1. Network Planning Methods Example PERT & CPM

2. Terms Used in Project Management
Activity : A certain amount of work or task required in the project
Activity duration: In CPM the best estimate of time to complete an activity . In PERT the expected time or average time to complete an activity
Critical activity : An activity that has no room for schedule slippages : if it slips the entire the entire project completion will slip. An activity with zero slack

3. Critical path: The chain of critical activities for the project
Critical path: The chain of critical activities for the project .The longest path through the network
Dummy activity :An activity that consumes no time but shows precedence among activities
Earliest finish (EF): The earliest that an activity can finish from the beginning of the project
Earliest start ( ES): The earliest that an activity can start from the beginning of the project

4. Event :A beginning , a completion point ,or a milestone accomplishment within the project . An activity begins and ends with events
Latest finish (LF) : The latest that an activity can finish from the beginning of the project
Latest start (LS) :The latest that an activity can start from the beginning of the project
Most likely time ( t m) : The time for completing the activity that is is the consensus best estimate, used in PERT

5. Optimistic Time (to): The time for completing an activity if all goes well : used in PERT
Pessimistic Time (tp): The time for completing an activity if bad luck is encountered : used in PERT
Predecessor activity : An activity that must occur before another activity .
Slack : The amount of time that an activity or group of activities can slip without causing a delay in the completion of the project
Successor activity : An activity that must occur after another activity

6. Conventions used in drawing network diagrams (Arrows & Circles )
Activity on Arrow (AOA) : The activities are denoted by Arrows and events are denoted by circles
Activity on Node(AON) : Activities are denoted by circles(or nodes) and the precedence relation ships between activities are indicated by arrows

7. AOA Project Network for House3 2 1 4 6 7 5
Lay foundation
Design house and obtain financing
Order and receive materials
Dummy
Finish work
Select carpet
Select paint
Build house
AON Project Network for House 1 3 2 4 5 6 7
Start
Design house and obtain financing
Order and receive materials
Select paint
Select carpet
Lay foundations
Build house
Finish work

8. Situations in network diagramB C
A must finish before either B or C can start A B C
both A and B must finish before C can start D C B A
both A and C must finish before either of B or D can start A C B D
Dummy
A must finish before B can start
both A and C must finish before D can start

9. Backward Pass Forward Pass EF= ES + t Latest Start Time (LS)
Earliest Start Time (ES)
earliest time an activity can start
ES = maximum EF of immediate predecessors
Earliest finish time (EF)
earliest time an activity can finish
earliest start time plus activity time
EF= ES + t
Backward Pass
Latest Start Time (LS)
Latest time an activity can start without delaying critical path time
LS= LF - t
Latest finish time (LF)
latest time an activity can be completed without delaying critical path time
LS = minimum LS of immediate predecessors

10. CPM analysis Draw the CPM network
Analyze the paths through the network
Determine the float for each activity
Compute the activity’s float
float = LS - ES = LF - EF
Float is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project
Find the critical path is that the sequence of activities and events where there is no “slack” i.e.. Zero slack
Longest path through a network
Find the project duration is minimum project completion time

11. PERT / CPM Network planning methods that generate:
Relationship between activities
Project duration
Critical path
Slack for non – critical activities
Crashing (cost / time trade-offs)
Resource usage

12. St. Paul’s Hospital Immediate Activity Description Predecessor(s)
A Select administrative and medical staff.
B Select site and do site survey.
C Select equipment.
D Prepare final construction plans and layout.
E Bring utilities to the site.
F Interview applicants and fill positions in nursing,
support staff, maintenance, and security.
G Purchase and take delivery of equipment.
H Construct the hospital.
I Develop an information system.
J Install the equipment.
K Train nurses and support staff. — A B C D
E,G,H
F,I,J

13. St. Paul’s Hospital Immediate Activity Description Predecessor(s)
AON Network
Finish
Start A B C D E F G H I J K
A Select administrative and medical staff.
B Select site and do site survey.
C Select equipment.
D Prepare final construction plans and layout.
E Bring utilities to the site.
F Interview applicants and fill positions in nursing,
support staff, maintenance, and security.
G Purchase and take delivery of equipment.
H Construct the hospital.
I Develop an information system.
J Install the equipment.
K Train nurses and support staff. — A B C D
E,G,H
F,I,J

