Project Scheduling: PERTCPM

1
Project Scheduling PERT/CPM
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

3
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

4
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

5
(No Transcript)
6
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.

7
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

8
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

9
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

10
The Basics of Using PERT/CPM
11
The Project Network Model
12
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

13
Slack Time
14
Project Network
15
Example
16
Partial Network
How should activity K be added?
17
This works, but there is a better way.
18
(No Transcript)
19
Earliest Time for an Event
20
Earliest Time for Each Event
Expected time to complete the project is 44 days.
21
Latest Time for an Event
22
Latest Time for Each Event
Expected time to complete the project is 44 days.
23
Slack Time
24
Critical Activities
25
Probabilistic Time Estimation
26

• 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

27
Transforming Plan to Network
28

• 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

29
GANTT Chart
30
Gantt Charts
Henry Laurence Gantt (1861-1919)
31

• 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

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

33
Planning and Scheduling
34
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

35
Making a Gantt chart

• Step 1 list the tasks in the project

36
Making a Gantt chart

• Step 2 add task durations

37
Making a Gantt chart

• Step 3 add dependencies (which tasks cannot
  start before another task finishes)

38
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

39
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.
40

• 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 2311.521 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

41

• 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
  days slack.

42

• Critical tasks, by definition, can have NO slack.
• Tip
• If ever asked Can task Xs duration be changed
  without affecting the end date of the project?,
  if it is a critical task the answer is always NO!

43
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

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

45
Limitations to CPM/PERT

• Clearly defined, independent and stable
  activities
• Specified precedence relationships
• Subjective time estimates
• Over emphasis on critical paths

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

47
Probabilistic PERT/CPM
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)

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

50
Normal Distribution Table for Negative Values of Z
51
Normal Distribution Table for Positive Values of Z
Z Probability --------------------- 0.0
0.5000 0.1 0.5398 0.2 0.5793 0.3 0.6179
0.4 0.6554 0.5 0.6915 0.6 0.7257 0.7
0.7580 0.8 0.7881 0.9 0.8159 1.0 0.8413
1.1 0.8643 1.2 0.8849 1.3 0.9032 1.4
0.9192 1.5 0.9332
Z Probability --------------------- 1.6
0.9452 1.7 0.9554 1.8 0.9641 1.9
0.9713 2.0 0.9772 2.1 0.9821 2.2
0.9861 2.3 0.9893 2.4 0.9918 2.5
0.9938 2.6 0.9953 2.7 0.9965 2.8
0.9974 2.9 0.9981 3.0 0.9987 gt3.0 1
52
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
  T7days. First, work out a value (calles the
  normal variate) Z, as follows
• Z(T- TE )/ ?(7-5)/21
• Read off the Normal Distribution Tables, the
  probability for Z1. We get the value 0.8413.
  Thus the probability that the project will take 7
  days or less is 0.8413
• 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
  1-0.84130.1587

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 Z11.2, P10.8849
• Z21.3, P20.9039
• Use the interpolation formula
• PP1Z-Z1 (P2-P1)
• Z2-Z1
• Therefore at Z1.275,
• P0.8849 1.275 -1.2 (0.9039-0.8849) 0.8992
• 1.3-1.2

54
Crash and Normal Times and Costs
Activity Cost
Crash
Crash Cost - Normal Cost
34,000 33,000 32,000 31,000 30,000
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
55
CRASH COSTING

• 1. Find critical path.
• 2. Find cheapest act. in critical path
• 3. Reduce time until
• a. Cant 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.

56
Time-Cost Trade-Off
10-9
57
Beta Probability Distribution with Three Time
Estimates
Probability
Probability of 1 in 100 (b) Occuring
Probability of 1 in 100 (a) Occuring
Optimistic Time (a)
Most Likely Time (m)
Pessimistic Time (b)
Activity Time
58
Time Estimates (in weeks) for project
Optimistic a
Most Probable- m
Pessimistic b
Expected Time t (a 4m b)/6
Variance (b - a)/62
Activity
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
2 3 2 4 4 3 5 2
Total 25 weeks
59
Probability of Project Meeting the Deadline
Project Standard Deviation, ?T

Project Variance
Due Date - Expected Completion Date
Z

?T
16 - 15


0.57
1.76
.57 Standard Deviations
Probability (T ? 16 Weeks) is 71.6
16 Weeks
15 Weeks
Time
60
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.

61
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.

62
Example How Are We Doing?

• Consider the following PERT network

63
Example How Are We Doing?

• Earliest/Latest Times
• Activity ES EF LS
  LF Slack
• A 0 9
  0 9 0
• B 0 8
  5 13 5
• C 0 10
  7 17 7
• D 8
  11 22 25 14
• E 8 12
  13 17 5
• F 9 13
  13 17 4
• G 9 12
  9 12 0
• H 12 17
  12 17 0
• I 12 16
  21 25 9
• J 17 25
  17 25 0

64
Example How Are We Doing?

• Activity Status (end of eleventh week)
• Activity Actual Cost
  Complete
• A 6,200
  100
• B 5,700
  100
• C 5,600
  90
• D
  0 0
• E 1,000
  25
• F 5,000
  75
• G 2,000
  50
• H
  0 0
• I
  0 0
• J
  0 0

65
Example How Are We Doing?

• Cost Status Report
• (Assuming a budgeted cost of 6000 for each
  activity)
• Activity Actual Cost Value
  Difference
• A 6,200 (1.00)x6000
  6000 200
• B 5,700 (1.00)x6000
  6000 - 300
• C 5,600
  (.90)x6000 5400 200
• D 0
  0 0
• E 1,000 (.25)x6000
  1500 - 500
• F 5,000
  (.75)x6000 4500 500
• G 2,000
  (.50)x6000 3000 -1000
• H 0
  0 0
• I 0
  0 0
• J 0
  0 0
• Totals 25,500
  26,400 - 900