functional cost and hour summaries Raw materials and expenditure forecasts Variance reports Time analysis reports 0
10
20 30 Time, Minutes
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40 3 – 39
Work status reports © 2008 Prentice Hall, Inc.
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Six Steps PERT & CPM
PERT and CPM Network techniques
1. Define the project and prepare the work breakdown structure
Developed in 1950‘s CPM by Kelley and Walker for DuPont‘s chemical plants (1957)
2. Develop relationships among the activities - decide which activities must precede and which must follow others
PERT by Booz, Allen & Hamilton with the U.S. Navy, for Polaris missile (1958)
Consider precedence relationships and interdependencies
3. Draw the network connecting all of the activities
Each uses a different estimate of activity times © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
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7
Questions PERT & CPM Can Answer
Six Steps PERT & CPM 4. Assign time and/or cost estimates to each activity
1. When will the entire project be completed?
5. Compute the longest time path through the network – this is called the critical path
2. What are the critical activities or tasks in the project?
6. Use the network to help plan, schedule, monitor, and control the project
4. What is the probability the project will be completed by a specific date?
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3. Which are the noncritical activities?
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© 2008 Prentice Hall, Inc.
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A Comparison of AON and AOA Network Conventions
Questions PERT & CPM Can Answer
Activity on Node (AON)
5. Is the project on schedule, behind schedule, or ahead of schedule? 6. Is the money spent equal to, less than, or greater than the budget?
(a) A A
7. Are there enough resources available to finish the project on time?
(b)
C B C
Figure 3.5 3 – 45
B and C cannot begin until A is completed
A
(c)
A comes before B, which comes before C A and B must both be completed before C can start
B
8. If the project must be finished in a shorter time, what is the way to accomplish this at least cost? © 2008 Prentice Hall, Inc.
C
B
Activity Meaning
Activity on Arrow (AOA)
A
B
C
A B
C
B A
C
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A Comparison of AON and AOA Network Conventions
A Comparison of AON and AOA Network Conventions
Activity on Node (AON)
Activity on Node (AON)
A
C
B
D
(d)
Activity Meaning C and D cannot begin until both A and B are completed
Activity on Arrow (AOA) A
C
B
D
A
B
(f) A
C
B
D
(e)
C cannot begin until both A and B are completed; D cannot begin until B is completed. A dummy activity is introduced in AOA
C A
C Dummy activity
B
B and C cannot begin until A is completed. D cannot begin until both B and C are completed. A dummy activity is again introduced in AOA.
Activity on Arrow (AOA)
A Dummy activity
B
D C
D
Figure 3.5 © 2008 Prentice Hall, Inc.
D
Activity Meaning
Figure 3.5 3 – 47
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8
AON Example
AON Network for Milwaukee Paper
Milwaukee Paper Manufacturing's Activities and Predecessors for installing air pollution control equipment in its facility Activity
Immediate Predecessors
Description
A
Build internal components
—
B
Modify roof and floor
—
C
Construct collection stack
D
Pour concrete and install frame
A, B
E
Build high-temperature burner
C
F
Install pollution control system
C
G
Install air pollution device
D, E
H
Inspect and test
F, G
A
A
Activity A (Build Internal Components)
B
Activity B (Modify Roof and Floor)
Start
Start Activity
Figure 3.6 Table 3.1
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© 2008 Prentice Hall, Inc.
