1. Project Scheduling: PERT/CPM
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2. Characteristics of a Project
A unique, one-time effort
Requires the completion of a large number of interrelated activities
Resources, such as time and/or money, are limited
Typically has its own management structure
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3. M. En C. Eduardo Bustos Farias
Project Management
A project manager is appointed to head the project management team
The team members are drawn from various departments and are temporarily assigned to the project
The team is responsible for the planning, scheduling and controlling the project to its completion
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4. M. En C. Eduardo Bustos Farias
PERT and CPM
PERT: Program Evaluation and Review Technique
CPM: Critical Path Method
Graphically displays project activities
Estimates how long the project will take
Indicates most critical activities
Show where delays will not affect project
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5. M. En C. Eduardo Bustos Farias
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6. M. En C. Eduardo Bustos Farias
Project Schedule
Converts action plan into operating timetable
Basis for monitoring & controlling project activity
More important for projects than for day-to-day operations
projects lack continuity of on-going functions
more complex coordination needed
One schedule for each major task level in WBS
Maintain consistency among schedules
Final schedule reflects interdependencies, departments.
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7. M. En C. Eduardo Bustos Farias
Network Model
Serves as a framework for:
planning, scheduling, monitoring, controlling
interdependencies and task coordination
when individuals need to be available
communication among departments and functions needed on the project
Identifies critical activities and slack time
Reduces interpersonal conflict
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8. M. En C. Eduardo Bustos Farias
PERT / CPM
PERT:
Program Evaluation and Review Technique
estimates probability of on-time completion
CPM:
Critical Path Method
deterministic time estimates
control both time and cost
Similar purposes, techniques, notation
Both identify critical path and slack time
Time vs. performance improvement
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9. M. En C. Eduardo Bustos Farias
PERT / CPM Definitions
Activity: task or set of tasks
uses resources and takes time
Event: result of completing an activity:
has identifiable end state at a point in time
Network: combined activities & events in a project
Path: series of connected activities
Critical: activities, events, or paths which, if delayed, will delay project completion
Critical path: sequence of critical activities from start to finish
Node / Arrow (Arc) - PERT / CPM notation
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10. The Basics of Using PERT/CPM
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11. The Project Network Model
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12. M. En C. Eduardo Bustos Farias
PERT / CPM Notations
EOT:
earliest occurrence time for event
time required for longest path leading to event
LOT: latest occurrence time for event
EST: earliest starting time for activity
LST: latest starting time for activity
Critical time: shortest time in which the project can be completed
Notation: AOA, AON, dummy activities
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13. M. En C. Eduardo Bustos Farias
Slack Time
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14. M. En C. Eduardo Bustos Farias
Project Network
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15. M. En C. Eduardo Bustos Farias
Example
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16. M. En C. Eduardo Bustos Farias
Partial Network
How should activity K be added?
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17. M. En C. Eduardo Bustos Farias
This works, but there is a better way.
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18. M. En C. Eduardo Bustos Farias
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19. Earliest Time for an Event
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20. Earliest Time for Each Event
Expected time to complete the project is 44 days.
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21. Latest Time for an Event
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22. Latest Time for Each Event
Expected time to complete the project is 44 days.
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23. M. En C. Eduardo Bustos Farias
Slack Time
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24. M. En C. Eduardo Bustos Farias
Critical Activities
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25. Probabilistic Time Estimation
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26. M. En C. Eduardo Bustos Farias
Expected completion time:
Based on optimistic, pessimistic, most likely
Take weighted average of the 3 times
TE = (a + 4m + b)/6
Uncertainty = variance (range of values)
Probability of completion of project in desired time D
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27. Transforming Plan to Network
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28. M. En C. Eduardo Bustos Farias
Know activities which comprise project
Determine predecessor and successor activities
Time and resources for activities
Interconnections depend on technical interdependencies
Expected completion time
as soon as possible versus as late as possible
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29. M. En C. Eduardo Bustos Farias
GANTT Chart
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30. Gantt Charts Henry Laurence Gantt (1861-1919) Metodos Cuantitativos
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31. M. En C. Eduardo Bustos Farias
Planned and actual progress
for multiple tasks on horizontal time scale
easy to read, easy to construct
effective monitoring and control of progress
requires frequent updating
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32. Components of GANTT Chart
Activities - scheduled and actual
Precedence relationships
Milestones (identifiable points in project)
usually represents reporting requirements
usually corresponds to critical events
Can add budget information
Does not show technical interdependencies
Need PERT network to interpret, control, and compensate for delays
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33. Planning and Scheduling
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34. M. En C. Eduardo Bustos Farias
Gantt Basics
Basically, a timeline with tasks that can be connected to each other
Note the spelling!
It is not all-capitals!
