cpm- pert.ppt
TRANSCRIPT
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Network Analysis :
CPM & PERT
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Introduction
Network analysis is one of the important tools for project management.
Whether major or minor a project has to be completed in a definite time
& at a definite cost.
The necessary information of any information can be represented as a
project network.
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Methodology Involved in Network Analysis
Describing the Project
Diagramming the network
Estimating the time of completion
Deterministic
estimates
Probabilistic
estimates
Monitoring the project progress
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Key terminology
Activity : All projects may be viewed as composed of activities. It is the
smallest unit of work consuming both time& resources that project
manager should schedule & control.
An activity is represented by an arrow in network diagram
The head of the arrow shows sequence ofactivities.
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Classification of activities
Predecessor activity: Activities that must be completed immediately priorto the start of another activity are called predecessor activities.
Successor activity: activities that cannot be started until one or more ofother activities are completed but immediately succeed them are called
successor activities.
Concurrent activities: activities that can be accomplished together areknown as concurrent activities.
Dummy activity: An activity which does not consume any resource butmerely depicts the dependence of one activity on other is called dummyactivity.
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Event
The beginning & end of an activities are called as events .
Events are represented by numbered circles called nodes.
i j
Event
start
Event
finish
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Path & Network
An unbroken chain of activity arrows connecting the initial event to some
other event is called a path.
A network is the graphical representation of logically & sequentially
connected arrows & nodes representing activities & events of a project . Itis a diagram depicting precedence relationships between different
activities.
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Application of network analysis
Construction industry
Manufacturing
Research development
Administration
Marketing planning
Inventory planning
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Advantages
Planning & controlling projects
Flexibility
Designation of responsibilities
Achievement of objective with least cost
Better managerial control
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Types of Events
Merge event
Burst event
Merge & Burst Event
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Guidelines for Network Construction
A complete network diagram should have one stand point & one finish
point.
The flow of the diagram should be from left to right.
Arrows should not be crossed unless it is completely unavoidable.
Arrows should be kept straight & curved or bent. Angle between arrows should as large as possible.
Each activity must have a tail or head event.. No two or more activities
may have same tail & head events.
Once the diagram is complete the nodes should be numbered from left to
right. It should then be possible to address each activity uniquely by its tail& head event.
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Example
Activity Predecessor
activity
A none
B none
C A
D A
E B
F C
G D & E
1
3
2
5
4
6
A
B
C
D
E
F
G
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Draw the network diagram for the following
Activity Predecessor
activity
A none
B A
C A
D B
E C
F D ,E
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1 2
3
4
5 6
A
B
C
D
E
F
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Basic Terminologies
Earliest start time ( EI) : This is the earliest possible time that an activity
can begin. All predecessor activities must be finished before an activity
can began.
Earliest finish time ( EJ) : This is the earliest possible time in which an
activity can be finished.
= earliest start time ( EI) + Duration of the activity ( TIJ)
Latest start time ( LI) : This is the latest time that an activity can began &
not delay the completion time of overall project.
= latest finish time ( LJ) duration of the activity ( TIJ)
Latest finish time ( LJ) : This is the latest time that an activity can befinished & not delay the completion time of the overall project
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Total project time : This is the shortest possible time in which
the project is completed.
Float : There are many activities where the maximum time
available to finish the activity is more than the time required
to complete the activity. The difference between the two
times is known as float available for the activity.
There are three types of float:
Total float : It is the spare time available when all preceding
activities occur at earliest possible times & all success dingactivities occur at latest possible times.
Total float = Latest start Earliest finish.
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Forward pass Method
Based on the fixed occurrence time of the initial network event , the forwardpass method yields the earliest start time & earliest finish times for each activity& indirectly earliest expected occurrence of each event.
The computation begins from the start node & move to the end node. Toaccomplish this , the forward pass computations start with an assumed earliestoccurrence time of zero for the initial project event E1 = 0
Earliest start time for activity ( I,j) is the earliest event time of the tail end eventESIJ = EI
Earliest finish time of the activity is the earliest start time of the activity plus the
duration of the activity. EFij= ES ij+ tij Earliest occurrence time of the event j is the maximum of the earliest finish times
of all the activities into that event.
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Backward Pass Method
The latest occurrence time specifies the time by which all the activities
entering into that event , must be completed without delaying the total
project.