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AON Network for Milwaukee Paper
AON Network for Milwaukee Paper
Activity A Precedes Activity C F A
A
C
E
Start
Start
B
3 – 51
C
3
D (Pour Concrete/ Install Frame)
Figure 3.8
3 – 52
Determining the Project Schedule Perform a Critical Path Analysis
4
The critical path is the longest path through the network
Dummy Activity
1
G
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AOA Network for Milwaukee Paper (Construct Stack)
D
Arrows Show Precedence Relationships
Figure 3.7
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2
H B
D Activities A and B Precede Activity D
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C
6
H (Inspect/ Test)
The critical path is the shortest time in which the project can be completed
7
Any delay in critical path activities delays the project Critical path activities have no slack time
5 Figure 3.9 3 – 53
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9
Determining the Project Schedule
Determining the Project Schedule
Perform a Critical Path Analysis Activity A B C D E F G H
Description Build internal components Modify roof and floor Construct collection stack Pour concrete and install frame Build high-temperature burner Install pollution control system Install air pollution device Inspect and test Total Time (weeks)
Perform a Critical Path Analysis
Time (weeks) 2 3 2 4 4 3 5 2 25
Earliest start (ES) = earliest time at which an activity can Activity Description Time (weeks) start, assuming all predecessors have A Build internal components 2 been completed B Modify roof and floor 3 Earliest finish (EF) = earliest time at which an activity can be finished C Construct collection stack 2 D start (LS) Pour=concrete and Latest latest time at install which frame an activity can4 start so as to not delay the completion E Build high-temperature burner 4 of thecontrol entire project F Install time pollution system 3 LatestGfinish (LF) = latest time by which an activity has Install air pollution device 5 to be finished so as to not delay the H Inspect and test 2 completion time of the entire project Table Total Time (weeks) 25 3.2
Table 3.2 © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
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Determining the Project Schedule
Forward Pass Begin at starting event and work forward
Perform a Critical Path Analysis
Earliest Start Time Rule:
Activity Name or Symbol A
Earliest Start
ES
Latest Start
LS
EF
LF 2
If an activity has only a single immediate predecessor, its ES equals the EF of the predecessor
Earliest Finish
If an activity has multiple immediate predecessors, its ES is the maximum of all the EF values of its predecessors
Latest Finish
ES = Max {EF of all immediate predecessors} Activity Duration
Figure 3.10 © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
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ES/EF Network for Milwaukee Paper
Forward Pass Begin at starting event and work forward ES
Earliest Finish Time Rule:
0
0
0
EF = ES + Activity time
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EF = ES + Activity time Start
The earliest finish time (EF) of an activity is the sum of its earliest start time (ES) and its activity time
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10
ES/EF Network for Milwaukee Paper EF of A = ES of A + 2
ES of A 0
Start
0
A 0
0
ES/EF Network for Milwaukee Paper A
2
2
2
0
0
Start
EF of B = ES of B + 3
ES of B
0
B 0
0
3
2 3 © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
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ES/EF Network for Milwaukee Paper 0
A
2
2
2 0
Start
C
ES/EF Network for Milwaukee Paper 0
4
A
2
2
2
2
0
0
Start
C
A and B must both be finished before D can be started
4
2
0
= Max (2, 3) 0 0
B
3
3
0
3
3 – 63
A
2
2
2 0
C
4 3 – 64
ES/EF Network for Milwaukee Paper 0
4
A
2
2
2
2
0
0
0
Start
C
0
3
3
3
D
7
2
F
7
3
0
4
E
8
13
4 0
4
4
4
0 B
7
3
© 2008 Prentice Hall, Inc.
ES/EF Network for Milwaukee Paper 0
B
3
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Start
D
0
B
3
3
3
D
4
7
H
15
2 G 8
13
5 Figure 3.11
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© 2008 Prentice Hall, Inc.
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11
Backward Pass
Backward Pass
Begin with the last event and work backwards
Begin with the last event and work backwards
Latest Finish Time Rule:
Latest Start Time Rule:
If an activity is an immediate predecessor for just a single activity, its LF equals the LS of the activity that immediately follows it
The latest start time (LS) of an activity is the difference of its latest finish time (LF) and its activity time
If an activity is an immediate predecessor to more than one activity, its LF is the minimum of all LS values of all activities that immediately follow it
LS = LF – Activity time
LF = Min {LS of all immediate following activities} © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
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LS/LF Times for Milwaukee Paper 0
A
2
2
2 0
Start
C
4
4
2
F
LS/LF Times for Milwaukee Paper 7
4
0
E
8
13 13
4 B
3
H
2
0
15 15
Start
3
7
8
4
2
2
2 0
Start
2
C
2
4
4
4
10
0
4 4
0 0
B
3
© 2008 Prentice Hall, Inc.
