1. Lecture 09
Project Management
ISE Dept.-IU
Office: Room 508

2. Chapter Outline 13.1 Introduction 13.2 Project Scheduling: PERT/CPM
Work Breakdown Structure (WBS)
Gantt Chart
PERT/CPM Terminology
PERT/CPM Procedure
Drawing PERT/CPM Network
Example (General Foundry)
Activity Times
How to Find Critical Path
Probability of Project Completion
13.3 Project Monitoring and Controlling: PERT/Cost
Budgeting
Controlling
Appendix: Normal Distribution Table

3. Introduction Project: a combination of Resources Money Manpower etc.
to finish a set of pre-determined tasks in a specified time.
Project Management: set of principles and tools for
Defining
Planning
Executing
Controlling
Completing a PROJECT
A project is a series of tasks (jobs) performed sequentially or in parallel aiming to achieve an important goal, and requiring a significant amount of resources and time
Project management is the planning, scheduling, and controlling of those activities that must be performed to achieve project objectives.
Series of actions to achieve a result”
A project is a sequence of unique, complex, and connected activities having one goal or purpose and that must be completed by a specific time, within budget, and according to specifications.

4. Why Project Management?
Introduction
Why Project Management?
Organize your approach
Generate a credible schedule
Track progress and control your project
Identify where to focus your efforts
Identify problems early – before they are crises
Saves your TIME….MONEY

5. Introduction
The first step in planning and scheduling a project is to develop the work breakdown structure
Time, cost, resource requirements, predecessors, and people required are identified for each activity
Then a schedule for the project can be developed:
the program evaluation and review technique (PERT) and
the critical path method (CPM)
to help plan, schedule, monitor, and control projects
PERT used three time estimates to develop a probabilistic estimate of completion time
CPM was a more deterministic technique
They have become so similar they are commonly considered one technique, PERT/CPM
Series of actions to achieve a result”

6. Historical Evolution Gantt Chart
Henry Laurence Gantt, ( ): a mechanical engineer and management consultant, developed the Gantt chart in the 1910s.
Gantt charts were employed on major infrastructure projects including the Hoover Dam and Interstate highway system

7. The USS George Washington.
Historical Evolution
CPM and PERT
Critical Path Method (CPM,1957) was developed jointly by representatives of Du Pont and Remington-Rand.
Program Evaluation and Review Technique (PERT,1958) was developed jointly by representatives of the United States Navy and the management consulting firm of Booze, Allen, and Hamilton.
The USS George Washington.
Ballistic Missile Project included more than:
250 prime contractors
9,000 subcontractors.
70,000 different activities
PERT bringing the Polaris missile submarine to combat readiness approximately two years ahead of the originally scheduled completion date
In the late 1950s, two methods for managing projects emerged concurrently: PERT and CPM

8. Work Breakdown Structure
1. Project
2. Major tasks in the project
3. Subtasks in the major tasks
4. Activities (or work packages) to be completed
When work is broken down into its components it is easier to understand what resources are needed and how to proceed. In addition, when work is broken down into its components then milestones can be set and work progress can be monitored. Finally, breaking work down allows us to recognize the sequence with which work must be done so that it is completed at the earliest possible time and under budget.

9. Gantt Charts Time on horizontal axis,
Activities on vertical axis. Each bar per activity
Length of bar = required activity time
Left end of bar at Earliest Start Time
Activity
Activity 1
Activity 2
Milestone
day 1 day 2 day Time

10. Terminology
Activity
A task or a certain amount of work required in the project
Requires time to complete
Dummy Activity
Indicates only precedence relationships
Does not require any time of effort
Event
Signals the beginning or ending of an activity
Designates a point in time
Network
Shows the sequential relationships among activities using nodes and arrows
Path
A connected sequence of activities leading from the starting event to the ending event
Critical Path
The longest path (time); determines the project duration
Critical Activities
All of the activities that make up the critical path