14. St. Paul’s Hospital Completion Time Immediate
Finish
Start K 9 I 15 F 10 C D E 24 G 35 H 40 J 4 A 12 B
Immediate
Activity Description Predecessor(s)
A Select administrative and medical staff.
B Select site and do site survey.
C Select equipment.
D Prepare final construction plans and layout.
E Bring utilities to the site.
F Interview applicants and fill positions in nursing,
support staff, maintenance, and security.
G Purchase and take delivery of equipment.
H Construct the hospital.
I Develop an information system.
J Install the equipment.
K Train nurses and support staff. — A B C D
E,G,H
F,I,J

15. St. Paul’s Hospital Path Expected Time (wks) A-I-K 36 A-F-K 31
A-C-G-J-K 70
B-D-H-J-K 72
B-E-J-K 46
St. Paul’s Hospital
Critical Path
Completion Time
Finish
Start K 9 I 15 F 10 C D E 24 G 35 H 40 J 4 A 12 B
Immediate
Activity Description Predecessor(s)
A Select administrative and medical staff.
B Select site and do site survey.
C Select equipment.
D Prepare final construction plans and layout.
E Bring utilities to the site.
F Interview applicants and fill positions in nursing,
support staff, maintenance, and security.
G Purchase and take delivery of equipment.
H Construct the hospital.
I Develop an information system.
J Install the equipment.
K Train nurses and support staff. — A B C D
E,G,H
F,I,J

16. Critical Path The longest path in the network
Defines the shortest time project can be completed
Critical path activity delay project delay

17. Earliest Start and Earliest Finish
Begin at starting event and work forward
ES is earliest start
ES = 0 for starting activities
ES = Maximum EF of all predecessors for non-starting activities
EF is earliest finish
EF = ES + Activity time ES LS EF LF
Activity Name
Activity Duration

18. Earliest Start / Earliest Finish15 A 12 F 10 K 9 C 10 G 35
Start
Finish B 9 D 10 H 40 J 4 E 24

19. Earliest Start / Earliest Finish15
Earliest finish time
Earliest start time A 12 F 10 K 9 C 10 G 35
Start
Finish
Critical path B 9 D 10 H 40 J 4 E 24

20. Latest Start and Latest Finish
Begin at ending event and work backward
LF is latest finish
LF = Maximum EF for ending activities
LF = Minimum LS of all successors for non-ending activities
LS is latest start
LS = LF – Activity time
Activity Name ES EF LS LF
Activity Duration

21. Latest Start / Latest Finish15
Latest start time
Latest finish time A 12 F 10 K 9 C 10 G 35
Start
Finish
Critical path B 9 D 10 H 40 J 4
What do you notice about ES/LS & EF/LF? E 24

22. What do you notice about ES/LS & EF/LF?
For Activity A
ES = 0
LS = 2
Meaning: Due to some reason of if activity A is not started at 0 weeks but 1, 2 or 3 weeks, even then completion of project is not delayed
For Activity B
LS = 0
Meaning
Any delay in start would delay project completion.

23. Activity Slack Analysis15
Slack = LS – ES or
Slack = LF – EF
Latest start time
Latest finish time A 12 F 10 K 9 C 10 G 35
SlackK = 63 – 63 = 0 or
SlackK = 72 – 72 = 0
Start
Finish
Critical path B 9 D 10 H 40 J 4 E 24

24. Activity Slack Analysis15
Node Duration ES LS Slack A B C D E F G H I J K
Latest start time
Latest finish time A 12 F 10 K 9 C 10 G 35
Start
Finish
Critical path B 9 D 10 H 40 J 4
Activity slack = maximum delay time Critical path activities have zero slack E 24

25. Activity Slack How much would we like to reduce
the time for activity B? C 15 A 5
Finish
Start B 20 D 10

26. PERT tp + 4 tm + to tp - to 6 Mean (expected time): te =
PERT is based on the assumption that an activity’s duration follows a probability distribution instead of being a single value
Three time estimates are required to compute the parameters of an activity’s duration distribution:
pessimistic time (tp ) - the time the activity would take if things did not go well
most likely time (tm ) - the consensus best estimate of the activity’s duration
optimistic time (to ) - the time the activity would take if things did go well
Mean (expected time): te =
tp + 4 tm + to 6
Variance: Vt =2 =
tp - to 2

27. PERT analysis Draw the network.
Analyze the paths through the network and find the critical path.
The length of the critical path is the mean of the project duration probability distribution which is assumed to be normal
The standard deviation of the project duration probability distribution is computed by adding the variances of the critical activities (all of the activities that make up the critical path) and taking the square root of that sum
Probability computations can now be made using the normal distribution table.