3
3
D
4
7
E
4
F
3
2
3
7 13
13 13
B
3
3
3
D
H
2
15 15
G
7
8
4
13 5
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LS/LF Times for Milwaukee Paper 7
0
13
0
8
13
8
13
H
2
15
0
15
0
Start
0
G
2
2
2
C
2
4
4
4
10
0
4
13
0
13
1
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2
2
4
8
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A
0
8
5
10
F
4
LS/LF Times for LF = Min(4, 10) Milwaukee Paper A
4
4
8 of LF =4 Min(LS following activity)
LF = EF of Project 3 – 69
C
E
0
© 2008 Prentice Hall, Inc.
0
2
0
13 5
2
0
LS = LF D – Activity time G 3
A
2
3
0
0
0
B
3
3
3
4
4
D
4
E
4
F
3
7 13
8
13
8
13
H
2
15 15
G
7
8
8
8
13
5
13
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12
Computing Slack Time
Computing Slack Time
After computing the ES, EF, LS, and LF times for all activities, compute the slack or free time for each activity Slack is the length of time an activity can be delayed without delaying the entire project Slack = LS – ES
Slack = LF – EF
or
Activity
Earliest Start ES
Earliest Finish EF
Latest Start LS
A B C D E F G H
0 0 2 3 4 4 8 13
2 3 4 7 8 7 13 15
0 1 2 4 4 10 8 13
Latest Finish LF
2 4 4 8 8 13 13 15
Slack LS – ES
On Critical Path
0 1 0 1 0 6 0 0
Yes No Yes No Yes No Yes Yes Table 3.3
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© 2008 Prentice Hall, Inc.
ES – EF Gantt Chart for Milwaukee Paper
Critical Path for Milwaukee Paper 0 0
0 0
Start
0
A
2
2
2
2
2
C
2
4
4
4
10
0
4
0
4
0 1
B
3
3
3
4
4
D
4
E
4
F
3
1
7 13
8
13
H
13
8
13
4
5
6
7
8
9
10 11 12 13 14 15 16
2
C Construct collection stack
15
D Pour concrete and install frame E Build hightemperature burner
15
G 8
8
3
B Modify roof and floor
13
7
2
A Build internal components
8
5
3 – 74
F Install pollution control system G Install air pollution device
H Inspect and test
Critical path: A-C-E-G-H
15 wks
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2
3
4
5
6
7
8
9
3 – 76
Another Example (AOA)
LS – LF Gantt Chart for Milwaukee Paper 1
© 2008 Prentice Hall, Inc.
Consider the following consulting project:
10 11 12 13 14 15 16
Activity Designation Immed. Pred. Time (Weeks) Assess customer's needs A None 2 Write and submit proposal B A 1 Obtain approval C B 1 Develop service vision and goals D C 2 Train employees E C 5 Quality improvement pilot groups F D, E 5 Write assessment report G F 1
A Build internal components
B Modify roof and floor C Construct collection stack D Pour concrete and install frame E Build hightemperature burner F Install pollution control system G Install air pollution device
Develop an AOA network diagram diagram and determine the duration of the critical path and slack times for all activities
H Inspect and test © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
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13
AOA project network
1
2 A
2
1 B
3
1 C
4
2 D
5 F
6
5 E
7
Forward pass 1 G
1
8
0
2 A ES=0 EF=2
2
1 B ES=2 EF=3
3
1 C ES=3 EF=4
DUMMY
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ES=0 EF=2
2
1 B ES=2 EF=3
3
1 C ES=3 EF=4
4
2 D ES=4 EF=6
EF=9
5 F
6
5ES=9 ES=4 E EF=9
ES=9 EF=14
7
1 G
1
8
0
2 A ES=0 EF=2
2
1 B ES=2 EF=3
1
ES=0 EF=2
2
ES=2 EF=3
3
1 C
LS=7 LF=9
ES=3 EF=4
4
2 D ES=4 EF=6
© 2008 Prentice Hall, Inc.