Can be created with simple tools like Excel, but specialised tools like Microsoft Project make life easier
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35. M. En C. Eduardo Bustos Farias
Making a Gantt chart
Step 1 – list the tasks in the project
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36. M. En C. Eduardo Bustos Farias
Making a Gantt chart
Step 2 – add task durations
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37. M. En C. Eduardo Bustos Farias
Making a Gantt chart
Step 3 – add dependencies (which tasks cannot start before another task finishes)
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38. M. En C. Eduardo Bustos Farias
Notes
The arrows indicate dependencies.
Task 1 is a predecessor of task 2 – i.e. task 2 cannot start before task 1 ends.
Task 3 is dependent on task 2. Task 7 is dependent on two other tasks
Electrics, plumbing and landscaping are concurrent tasks and can happen at the same time, so they overlap on the chart. All 3 can start after task 4 ends.
Painting must wait for both electrics and plumbing to be finished.
Task 9 has zero duration, and is a milestone
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39. M. En C. Eduardo Bustos Farias
Making a Gantt chart
Step 4 – find the critical path
The critical path is the sequence of tasks from beginning to end that takes the longest time to complete.
It is also the shortest possible time that the project can be finished in.
Any task on the critical path is called a critical task.
No critical task can have its duration changed without affecting the end date of the project.
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40. M. En C. Eduardo Bustos Farias
MS Project can work out the critical path for you!
The length of the critical path is the sum of the lengths of all critical tasks (the red tasks 1,2,3,4,5,7) which is = 10.5 days.
In other words, the minimum amount of time required to get all tasks completed is 10.5 days
The other tasks (6,8) can each run over-time before affecting the end date of the project
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41. M. En C. Eduardo Bustos Farias
The amount of time a task can be extended before it affects other tasks is called slack (or float).
Both tasks 6 and 8 can take one extra day before they affects a following task, so each has one day’s slack.
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42. M. En C. Eduardo Bustos Farias
Critical tasks, by definition, can have NO slack.
Tip:
If ever asked Can task X’s duration be changed without affecting the end date of the project?, if it is a critical task the answer is always NO!
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43. M. En C. Eduardo Bustos Farias
Benefits of CPM/PERT
Useful at many stages of project management
Mathematically simple
Give critical path and slack time
Provide project documentation
Useful in monitoring costs
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44. Advantages of PERT/CPM
useful at several stages of project management
straightforward in concept, and not mathematically complex
uses graphical displays employing networks to help user perceive relationships among project activities
critical path and slack time analyses help pinpoint activities that need to be closely watched
networks generated provide valuable project documentation and graphically point out who is responsible for various project activities
applicable to a wide variety of projects and industries
useful in monitoring not only schedules, but costs as well
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45. Limitations to CPM/PERT
Clearly defined, independent and stable activities
Specified precedence relationships
Subjective time estimates
Over emphasis on critical paths
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46. Limitations of PERT/CPM
project activities must be clearly defined, independent, and stable in their relationships
precedence relationships must be specified and networked together
time activities in PERT are assumed to follow the beta probability distribution -- this may be difficult to verify
time estimates tend to be subjective, and are subject to fudging by managers
there is inherent danger in too much emphasis being placed on the critical path
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47. Probabilistic PERT/CPM
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48. Mean and Standard Deviation of Project Duration
Once the expected time te for all activities has been computed, proceed to use te in place of the single activity duration in CPM to work out the critical path and the project duration
The resulting project duration is the mean project duration TE
We also need to work out the standard deviation of the project duration  as follows:
Project Duration = (Summation of i2 f all the activities on the critical path)
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49. Probability of Different Project Durations
From statistics, once we know the mean project duration, TE, and the standard deviation of the project duration,  we can work out the probability that the project duration will be shorter than any specific time, T (i.e. the project will take T days or less) through the following formula:
Z=(T- TE )/  , where Z is the quantity called the Normal variate
Knowing Z, we can read off the probability from Normal Distribution Tables which are provided in nest slides
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50. Normal Distribution Table for Negative Values of Z