These are computed by reversing the method of calculation used for
earliest event times.
Latest finish time of an activity is equal to the latest vent time j LFIJ= LJ.
Latest start time of an activity is given by latest completion time minus the
activity time .
LSIJ = LFIJ- tij
Latest event time for event is the minimum of the latest start time of allactivities originating from that event.
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1
25
3 4
6
16
30
15
12
20 15
16
10 3
Network Diagram
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Earliest Event Time
The total project time is the shortest time in which the project can be
completed & this is determined by sequence of activities on the critical
path. In order to calculate the total project time carry out the forward
pass.
Start from the left of the arrow of diagram
Give the first event the time 0
Proceed to each event in order & compute the earliest possible time at
which event can occur.
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1/ 0
2/165/38
3/20 4/35
6/51
16
30
15
12
20 15
16
10 3
Calculation of earliest
event time
0+16
0+20+10 0+20+15+3
0+16+15
Taking the
maximum one
0+20+15
0+ 30
38+ 12
35+16
To the earliest time of each immediately preceding event add
the duration of activity which connects it & selects the highest
of the values obtained.
Forwardpass
0+ 20
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Latest event time
Latest event time : carry out the backward pass
Start from right
Give to this event its earliest time i.e is 51 in this case
By subtracting the duration time for each corresponding job calculate the
latest possible occurrence time for any event , assuming that final event isfixed.
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1/ 0/0
2/16/245/38/39
3/20/204/35/35
6/51/51
16
30
15
12
20 15
16
10 3
Calculation of latest
event time
24-16
39-10
39-15
Taking the
minimum one
35-15
51-30
51-12
51-16
From the latest time of each immediately succeeding event ,
subtract the duration of the job which connects it & selects
the lowest value obtained.
Backwardpass
39-3
20-20
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Critical path
Those activities which contribute directly to the overall duration of the
project constitute critical activities, the critical activities form a chain
running through the network which is called critical path.
Critical event: the slack of an event is the difference between the latest &earliest events time. The events with zero slack time are called as critical
events.
Critical activities: The difference between latest start time & earliest start
time of an activity will indicate amount of time by which the activity canbe delayed without affecting the total project duration. The difference is
usually called total float. Activities with 0 total float are called as critical
activities
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Critical path
The critical path is the longest path in the network from the starting event
to ending event & defines the minimum time required to complete the
project.
The critical path is denoted by darker or double lines.
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1/ 0/0
2/16/245/38/39
3/20/204/35/35
6/51/51
16
30
15
12
20 15
16
10 3
Critical Path
The critical path lies along those jobs whose earliest & latest
times for the start & finish events are same & whose duration
times are equal to the difference between start & finish
events time.
Darker line is critical path
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Earliest start time : (2, 5) earliest time of event 2 16 days
Earliest finish time : ( 2, 5) earliest start time + duration of activity
EI + TIJ = 16 + 15 = 31days
Latest finish time : ( 2, 5) latest event time of finish event
39 days
Latest start time : ( 2, 5) latest finish time duration of activity
LJ - TIJ
39 15 = 24 days
Calculation of time estimates
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Job Duration Earliest starttime
Latest starttime
Earliestfinish
time
Latestfinish
time
(1,2) 16 0 8 16 24
(1,3) 20 0 0 20 20
(1,6) 30 0 21 30 51
(2,5) 15 16 24 31 39
(3,4) 15 20 20 35 35
(3,5) 10 20 29 30 39
(4,5) 3 35 36 38 39
(4,6) 16 35 35 51 51
(5,6) 12 38 39 50 51
Time estimations
Darker boxes indicate critical activities
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Types of float
Total float : The amount of time by which completion of an activity couldbe delayed beyond the earliest expected completion time withoutaffecting the overall project duration time.
Latest finish time earliest start time duration of an activity
Free float : This is concerned commencement of subsequent activity . Itmay be defined as time by which the completion of an activity can bedelayed beyond the earliest finish time without effecting the earliest startof a subsequent activity.
Independent Float : it may be defined as the amount of time by which thestart of an activity can be delayed without affecting the earliest start timeof any successor activity , assuming that preceding activity has finished atits latest finish time.