ES=3 EF=4
5 F
6
5
ES=9 EF=14
4
2 D ES=4 EF=6
1 G
8
0
DUMMY
5
5 F
6
5ES=9 ES=4 E EF=9 EF=9
ES=9 EF=14
7
1 G ES=14 EF=15
8
0
DUMMY
5
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Backward pass
LS=9 LF=14
5ES=9 ES=4 E EF=9 EF=9 LS=4 LF=9
3
1 C
DUMMY
Backward pass ?
7
3 – 80
5
3 – 81
1 B
5ES=9 ES=4 E EF=9
?
Forward pass
© 2008 Prentice Hall, Inc.
2 A
ES=4 EF=6
5 F
6
© 2008 Prentice Hall, Inc.
Forward pass 2 A
2 D
EF=9
5
1
4
LS=14 LF=15
7
1 G ES=14 EF=15
LS=0 LF=2
1
8
0
2 A ES=0 EF=2
DUMMY
LS=9 LF=9
2
LS=2 LF=3
LS=3 LF=4
LS=7 LF=9
1 B
1 C
2 D
ES=2 EF=3
3
ES=3 EF=4
4
ES=4 EF=6
© 2008 Prentice Hall, Inc.
5 F
6
5ES=9 ES=4 E EF=9 EF=9 LS=4 LF=9
3 – 83
LS=9 LF=14
5
ES=9 EF=14
LS=14 LF=15
7
1 G ES=14 EF=15
8
0
DUMMY
LS=9 LF=9
3 – 84
14
Calculate slack and obtain the critical path
1
LS=0 LF=2
LS=2 LF=3
LS=3 LF=4
LS=7 LF=9
2 A
1 B
1 C
2 D
2
ES=0 EF=2
ES=2 EF=3
Slack = LF - EF or
3
ES=3 EF=4
4
ES=4 EF=6
LS=9 LF=14
EF=9 LS=4 LF=9
LS=14 LF=15
5 F
6
7
ES=9 EF=14
5ES=9 0 ES=4 E EF=9 DUMM Y
5
Variability in Activity Times
1 G ES=14 EF=15
CPM assumes we know a fixed time estimate for each activity and there is no variability in activity times
8
PERT uses a probability distribution for activity times to allow for variability
LS=9 LF=9
All activities have zero slack except D, which has a slack of 3 wks. The critical path consists of activities with zero (0) slack times; therefore the critical path is 1-2-34-5-6-7-8.
= LS - ES © 2008 Prentice Hall, Inc.
3 – 85
Variability in Activity Times
© 2008 Prentice Hall, Inc.
3 – 86
Variability in Activity Times Estimate follows beta distribution Expected time: t = (a + 4m + b)/6 Variance of times: v = [(b – a)/6]2
Three time estimates are required Optimistic time (a) – if everything goes according to plan Pessimistic time (b) – assuming very unfavorable conditions Most likely time (m) – most realistic estimate
© 2008 Prentice Hall, Inc.
3 – 87
© 2008 Prentice Hall, Inc.
Variability in Activity Times
Computing Variance
Probability
Estimate follows beta distribution Expected time: Figure 3.12 t = (a + 4m + b)/6 Probability Variance ofoftimes: 1 in 100 of Probability < a occurring v = [(b − a)/6]2 of 1 in 100 of > b occurring Activity Time Optimistic Time (a) © 2008 Prentice Hall, Inc.
Most Likely Time (m)
3 – 88
Optimistic
Most Likely
Pessimistic
Expected Time
Variance
Activity
a
m
b
t = (a + 4m + b)/6
[(b – a)/6]2
A B C D E F G H
1 2 1 2 1 1 3 1
2 3 2 4 4 2 4 2
3 4 3 6 7 9 11 3
Pessimistic Time (b)
2 3 2 4 4 3 5 2
.11 .11 .11 .44 1.00 1.78 1.78 .11 Table 3.4
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© 2008 Prentice Hall, Inc.
3 – 90
15
Probability of Project Completion
Probability of Project Completion
Project variance is computed by summing the variances of critical activities
Project variance is computed by summing the variances of critical Project variance activities sp2 = .11 + .11 + 1.00 + 1.78 + .11 = 3.11
sp2 = Project variance = (variances of activities on critical path)
Project standard deviation sp =
Project variance
= © 2008 Prentice Hall, Inc.