11. Terminology
For an activity, there are 4 types of quantities must be considered
Earliest Start Time (ES)
The earliest that an activity can begin; assumes all preceding activities have been completed
ES = 0 for starting activities
ES = Maximum EF of all predecessors for non-starting activities
Earliest Finish Time (EF)
EF = ES + activity time
Latest Finish Time (LF)
The latest that an activity can finish and not change the project completion time
LF = Maximum EF for ending activities
LF = Minimum LS of all successors for non-ending activities
Latest Start Time (LS)
LS = LF - activity time
Begin at starting event and work forward
Begin at ending event and work backward

12. PERT/CPM Procedure Six Steps
Define the project and all of its significant activities or tasks
Develop the relationships among the activities and decide which activities must precede others
Draw the network connecting all of 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
Identifying precedence relationships
Sequencing activities
Determining activity times & costs
Estimating material & worker requirements
Determining critical activities
The critical path is important since any delay in these activities can delay the completion of the project

13. Drawing the PERT/CPM Network
There are two common techniques for drawing PERT/CPM networks
Activity-on-node (AON) where the nodes represent activities
One node represents the start of the project, one node for the end of the project, and nodes for each of the activities
The arcs are used to show the predecessors for each activity
Activity-on-arc (AOA) where the arcs are used to represent the activities

14. Drawing the PERT/CPM Network
AON
Activity Relationships
S precedes T, which precedes U.
S: predecessor of T
U: successor of T S T U S T U
S and T must be completed before U can be started.

15. Drawing the PERT/CPM Network
AON
Activity Relationships T U S
T and U cannot begin until S has been completed. S T U V
U and V can’t begin until both S and T have been completed.

16. Drawing the PERT/CPM Network
AON
Activity Relationships S T U V
U cannot begin until both S and T have been completed; V cannot begin until T has been completed. S T V U
T and U cannot begin until S has been completed and V cannot begin until both T and U have been completed.

17. General Foundry Example of PERT/CPM
General Foundry, Inc.: to install air pollution control
equipment in 16 weeks
Activities and immediate predecessors for G.F. Inc.
ACTIVITY
DESCRIPTION
IMMEDIATE PREDECESSORS A
Build internal components — B
Modify roof and floor C
Construct collection stack D
Pour concrete and install frame E
Build high-temperature burner F
Install control system G
Install air pollution device
D, E H
Inspect and test
F, G
Draw the network.

18. Activity Times CPM assigns just one time estimate to each activity and
this is used to find the critical path
PERT employs a probability distribution based on three time
estimates for each activity
The time estimates in PERT are
Optimistic time (a) = time an activity will take if everything goes as well as possible (a small probability (say, 1/100) of this occurring)
Pessimistic time (b) = time an activity would take assuming very unfavorable conditions. (a small probability of this occurring)
Most likely time (m) = most realistic time estimate to complete the activity

19. Activity Times
PERT often assumes time estimates follow a beta prob. distribution
To find the expected activity time (t),
the beta distribution weights the estimates:
To compute the dispersion or
variance of activity completion time:

20. Activity Times Time estimates (weeks) for General Foundry ACTIVITY
OPTIMISTIC, a
MOST PROBABLE, m
PESSIMISTIC, b
EXPECTED TIME, t = [(a + 4m + b)/6]
VARIANCE, [(b – a)/6]2 A 1 2 3
4/36 B 4 C D 6
16/36 E 7
36/36 F 9
64/36 G 11 5 H 25

21. Gantt Chart

22. Find the Critical Path
General Foundry’s network with expected activity times
ACTIVITY t
ES EF
LS LF
ACTIVITY
IMMEDIATE PREDECESSOR
EXPECTED TIME A — 2 B 3 C D 4 E F G
D, E 5 H
F, G
A 2
C 2
H 2
E 4
B 3
D 4
G 5
F 3
Start
Finish

23. ES and EF Times 2 4 2 4 8 8 3 7 13 ACTIVITY t ES EF LS LF
Early Finish Time = Early Start Time + Activity Time A C 2 2 4 E
Starting Activity 8
ES(G)= Max[EF(D), EF(E)] D G 13