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Calculation of free & independent float
Head slack = LJ - EJ
Tail slack = LiEi
Total float = LiEi - tij
Free float = total float head slack
Independent float = total float tail slack
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PERT
PERT is designed for scheduling complex projects that involve many inter-
related tasks. it improves planning process because:
1. It forms planner to define the projects various components activities.
2. It provides a basis for normal time estimates & yet allows for somemeasure of optimism or pessimism in estimating the completion dates.
3. It shows the effects of changes to overall plan s they contemplated.
4. It provides built in means for ongoing evaluation of the plan.
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PERT system of 3 time estimates
Optimistic time ( a or t0) : is that time estimate of an activity when
everything is assumed to go as per plan. In other words it is the estimate
of minimum possible time which an activity takes in completion under
ideal conditions.
Most likely time (m or tm): the time which the activity will take most
frequently if repeated number of times.
Pessimistic time ( b or t): the unlikely but possible performance time if
whatever could go wrong , goes wrong in series. In other words it is thelongest time the can take.
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Expected time (te)
The a , m & b are combined statically to develop the expected time te.
te = a + 4m +b
6
Standard deviation of the time of the time required to complete the
project
b- a
6
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Steps in PERT
Develop list of activities.
A rough network for PERT is drawn.
Events are numbered from left to right.
Time estimates for each activity are obtained.
Expected time for each activity is calculated : a + 4m +b / 6
Using these expected times calculate earliest & latest finish & start times of activities.
Estimate the critical path.
Calculate variance of each activity by : ( b a)2/ 6
Using this estimate compute the probability of meeting a specified completion date by usingthe standard normal equation
Z = Due date expected date of completion
project variance
Where Z = number of standard deviations the due date lies from the mean or expected date.
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Activity Most optimistic
time ( a)
Most likely time
(m)
Most pessimistic
time (b)
1- 2 4 8 12
2 -3 1 4 7
2- 4 8 12 16
3 - 5 3 5 7
4 - 5 0 0 0
4 - 6 3 6 9
5 - 7 3 6 9
5 - 8 4 6 8
7 - 9 4 8 12
8 - 9 2 5 8
9 10 4 10 16
6 - 10 4 6 8
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Using the information given below determine the following
1. Expected task time & their variance
2. The earliest & the latest expected times to reach each event
3. The critical path
4. The probability of an event occurring at proposed completion date if
the original contract time of completing project is 48 days.
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Activity ( a) (m) (b) Expected time
te= a +4m +b /6
2= 1 ( b a)2
6
1- 2 4 8 12 8 1.78
2 -3 1 4 7 4 1
2- 4 8 12 16 12 1.78
3 - 5 3 5 7 5 0.44
4 - 5 0 0 0 0 0
4 - 6 3 6 9 6 1
5 - 7 3 6 9 6 1
5 - 8 4 6 8 6 0.44
7 - 9 4 8 12 8 1.78
8 - 9 2 5 8 5 1
9 10 4 10 16 10 4
6 - 10 4 6 8 6 0.44
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1/0/0 2/8/8
4/20/20
6/26/38
3/12/15
5/20/20
7/26/26
8/26/29
9/34/34
10/44/44
Network Diagram & critical path
8
12
4
5
0
6
6
8
5
6
6
10
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Te = 8 + 12 +0 +6 +8 +10 = 44 days
2 = 1.78 + 1.78 + 0 + 1 + 1.78 + 4 = 10.34e
= 3.216
Probability that project will be completed in 48 days
Z = T - Te
e
= 48 - 44
3.216
= 1.24 ( from normal distribution table ) 0.895
Therefore 89% is the probability that project will be
completed on its due date.
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Difference between PERT & CPM
PERT
A probability model with
uncertainty in activity
duration . The duration of
each activity is computed
from multiple time estimates
with a view to take into
account time uncertainty.
It is applied widely for
planning & schedulingresearch projects.
PERT analysis does not
usually consider costs.
CPM
A deterministic model with well
known activity times based upon the
past experience.
It is used for construction projects &
business problems.
CPM deals with cost of project
schedules & minimization.
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Limitations of PERT /CPM
Network diagrams should have clear starting & ending points , which are
independent of each other which may not be possible in real life.
Another limitation is that it assumes that manager should focus on critical
activities.
Resources will be available when needed for completion for an an activity
is again unreal.
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Difficulties
Difficulty in securing realistic time estimates.
The planning & implementation of networks requires trained staff.
Developing clear logical network is troublesome.