1. BA 333 Operations Management
Project Management
PERT/CPM
Spring, 1998

2. Lecture Outline Project Management Introduction
Definition & Background
Components
event
activity
critical path
PERT/CPM

3. Introduction to Project Management
Definition
to plan, implement, and control the management of large, one time projects
Used in Construction, Shipbuilding, Weapons Systems Development, etc.
Applies to uncertain technology projects
Applies to variable cost resource allocation
History of PERT/CPM - Navy/Booze Allen Hamilton Consultants

4. Introduction to Project Scheduling

5. Components of Project Control Systems
Predecessor was Gantt Charts
Horizontal Bar Charts - Time Lines
Tasks
Milestones
Flow Charts - Relationships Among All Tasks
Activities (tasks that take time and resources)
sequential vs. concurrent
Events (an accomplishment occurring at a specific point in time)

6. Project Characteristics
Single unit
Many related activities
Difficult production planning & inventory control
General purpose equipment
High labor skills

7. Examples of Projects

8. Examples of Projects
Building construction

© 1995 Corel Corp.

9. Examples of Projects Sheer to waist pantyhose Building construction
New product introduction
New! Improved!
19 · Nude Sandalfoot
Medium to Tall (B)
No nonsense
Sheer to waist pantyhose
© 1995 Corel Corp.

10. Examples of Projects Building construction New product introduction
Training seminar
© Corel Corp.

11. Examples of Projects Building construction New product introduction
Training seminar
Research project
© Corel Corp.

12. Project Management Activities

13. Project Management Activities

14. Project Management Activities
Planning
Objectives
Resources
Work break-down sched.
Organization

15. Project Management Activities
Planning
Objectives
Resources
Work break-down sched.
Organization
Scheduling
Project activities
Start & end times
Network

16. Project Management Activities
Planning
Objectives
Resources
Work break-down sched.
Organization
Scheduling
Project activities
Start & end times
Network
Controlling
Monitor, compare, revise, action

17. Project Planning

18. Project Planning Establishing objectives Defining project
Creating work breakdown structure
Determining resources
Forming organization
© 1995 Corel Corp.

19. Project Organization Often temporary structure
Uses specialists from entire company
Headed by project manager
Coordinates activities
Monitors schedule & costs
Permanent structure called ‘matrix organization’
Eng.
Eng.
Mkt.
Acct.
Mgr.
© 1995 Corel Corp.

20. Project Scheduling

21. Project Scheduling Sequencing activities
Identifying precedence relationships
Determining activity times & costs
Estimating material & worker requirements
Determining critical activities
PERT
Test J
Build M A M J
Design J F
Month
Activity
© 1995 Corel Corp.

22. Project Scheduling Techniques
Gantt chart
Critical Path Method (CPM)
Program Evaluation & Review Technique (PERT)
© T/Maker Co.

23. Gantt Chart

24. Gantt Chart

25. PERT & CPM Network techniques Developed in 1950’s
CPM by DuPont for chemical plants
PERT by U.S. Navy for Polaris missile
Consider precedence relationships & interdependencies
Each uses a different estimate of activity times

26. Questions Answered by PERT & CPM
Completion date?
On schedule? Within budget?
Probability of completing by ...?
Critical activities?
Enough resources available?
How can the project be finished early at the least cost?

27. PERT & CPM Steps Identify activities Determine sequence Create network
Determine activity times
Find critical path
Earliest & latest start times
Earliest & latest finish times
Slack

28. Constructing Networks

29. Graphical Representation of Events and Activities
Flow Charting - Uses Nodes and Arrows
Arrows
An arrow leads from tail to head directionally
Nodes
A node is represented by a circle
Node
Arrow

30. Activity On Node
Task is Represented by Node as the Completion of an Activity
Arrows Represent the Sequential Linkages Between Activities
For Example, Node 1 is Begin, Node 2 is Complete Task 1, Node 3 is Complete Task 2 1 2 3

31. Activity On Arrow
Task is Represented by an Arrow Bounded on Either End by a Node (Event)
Each Event is Identified by a Number
The Activity is Designated by the Leading Event Number and the Following Event Number - i.e. Activity 1 - 2 1 2

32. Designating Task Relationships
Sequential vs. Concurrent Activities 1 2 3
Sequential Task Relationship 1 2 3 4
Concurrent Task Relationships