24. LS and LF Times C 2 F 3 2 4 4 7 2 4 10 13 LF(C)=Min[LS(E), LS(F)] E 4
ACTIVITY t
ES EF
LS LF
LS and LF Times
Late Start Time = Late Finish Time - Activity Time C F 2 4 4 7 2 4 10 13
LF(C)=Min[LS(E), LS(F)] E H 4 8 13 15 15
Finish 4 8 13 G 8 13 8 13

25. How to Find the Critical Path (General Foundry’s example)
Early Finish Time = Early Start Time + Activity Time
ACTIVITY t
ES EF
LS LF
At the start of the project we set the time to zero
Thus ES = 0 for both A and B
A 2
C 2
F 3 2 2 4 4 7
E 4
H 2
Start 4 8 13 15
Finish
B 3
D 4
G 5 3 3 3 3 7 8 13
Project’s EF = => LF = 15

26. How to Find the Critical Path (General Foundry’s example)
ACTIVITY t
ES EF
LS LF
LS and LF Times
Late Start Time = Late Finish Time - Activity Time
A 2
C 2
F 3 2 2 2 2 4 4 7 2 2 4 10 13
E 4
H 2
Start 4 8 13 15
Finish 4 8 13 15
B 3
D 4
G 5 3 3 3 3 7 8 13 1 4 4 8 8 13

27. How to Find the Critical Path
Slack time that each activity:
Slack = LS – ES, or Slack = LF – EF
Activities with no slack time are called critical activities and they are said to be on the critical path
ACTIVITY
EARLIEST START, ES
EARLIEST FINISH, EF
LATEST START, LS
LATEST FINISH, LF
SLACK, LS – ES
ON CRITICAL PATH? A 2
Yes B 3 1 4 No C D 7 8 E F 10 13 6 G H 15
Slack time is the amount of time that the activities can delay but do not delay the finish time of the whole project.

28. How to Find the Critical Path
General Foundry’s critical path
A 2
0 2
C 2
2 4
H 2
13 15
E 4
4 8
B 3
0 3
1 4
D 4
3 7
G 5
8 13
F 3
4 7
10 13
Start
Finish

29. Probability of Project Completion
The critical path analysis determine the expected project completion time of 15 weeks
But variation in activities on the critical path can affect overall project completion
Project variance = ∑
variances of activities on the critical path
ACTIVITY
VARIANCE A
4/36 B C D
16/36 E
36/36 F
64/36 G H
Project variance = 4/36 + 4/ / /36 + 4/36
= 112/36
= 3.111
We assume activity times are independent and total project completion time is normally distributed

30. Probability of Project Completion
Determine the probability that a project is completed within a specified period of time:
using standard normal distribution
where
m = tp = project mean time (or expected date of completion)
s = project standard deviation
x = proposed project time (or due date)
Z = number of standard deviations x is from mean
x - m
Z = s 30

31. P(T<16) = P(z < (16 -15)/1.76) = P(z < 0.57) = 0.716
What’s probability that project will finish before 16 weeks?
P(T<16) = P(z < (16 -15)/1.76) = P(z < 0.57) = 0.716
From Appendix A we find the probability of associated with this Z value
That means there is a 71.6% probability this project can be completed in 16 weeks or less
What’s probability that project will finish from 13 to 18 weeks?
P(13<T<18) = P((13 -15)/1.76 <z < (18 -15)/1.76)
= P( <z < 1.7)

32. What PERT Was Able to Provide
From PERT, G.F. Inc. knows
The project’s expected completion date is 15 weeks
There is a 71.6% chance that the equipment will be in place within the 16-week deadline
Five activities (A, C, E, G, H) are on the critical path
Three activities (B, D, F) are not critical but have some slack time built in
A detailed schedule of activity starting and ending dates has been made available

33. PERT/COST
PERT does not consider the very important factor of project: COST
PERT/Cost allows a manager to plan, schedule, monitor, and control cost and time
Budgeting:
The overall approach in the budgeting process of a project is to determine how much is to be spent every week or month
Four steps for budgeting
- Identifying the cost for each activity
- Creating work package (a logical collection of activities)
if available
- Converting cost per activity to cost per time period
- Determining how much spending for each time period in order to finish project.