Probability
<3.0
-1.5
3.0
-1.4
-2.9
-1.3
-2.8
-1.2
-2.7
-1.1
-2.6
-1.0
-2.5
-0.9
-2.4
-0.8
-2.3
-0.7
-2.2
-0.6
-2.1
-0.5
-2.0
-0.4
-1.9
-0.3
-1.8
-0.2
-1.7
-0.1
-1.6
0.0
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51. Normal Distribution Table for Positive Values of Z
Z | Probability
0.0 |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1.0 |
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
Z | Probability
1.6 |
1.7 |
1.8 |
1.9 |
2.0 |
2.1 |
2.2 |
2.3 |
2.4 |
2.5 |
2.6 |
2.7 |
2.8 |
2.9 |
3.0 |
>3.0| 1
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52. M. En C. Eduardo Bustos Farias
Example
Consider a project with TE = 5days and =2 days.If we wish to find out the probability that the project will take 7 days or less. Thus T=7days. First, work out a value (calles the normal variate) Z, as follows:
Z=(T- TE )/ =(7-5)/2=1
Read off the Normal Distribution Tables, the probability for Z=1. We get the value Thus the probability that the project will take 7 days or less is
If we need to find the probability that the project takes more than 7 days, we make use of the fact that:
Probability that project takes more than x days= 1-Probability that project takes x days or less
Probability that project takes more than 7 days= 1-Probability that project takes 7 days or less = =0.1587
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53. Interpolating from the Normal Distribution Table
In the previous example, the ‘Z’ value was 1.0 and could be read off directly. If you had a value like 1.01, you could still round it off to 1.0
However there will be instances when you will get a value like 1.275, in which case you will need to interpolate from the table
From the table Z1=1.2, P1=0.8849
Z2=1.3, P2=0.9039
Use the interpolation formula:
P=P1+Z-Z1 *(P2-P1)
Z2-Z1
Therefore at Z=1.275,
P= * ( ) =
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54. Crash and Normal Times and Costs
Activity
Cost
Crash
$34,000
$33,000
$32,000
$31,000
$30,000
Crash Cost - Normal Cost
Crash Cost/Week =
Normal Time - Crash Time
Crash
Cost
$34,000 - $30,000 =
3 - 1
$4,000 =
= $2,000/Week
2 Weeks
Normal
Normal
Cost 1 2 3
Time (Weeks)
Crash Time
Normal Time
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55. M. En C. Eduardo Bustos Farias
CRASH COSTING
1. Find critical path.
2. Find cheapest act. in critical path
3. Reduce time until:
a. Can’t be reduced
b. Another path becomes critical
c. Increase in direct costs exceeds savings from shortening project
4. Return to Step 1, as long as savings.
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56. M. En C. Eduardo Bustos Farias
Time-Cost Trade-Off
Cost
Time
Costs of Crashing
Indirect/Penalty Costs
Total Costs
10-9
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57. Beta Probability Distribution with Three Time Estimates
Probability of
1 in 100
(a) Occuring
Probability of
1 in 100
(b) Occuring
Optimistic
Time
(a)
Most
Likely
Time
(m)
Pessimistic
Time
(b)
Activity Time
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58. Time Estimates (in weeks) for project
Variance =
b - a 6 ( ) 2
t =
a + 4m + b 6
Optimistic a
Most
Probable- m
Pessimistic b
Expected Time
t = [(a + 4m + b)/6]
Variance
[(b - a)/6]2
Activity A B C D E F G H 1 2 3 2 3 4 3 4 6 7 9 11 2 3 4 5
3 - 1 6 ( ) 4 36 = 2
4 - 2 6 ( ) 4 36 = 2
3 - 1 6 ( ) 4 36 = 2
6 - 2 6 ( ) 16 36 = 2
7 - 1 6 ( ) 36 = 2
9 - 1 6 ( ) 64 36 = 2
11 - 3 6 ( ) 64 36 = 2
3 - 1 6 ( ) 4 36 = 2
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Total 25 weeks

59. Probability of Project Meeting the Deadline
Project Standard
Deviation, T =
Project Variance
Due Date - Expected Completion Date Z = T = =
0.57
1.76
.57 Standard Deviations
Probability
(T  16 Weeks)
is 71.6% 15
Weeks 16
Weeks
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Time

60. M. En C. Eduardo Bustos Farias
PERT/Cost
PERT/Cost is a technique for monitoring costs during a project.
Work packages (groups of related activities) with estimated budgets and completion times are evaluated.
A cost status report may be calculated by determining the cost overrun or underrun for each work package.
Cost overrun or underrun is calculated by subtracting the budgeted cost from the actual cost of the work package.
For work in progress, overrun or underrun may be determined by subtracting the prorated budget cost from the actual cost to date.
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61. M. En C. Eduardo Bustos Farias
PERT/Cost
The overall project cost overrun or underrun at a particular time during a project is determined by summing the individual cost overruns and underruns to date of the work packages.
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62. Example: How Are We Doing?
Consider the following PERT network:
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63. Example: How Are We Doing?
Earliest/Latest Times
Activity ES EF LS LF Slack A B C D E F G H I J
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64. Example: How Are We Doing?
Activity Status (end of eleventh week)
Activity Actual Cost % Complete
A $6,
B ,
C , D
E ,
F ,
G , H I J
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65. Example: How Are We Doing?
Cost Status Report
(Assuming a budgeted cost of $6000 for each activity)
Activity Actual Cost Value Difference
A $6, (1.00)x6000 = $200
B , (1.00)x6000 =
C , (.90)x6000 = D
E , (.25)x6000 =
F , (.75)x6000 =
G , (.50)x6000 = H I J
Totals $25, $26, $- 900
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