33. Designating “DUMMY” Activities
Represented by Dashed Arrows
Show Sequential Relationships Among Tasks, but Take No time or Resources 2 1 4
Dummy Activity 2-3
indicates that both
Activities 1-2 and 2-3 must
be Completed before
beginning Activity 3-4 3

34. Network Terms

35. Network Terms
Project: Obtain a college degree (B.S.)

36. Network Terms
Project: Obtain a college degree (B.S.)
Register 1

37. 1 Network Terms Project: Obtain a college degree (B.S.) Register
Event (Node)

38. 1 Network Terms Project: Obtain a college degree (B.S.) Register
Attend class, study etc. 1
4 Years
Event (Node)

39. 1 Network Terms Project: Obtain a college degree (B.S.) Register
Attend class, study etc. 1
4 Years
Activity (Arrow)
Event (Node)

40. 1 2 Network Terms Project: Obtain a college degree (B.S.)
Receive diploma
Register
Attend class, study etc. 1 2
4 Years
Activity (Arrow)
Event (Node)
Event (Node)

41. Activity Relationships

42. Activity Relationships1

43. Activity Relationships2 A 1 B 3
A & B can occur concurrently

44. Activity Relationships
A must be done before C & D can begin 2 D A C 1 4 B 3

45. Activity Relationships2 D A C 1 4 B 3 E
B & C must be done before E can begin

46. Activity Relationships
A must be done before C & D can begin 2 D A C 1 4 B 3 E
A & B can occur concurrently
B & C must be done before E can begin

47. Dummy Activities
Activities are defined often by beginning & ending events
Example: Activity 2-3
Every activity must have unique pair of beginning & ending events
Computer programs get confused
Dummy activities maintain precedence
Consume no time or resources

48. Dummy Activities Example

49. Dummy Activities Example
2-3
Incorrect
1-2
3-4 1 2 3 4
2-3

50. Dummy Activities Example
2-3
Incorrect
1-2
3-4 1 2 3 4
2-3
Different activities; same designation

51. Dummy Activities Example
Incorrect
2-3
1-2
3-4 1 2 3 4
2-3
Correct
1-2
2-4
4-5 1 2 4 5
2-3 3
3-4: Dummy activity

52. Network Diagramming First Step in Project Management
Begins with a Work Breakdown
Lists the “WHAT’ of a Project
Begins with Finished Project
Consists of Tree Chart, with Each Branch Listing the “WHAT’s” at that Level
Then List Each Task that Must Be Completed to Accomplish the “WHAT”

53. Example Work Breakdown
House
Site Prep
Masonry
Carpentry
Finishing
Exterior
Walls
Footings
Piers
Chimney
Mixed
Concrete
Concrete
Poured
Forms
Removed
Forms Laid

54. Listing Of Activities Follows the “WHAT” with List of “HOW”
Each “WHAT” Results in Detailed List of the “Specific” Tasks Necessary to Accomplish the “WHAT”
Followed by Specification of Sequential and Concurrent Relationships Among Tasks
Results in Network Flow Diagram Representing the Tasks and Their Relationships

55. Activity Time Estimates
CPM - One Time Estimate per Activity
PERT - Three Time Estimates per Activity
a = Optimistic Time Estimate
m = Most Likely Time Estimate
b = Pessimistic Time Estimate
Can Calculate Activity Mean Time Estimate and Variance

56. PERT Time Estimates Activity Mean Time Estimate = te
Activity Variance Estimate = Sigmae
te = (a + 4m + b)/6
Sigmae = (b - a)/6
Can Use Central Limit Theorem to Estimate Project Time

57. Example Network Flow Diagram7 6 5 4 3 2 1 A G C I H E B J F

58. Example Activity Characteristicsb te
Sigmae
A /3
B /3
C /3
D /3
E /3
F /3
G /3
H /3
I /3
J /3

59. Example Network Flow Diagram
te =7 7 6 5 4 3 2 1
te =12
te =13
te =11
te =4
te =8
te =7
te =10
te =11
te =10

60. Early Start & Early Finish
The Early Start Time for an Activity Emanating from an Event is the Earliest Point in Time that an Activity can Begin
Determined by the Latest Early Finish of All Activities Terminating in an Event
The Early Finish for an Activity is the Sum of its Early Start Time and its te