34. Budgeting for General Foundry
Example 3 (text book – p. 534)
Consider General Foundry project. The data: expected processing time, ES, LS, budget for each activity are given in the following Table
Activity costs for General Foundry
ACTIVITY
EARLIEST START, ES
LATEST START, LS
EXPECTED TIME, t
TOTAL BUDGETED COST ($)
BUDGETED COST PER WEEK ($) A 2
22,000
11,000 B 1 3
30,000
10,000 C
26,000
13,000 D 4
48,000
12,000 E
56,000
14,000 F 10 G 8 5
80,000
16,000 H 13
8,000
Total
308,000

35. Budgeting for General Foundry
Early Start budgeted cost for General Foundry
WEEK
ACTIVITY 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
TOTAL A 22 B 30 C 26 D 48 E 56 F G 16 80 H
308
Total per week 21 23 25 36
Total to date 42 65 90
126
162
198
212
228
244
260
276
292
300

36. Budgeting for General Foundry
Late start budgeted cost for General Foundry
WEEK
ACTIVITY 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
TOTAL A 22 B 30 C 26 D 48 E 56 F G 16 80 H
308
Total per week 21 23
Total to date 32 55 78
104
130
156
182
198
214
240
266
292
300

37. Using PERT/COST approach, we are easily to control project implementation in terms of time and cost.
Example: at 6th week, project manager review the progress and found that:
ACTIVITY
TOTAL BUDGETED COST ($)
PERCENT OF COMPLETION
VALUE OF WORK COMPLETED ($) A
22,000
100 B
30,000 C
26,000 D
48,000 10
4,800 E
56,000 20
11,200 F
6,000 G
80,000 H
16,000
Questions:
Project is on schedule?
What is value of work completed?
Are there any cost overrun?

38. The overall project is overrun budget now!
Using these formula:
Value of Work Completed = % of Work completed x activity budget
Difference = Actual Cost – Value of Work completed
If Difference > 0  Activity/Project is overrun
If Difference < 0  Activity/Project is under control
The overall project is overrun budget now!
ACTIVITY
TOTAL BUDGETED COST ($)
PERCENT OF COMPLETION
VALUE OF WORK COMPLETED ($)
ACTUAL COST ($)
ACTIVITY DIFFERENCE ($) A
22,000
100
20,000
–2,000 B
30,000
36,000
6,000 C
26,000 D
48,000 10
4,800
1,200 E
56,000 20
11,200
8,800 F
4,000 G
80,000 H
16,000
Total
100,000
112,000
12,000
Overrun

39. Project Crashing
Projects will sometimes have deadlines that are impossible to meet using normal procedures
By using exceptional methods it may be possible to finish the project in less time than normally required
However, this usually increases the cost of the project
Reducing a project’s completion time is called crashing

40. Project Crashing
Crashing a project starts with using the normal time to create the critical path
The normal cost is the cost for completing the activity using normal procedures
If the project will not meet the required deadline, extraordinary measures must be taken
The crash time is the shortest possible activity time and will require additional resources
The crash cost is the price of completing the activity in the earlier-than-normal time

41. Four Steps to Project Crashing
Find the normal critical path and identify the critical activities
Compute the crash cost per week (or other time period) for all activities in the network using the formula
Crash cost/Time period =
Crash cost – Normal cost
Normal time – Crash time

42. Four Steps to Project Crashing
Select the activity on the critical path with the smallest crash cost per week and crash this activity to the maximum extent possible or to the point at which your desired deadline has been reached
Check to be sure that the critical path you were crashing is still critical. If the critical path is still the longest path through the network, return to step 3. If not, find the new critical path and return to step 2.