3 – 91
3.11 = 1.76 weeks
© 2008 Prentice Hall, Inc.
Probability of Project Completion
3 – 92
Probability of Project Completion
PERT makes two more assumptions:
Standard deviation = 1.76 weeks
Total project completion times follow a normal probability distribution Activity times are statistically independent 15 Weeks (Expected Completion Time)
Figure 3.13 © 2008 Prentice Hall, Inc.
3 – 93
© 2008 Prentice Hall, Inc.
Probability of Project Completion
3 – 94
Probability of Project Completion From Appendix I
What is the probability this project can be completed on or before the 16 week deadline?
What is the probability this project can .00 .01 .07 .08 be completed on or before the 16 week .1 .50000 .50399 .52790 .53188 deadline?.2 .53983 .54380 .56749 .57142
Z = due – expected date /sp date
.5
of completion
.6
= (16 wks – 15 wks)/1.76 = 0.57
© 2008 Prentice Hall, Inc.
Where Z is the number of standard deviations the due date or target date lies from the mean or expected date
date /s Z.69146 = due .69497 − expected.71566 .71904 p date
.72575
= 0.57
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© 2008 Prentice Hall, Inc.
of completion
.72907
.74857
.75175
= (16 wks − 15 wks)/1.76
Where Z is the number of standard deviations the due date or target date lies from the mean or expected date 3 – 96
16
Probability of Project Completion Probability (T ≤ 16 weeks) is 71.57%
Determining Project Completion Time
0.57 Standard deviations
Probability of 0.99 Probability of 0.01
15 Weeks
16 Weeks
Time
Figure 3.14 © 2008 Prentice Hall, Inc.
Figure 3.15 3 – 97
Determining Project Completion Time
Z
2.33
© 2008 Prentice Hall, Inc.
3 – 98
Variability of times for activities on noncritical paths must be considered when finding the probability of finishing in a specified time Variation in noncritical activity may cause change in critical path
= 19.1 weeks 99% probability that the project will be finished in 19.1 weeks 3 – 99
© 2008 Prentice Hall, Inc.
What Project Management Has Provided So Far
3 – 100
Trade-Offs And Project Crashing
The project‘s expected completion time is 15 weeks There is a 71.57% chance the equipment will be in place by the 16 week deadline
It is not uncommon to face the following situations: The project is behind schedule
Five activities (A, C, E, G, and H) are on the critical path Three activities (B, D, F) are not on the critical path and have slack time A detailed schedule is available © 2008 Prentice Hall, Inc.
0
Variability of Completion Time for Noncritical Paths
= 15 + (2.33)(1.76)
© 2008 Prentice Hall, Inc.
2.33 Standard deviations
From Appendix I
The completion time has been moved forward Shortening the duration of the project is called project crashing 3 – 101
© 2008 Prentice Hall, Inc.
3 – 102
17
Factors to Consider When Crashing A Project
Steps in Project Crashing 1. Compute the crash cost per time period. If crash costs are linear over time:
The amount by which an activity is crashed is, in fact, permissible
(Crash cost – Normal cost) Crash cost per period = (Normal time – Crash time)
Taken together, the shortened activity durations will enable us to finish the project by the due date
2. Using current activity times, find the critical path and identify the critical activities
The total cost of crashing is as small as possible © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
Steps in Project Crashing
Steps in Project Crashing
3. If there is only one critical path, then select the activity on this critical path that (a) can still be crashed, and (b) has the smallest crash cost per period. If there is more than one critical path, then select one activity from each critical path such that (a) each selected activity can still be crashed, and (b) the total crash cost of all selected activities is the smallest. Note that the same activity may be common to more than one critical path. © 2008 Prentice Hall, Inc.
4. Update all activity times. If the desired due date has been reached, stop. If not, return to Step 2.
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© 2008 Prentice Hall, Inc.
A B C D E F G H
2 3 2 4 4 3 5 2
1 1 1 2 2 2 2 1
Cost ($) Crash Cost Critical Normal Crash Per Wk ($) Path?