61. Example Network Flow Diagram
ES=12
ES=31
te =7 7 6 5 4 3 2 1
te =12
ES=18
ES=0
te =4
te =11
ES=52
te =13
te =8
ES=42
ES=11
te =7
te =10
te =11
te =10

62. Late Start & Late Finish
The Late Finish Time for an Activity Terminating in an Event is the Point in Time that it can be Completed Without Delaying the Completion of the Project
Determined by Assigning to the LF the Value of the Earliest LS of all Activities Emanating from the Event
The Late Start for an Activity is it Late Finish minus its te

63. Example Activity Characteristicsb te
Sigmae ES LS EF LF / / / / / / / / / /

64. Example Network Flow Diagram With Critical Path
ES|LS|EF|LF
t2-5=7
12|24|19|31 2 5
t1-2=12
0|2|12|14
t5-6=11
31|31|42|42
t4-5=13
18|18|31|31
t2-4=4
12|14|16|18
t4-6=8
18|34 |26|42 4 1 7
t3-4=7
11|11|18|18
t1-3=11
0|0|11|11
t6-7=10
42|42|52|52 6 3
t3-6=10
11|32|21|42

65. SLACK Total Slack Free Slack Critical Path
The Length of Delay in an Activity that Won’t Delay the Completion of the Project - LF- EF or LS-ES
Free Slack
The Length of Delay in an Activity that Won’t Delay the Beginning of Another Activity
Critical Path
Activities with the Minimum Total Slack - Often Total Slack on Critical Path Activities = 0

66. Probabilistic Estimates
Use of te and Sigmae Allows One to Make Probabilistic Estimates of Completion Dates
By Summing the te‘s of the Activities on the Critical Path You Can Estimate the Duration of the Entire Project
By Summing the Variance (Sigmae2) of the Activities on the Critical Path, You Can estimate the Total Variance of the Critical Path and Make One-Sided Interval Estimates of Project Completion Times

67. Probabilistic Estimates Example
Sigmae
(Sigmae)2
/3 4/9
/3 36/9
/3 25/9
/3 49/9
/3 16/9
Variance = 130/9 = 14.4
Std Dev = 3.8
Probability that the Project Duration is Less than 60 days = Pr(T<60)
Same as the Probability that Z < (60-52)/3.8 = 2.1
Therefore: Pr(T<60) = Pr(Z<2.1) = (see App. A, H&R, p. 842)

68. PERT Probability Example
You’re a project planner for General Dynamics. A submarine project has an expected completion time of 40 weeks, with a standard deviation of 5 weeks. What is the probability of finishing the sub in 50 weeks or less?
© Corel Corp.

69. Converting to Standardized Variable

70. Converting to Standardized Variable
Assume project completion time follows a normal distribution.

71. Converting to Standardized Variable
Assume project completion time follows a normal distribution.
Normal Distribution

72. Converting to Standardized Variable
Normal Distribution
Standardized Normal Distribution

73. Converting to Standardized Variable
Normal Distribution
Standardized Normal Distribution

74. Obtaining the Probability

75. Obtaining the Probability
Standardized Normal Probability Table (Portion)
Probabilities in body

76. Obtaining the Probability
Standardized Normal Probability Table (Portion)
.97725
Probabilities in body

77. Critical Path Method Uses Deterministic Time Estimates for Activities
Also Estimates Cost of Resources Levels for Each Activity
Generally You Can increase the Resource Commitment and Reduce the Time Estimate for and Activity
Use CPM to Analyze How To Reduce the Critical Path Most Efficiently

78. Benefits & Limitations of PERT/CPM

79. Benefits of PERT/CPM Useful at many stages of project management
Mathematically simple
Use graphical displays
Give critical path & slack time
Provide project documentation
Useful in monitoring costs

80. Limitations of PERT/CPM
Clearly defined, independent, & stable activities
Specified precedence relationships
Activity times (PERT) follow beta distribution
Subjective time estimates
Over emphasis on critical path

81. Conclusion Explained what a project is
Summarized the 3 main project management activities
Drew project networks
Compared PERT & CPM
Determined slack & critical path
Computed project probabilities

82. BA 333 Operations Management
Project Management
PERT/CPM
Spring, 1998
THE END