43. General Foundry Example
General Foundry has been given 14 weeks instead of 16 weeks to install the new equipment
The critical path for the project is 15 weeks
What options do they have?
The normal and crash times and costs are shown in Table 13.9
Crash costs are assumed to be linear and Figure shows the crash cost for activity B
Crashing activities B and A will shorten the completion time to 14 but it creates a second critical path
Any further crashing must be done to both critical paths

44. General Foundry Example
Normal and crash data for General Foundry
ACTIVITY
TIME (WEEKS)
COST ($)
CRASH COST PER WEEK ($)
CRITICAL PATH?
NORMAL
CRASH A 2 1
22,000
23,000
1,000
Yes B 3
30,000
34,000
2,000 No C
26,000
27,000 D 4
48,000
49,000 E
56,000
58,000 F
30,500
500 G 5
80,000
86,000 H
16,000
19,000
3,000
Table 13.9

45. General Foundry Example
Crash and normal times and costs for activity B
Activity Cost
Time (Weeks)
$34,000 –
$33,000 –
$32,000 –
$31,000 –
$30,000 – –
| | | |
Crash
Crash Cost/Week =
Crash Cost – Normal Cost
Normal Time – Crash Time
= = $2,000/Week
$4,000
2 Weeks
$34,000 – $30,000
3 – 1 =
Crash Cost
Normal
Normal Cost
Figure 13.11
Crash Time
Normal Time

46. Project Crashing with Linear Programming
Linear programming is another approach to finding the best project crashing schedule
We can illustrate its use on General Foundry’s network
The data needed are derived from the normal and crash data for General Foundry and the project network with activity times

47. Project Crashing with Linear Programming
General Foundry’s network with activity times
A 2
H 2
B 3
D 4
G 5
Finish
Start
C 2
E 4
F 3
Figure 13.12

48. Project Crashing with Linear Programming
The decision variables for the problem are
XA = EF for activity A
XB = EF for activity B
XC = EF for activity C
XD = EF for activity D
XE = EF for activity E
XF = EF for activity F
XG = EF for activity G
XH = EF for activity H
Xstart = start time for project (usually 0)
Xfinish = earliest finish time for the project

49. Project Crashing with Linear Programming
The decision variables for the problem are
Y = the number of weeks that each activity is crashed
YA = the number of weeks activity A is crashed and so forth
The objective function is
Minimize crash cost = 1,000YA + 2,000YB + 1,000YC + 1,000YD + 1,000YE + 500YF + 2,000YG + 3,000YH

50. Project Crashing with Linear Programming
Crash time constraints ensure activities are not crashed more than is allowed
This completion constraint specifies that the last event must take place before the project deadline
YA ≤ 1
YB ≤ 2
YC ≤ 1
YD ≤ 1
YE ≤ 2
YF ≤ 1
YG ≤ 3
YH ≤ 1
Xfinish ≤ 12
This constraint indicates the project is finished when activity H is finished
Xfinish ≥ XH

51. Project Crashing with Linear Programming
Constraints describing the network have the form
EF time ≥ EF time for predecessor + Activity time
EF ≥ EFpredecessor + (t – Y), or
X ≥ Xpredecessor + (t – Y)
For activity A, XA ≥ Xstart + (2 – YA) or XA – Xstart + YA ≥ 2
For activity B, XB ≥ Xstart + (3 – YB) or XB – Xstart + YB ≥ 3
For activity C, XC ≥ XA + (2 – YC) or XC – XA + YC ≥ 2
For activity D, XD ≥ XB + (4 – YD) or XD – XB + YD ≥ 4
For activity E, XE ≥ XC + (4 – YE) or XE – XC + YE ≥ 4
For activity F, XF ≥ XC + (3 – YF) or XF – XC + YF ≥ 3
For activity G, XG ≥ XD + (5 – YG) or XG – XD + YG ≥ 5
For activity G, XG ≥ XE + (5 – YG) or XG – XE + YG ≥ 5
For activity H, XH ≥ XF + (2 – YH) or XH – XF + YH ≥ 2
For activity H, XH ≥ XG + (2 – YH) or XH – XG + YH ≥ 2

52. Appendix: Normal Distribution Table

54. Homework
13.14, 13.15, 13.17, 13.18, 13.19