Activity Cost
22,000 30,000 26,000 48,000 56,000 30,000 80,000 16,000
$34,000 —
22,750 34,000 27,000 49,000 58,000 30,500 84,500 19,000
750 2,000 1,000 500 1,000 500 1,500 3,000
Yes No Yes No Yes No Yes Yes
Crash Crash Cost/Wk =
Crash $33,000 — Cost
$34,000 – $30,000 3– 1 $4,000 = = $2,000/Wk 2 Wks
$31,000 — $30,000 —
Normal Cost Figure 3.16 3 – 107
© 2008 Prentice Hall, Inc.
Crash Cost – Normal Cost Normal Time – Crash Time
=
$32,000 —
Table 3.5 © 2008 Prentice Hall, Inc.
3 – 106
Crash and Normal Times and Costs for Activity B
Crashing The Project Time (Wks) Activity Normal Crash
3 – 104
Normal
—
| 1 Crash Time
| 2
| 3 Normal Time
Time (Weeks) 3 – 108
18
TIME - COST TRADE-OFF PROCEDURE (CRASHING) : Another Illustration
Critical Path And Slack Times For Milwaukee Paper 0 0
0 0
Start
0
0
A
2
2 2
Slack = 0
2 2
C
2
4
10
Slack = 0
E
4
0
4
0 1
B
3
3
3
4
4
Slack = 1
D
4
4
TIME – COST TRADE-OFF
F
4
4
7 13
3
Slack = 6 8
13
8
13
Slack = 0
2
15 15
Slack = 0
G
7
8
13
8
8
13
Slack = 1
H
Activity A B C D
5
Normal time 2 5 4 3
Crash Time 1 2 3 1
Normal Cost 6 TL 9 6 5
Crash Cost TL/day 10 TL 4 TL 18 3 8 2 9 2
Cost/day = (Crash cost - Normal cost) / (Normal time Crash time) for example; for activity B: (18 -9) / (5 - 2) = 3 TL/day
Slack = 0
Figure 3.17
© 2008 Prentice Hall, Inc.
3 – 109
TIME-COST TRADE-OFF ILLUSTRATION
Others can be obtained similarly. © 2008 Prentice Hall, Inc.
3 – 110
TIME-COST TRADE-OFF ILLUSTRATION
Suppose the project network is as follows:
TIME – COST TRADE-OFF
TIME – COST TRADE-OFF
ES=2 EF=7 ES=0 EF=2 A,2 LS=0 LF=2
B;5
Activity A B C D
Normal time 2 5 4 3
Crash Time 1 2 3 1
Normal Cost 6 TL 9 6 5
Crash Cost TL/day 10 TL 4 TL 18 3 8 2 9 2
SHORTEN D BY 1 DAY
Maximum 1 day 3 1 2
Activity A B C D
Normal time 2 5 4 3
Crash Time 1 2 3 1
Normal Cost 6 TL 9 6 5
Crash Cost TL/day 10 TL 4 TL 18 3 8 2 9 2
Maximum 1 day 3 1 2
B;5
ES=7 EF=10
LS=2 LF=7
A,2
D,3 ES=2 EF=6
D,2
LS=7 LF=10
C,4
© 2008 Prentice Hall, Inc.
Maximum 1 day 3 1 2
C,4 Critical Path : A-B-D Duration = 10 days T. Cost = 26 TL
LS=3 LF=7
C.P : A-B-D Duration = 9 days T. Cost = 28 TL 3 – 111
TIME-COST TRADE-OFF ILLUSTRATION
© 2008 Prentice Hall, Inc.
