2 Construction Management and Planning Float Total Float is Calculated by Subtracting Early Start and Duration from the Activitys Late Finish Time An Activity that has Zero Total Float is a Critical Activity ID: 364364
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Slide1
In the name of Allah the Most Gracious the Most MercifulSlide2
2
Construction Management
and
PlanningSlide3
Float
Total Float is Calculated by Subtracting Early Start and Duration from the Activity’s Late Finish Time
An Activity that has Zero Total Float is a Critical Activity
An Activity’s Start may be Critical Even Though an Activity itself may not be Critical
Start Float may be Calculated by Subtracting an Activity’s Early Start Time from Its Late Start
TimeSlide4
Float
Finish Float is Calculated by Subtracting an Activity Early Finish Time from its Late Finish TimeSlide5
Project Scheduling
Probabilistic PERTSlide6
History of PERT
Project Evaluation and Review Technique (PERT)
U S Navy (1958) for the POLARIS missile program
Multiple task time estimates (probabilistic nature)
Activity-on-arrow network construction
Non-repetitive jobs (R & D work)6Slide7
PERT Probability Approach to Project Scheduling
Activity completion times are seldom known with certainty.
Completion time estimates can be estimated using the
Three Time Estimate approach
. In this approach, three time estimates are required for each activity:
a = an optimistic time to perform the activity
m = the most likely time to perform the activity
b = a pessimistic time to perform the activity Slide8
PERT
pessimistic time
(a) - the time the activity would take if things did not go well
most likely time
(
m) - the consensus best estimate of the activity’s durationoptimistic time (b) - the time the activity would take if things did go well8Slide9
3-Time Estimate Approach
Probability Distribution
With three time estimates, the activity completion time can be approximated by a
Beta distribution
.
Beta distributions can come in a variety of shapes:
a
m
b
b
a
m
m
a
bSlide10
Mean and Standard Deviation for Activity Completion Times
The best estimate for the mean is a weighted average of the three time estimates with weights 1/6, 4/6, and 1/6 respectively on a, m, and b.
Since most of the area is with the range from a to b (b-a), and since most of the area lies 3 standard deviations on either side of the mean (6 standard deviations total), then the standard deviation is approximated by Range/6.Slide11
The three assumptions imply that the overall project completion time is
normally
distributed, with:
The Project Completion Time Distribution
= Sum of the ’s
on the critical path
2
= Sum of the
2
’s
on the critical pathSlide12
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.12Slide13
Probability computation
13
Determine probability that project is completed within specified time
Z =
x -
where
= t
p
= project mean time
=
standard deviation
x = (proposed ) specified time Slide14
Normal Distribution of Project Time
14
=
t
p
Time
x
Z
ProbabilitySlide15
15
Immed. Optimistic Most Likely Pessimistic
Activity
Predec.
Time (Hr.
)
Time (Hr.)
Time (Hr.)
A -- 4 6 8
B -- 1 4.5 5
C A 3 3 3
D A 4 5 6
E A 0.5 1 1.5
F B,C 3 4 5
G B,C 1 1.5 5
H E,F 5 6 7
I E,F 2 5 8
J D,H 2.5 2.75 4.5
K G,I 3 5 7Slide16
16Slide17
PERT Example
17
Activity
Expected Time (μ) Variance (σ2)
(a + 4m + b)/6 [(b – a)/6]
2
A 6 4/9
B 4 4/9
C 3 0
D 5 1/9
E 1 1/36
F 4 1/9
G 2 4/9
H 6 1/9
I 5 1
J 3 1/9
K 5 4/9Slide18
18Slide19
19
σ
2
path
=
σ
2
A
+
σ
2
C
+
σ
2
F
+
σ
2
I
+
σ
2
K
= 4/9 + 0 + 1/9 + 1 + 4/9
= 2
σ
path
= 1.414
Mean project completion time = 23
Proposed completion time = 24
z
= (24 - 23)/
(24-23)/1.414 = .71
From the Standard Normal Distribution table:
P(z
<
.71) = .5 + .2612 = .7612Slide20
Using the PERT-CPM Template for Probabilistic Models
Instead of calculating
µ and
by hand, the Excel template may be used.
Instead of entering data in the
µ and columns, input the estimates for a, m, and b into columns C, D, and E.The template does all the required calculationsAfter the problem has been solved, probability analyses may be performed.Slide21
Enter a, m, b instead of
Call Solver
Click Solve
Go to PERT OUTPUT worksheetSlide22
Call Solver
Click SolveSlide23
To get a cumulative
probability, enter
a number hereSlide24
P(Project is completed in less than 180 days)