28. Probability computation
Determine probability that project is completed within specified time
Z =
x -  
where  = tp = project mean time
 = project standard mean time
x = (proposed ) specified time

29. Normal Distribution of Project Time
 = tp
Time x Z
Probability

30. PERT Example Immed. Optimistic Most Likely Pessimistic
Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.) A B
C A
D A
E A
F B,C
G B,C
H E,F
I E,F
J D,H
K G,I

31. PERT Example
PERT Network D A E H J C B I K F G

32. Activity Expected Time Variance
PERT Example
Activity Expected Time Variance
A /9
B /9 C
D /9
E /36
F /9
G /9
H /9 I
J /9
K /9

33. PERT Example Activity ES EF LS LF Slack A 0 6 0 6 0 *criticalB
C * D E
F * G H
I * J
K *

34. PERT Example
Vpath = VA + VC + VF + VI + VK
= 4/ / /9
= 2
path =
z = ( )/(24-23)/1.414 = .71
From the Standard Normal Distribution table:
P(z < .71) = =

35. PROJECT COST

36. Cost consideration in project
Project managers may have the option or requirement to crash the project, or accelerate the completion of the project.
This is accomplished by reducing the length of the critical path(s).
The length of the critical path is reduced by reducing the duration of the activities on the critical path.
If each activity requires the expenditure of an amount of money to reduce its duration by one unit of time, then the project manager selects the least cost critical activity, reduces it by one time unit, and traces that change through the remainder of the network.
When there is more than one critical path, each of the critical paths must be reduced.
If the length of the project needs to be reduced further, the process is repeated.

37. Project Crashing
Crashing
reducing project time by expending additional resources
Reduction in activity duration by any change in its resources, resource use, method or material is referred to as crashing of the activity
Crash time
an amount of time an activity is reduced
Crash cost
cost of reducing activity time
Goal
reduce project duration at minimum cost

38. Activity crashing Crash cost Crashing activity
Activity cost
Activity time
Crashing activity
Crash time
Crash cost
Slope = crash cost per unit time
Normal Activity
Normal time
Normal cost

39. Time-Cost Relationship
Crashing costs increase as project duration decreases
Indirect costs increase as project duration increases
Reduce project length as long as crashing costs are less than indirect costs
Time-Cost Tradeoff
cost
time
Min total cost = optimal project time
Direct cost
Total project cost
Indirect cost

40. Project Crashing example1 12 2 8 4 3 5 6 7

41. Time Cost data Activity Normal time Normal cost Rs Crash time
Crash cost Rs
Allowable crash time
slope 1 2 3 4 5 6 7 12 8
3000
2000
4000
50000
500
1500 9
2800
3500
6000
71000
1100
21000
400
700
8000
7000
75000

42. Project duration = 36 From….. To….. Project duration = 3112 2 8 3 4 5 6 7
Project duration = 36
From….. 1 7 2 8 3 4 5 6
R400 12
Project
duration = 31
Additional cost = R2000
To…..

43. GANTT CHART

44. Gantt Chart Gantt Chart was developed by…
Henry Laurence Gantt ( ) was a mechanical engineer and management consultant who is most famous for developing the ‘Gantt chart’ in the 1910s. These Gantt charts were employed on major infrastructure projects including the Hoover Dam and Interstate highway system. He refined production control and cost control techniques.

45. Example of Gantt Chart Month 0 2 4 6 8 10 | | | | | 1 3 5 7 9 Activity
| | | | |
Activity
Design house and obtain financing
Lay foundation
Order and receive materials
Build house
Select paint
Select carpet
Finish work
Month

46. Gantt Chart Activities in Buy a House