3 – 112
TIME-COST TRADE-OFF ILLUSTRATION
TIME – COST TRADE-OFF TIME – COST TRADE-OFF
SHORTEN D BY 1 MORE DAY
Activity A B C D
Normal time 2 5 4 3
Crash Time 1 2 3 1
Normal Cost 6 TL 9 6 5
Crash Cost TL/day 10 TL 4 TL 18 3 8 2 9 2
Maximum 1 day 3 1 2
SHORTEN B BY 1 DAY
B;5
A,2
B;4
A,2
D,1
C,4
© 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
Normal time 2 5 4 3
Crash Time 1 2 3 1
Normal Cost 6 TL 9 6 5
Crash Cost TL/day 10 TL 4 TL 18 3 8 2 9 2
Maximum 1 day 3 1 2
D,1
C,4 C.P : A-B-D Duration = 8 days T. Cost = 30 TL
Activity A B C D
C.P : A-B-D A-C-D Duration = 7 days T. Cost = 33 TL 3 – 114
19
TIME-COST TRADE-OFF ILLUSTRATION
TIME-COST TRADE-OFF ILLUSTRATION
A OR (B & C) CAN BE SHORTENED. LESS COSTLY TO TIME – COST TRADE-OFF SHORTEN A BY 1 DAY Normal Crash Normal Crash B;4
Activity A B C D
time 2 5 4 3
Time 1 2 3 1
A,1
Cost 6 TL 9 6 5
Cost TL/day 10 TL 4 TL 18 3 8 2 9 2
SHORTEN B & C TOGETHER BY 1 DAY. Maximum 1 day 3 1 2
B;3
Normal time 2 5 4 3
TIME – COST TRADE-OFF Crash Time 1 2 3 1
Normal Cost 6 TL 9 6 5
A,1
D,1
C,3
© 2008 Prentice Hall, Inc.
3 – 115
TIME-COST TRADE-OFF ILLUSTRATION
Crash Cost TL/day 10 TL 4 TL 18 3 8 2 9 2
Maximum 1 day 3 1 2
D,1
C.P. : A-B-D A-C-D Duration = 6 days T. Cost = 37 TL
C,4
Activity A B C D
C.P. : A-B-D A-C-D Duration = 5 days T. Cost = 42 TL
© 2008 Prentice Hall, Inc.
3 – 116
Advantages of PERT/CPM
WE CAN SHORTEN B BY 1 MORE DAY (MAX. 3 DAYS) TIME – COST TRADE-OFF
B;2
A,1
Activity A B C D
Normal time 2 5 4 3
Crash Time 1 2 3 1
Normal Cost 6 TL 9 6 5
Crash Cost TL/day 10 TL 4 TL 18 3 8 2 9 2
Maximum 1 day 3 1 2
C.P. : A-C-D Duration = 5 days T. Cost = 45 TL
TOTAL PROJECT COST IS NOW 45 TL; PROJECT DURATION IS STILL 5 DAYS. CAN NOT DECREASE PROJECT DURATION © 2008 Prentice Hall, Inc. ANY MORE..
2. Straightforward concept and not mathematically complex 3. Graphical networks help highlight relationships among project activities
D,1
C,3
1. Especially useful when scheduling and controlling large projects
4. Critical path and slack time analyses help pinpoint activities that need to be closely watched 3 – 117
© 2008 Prentice Hall, Inc.
Advantages of PERT/CPM
Limitations of PERT/CPM
5. Project documentation and graphics point out who is responsible for various activities
1. Project activities have to be clearly defined, independent, and stable in their relationships 2. Precedence relationships must be specified and networked together 3. Time estimates tend to be subjective and are subject to fudging by managers 4. There is an inherent danger of too much emphasis being placed on the longest, or critical, path
6. Applicable to a wide variety of projects 7. Useful in monitoring not only schedules but costs as well
© 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
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20
Using Microsoft Project
Project Management Software There are several popular packages for managing projects Primavera MacProject Pertmaster VisiSchedule Time Line Microsoft Project
Program 3.1 © 2008 Prentice Hall, Inc.
3 – 121
© 2008 Prentice Hall, Inc.
Using Microsoft Project
Using Microsoft Project
Program 3.2 © 2008 Prentice Hall, Inc.
Program 3.3 3 – 123
© 2008 Prentice Hall, Inc.
Using Microsoft Project
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Using Microsoft Project
Program 3.4 © 2008 Prentice Hall, Inc.
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Program 3.5 3 – 125
© 2008 Prentice Hall, Inc.
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21
Using Microsoft Project
Using Microsoft Project
Program 3.7 Program 3.6 © 2008 Prentice Hall, Inc.
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© 2008 Prentice Hall, Inc.
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