Transcript PowerPoint

3. MODELING UNCERTAINTY IN
CONSTRUCTION
Objective:
To develop an understanding of the impact of
uncertainty on the performance of a project, and to
introduce planning tools for handling uncertainty:
Summary:
3.1
3.2
3.4
3.5
Uncertainty in Construction
Deterministic Analysis
PERT Network Analysis and Modeling Uncertainty
CPM Network Analysis using Monte Carlo Sampling
1
3.1 UNCERTAINTY IN
CONSTRUCTION
Uncertainty in construction can occur in
many places:
–
–
–
–
productivity;
environmental conditions;
supply of information;
availability of labor; etc...
2
This lack of knowledge makes it difficult to
accurately estimate:
– project costs;
– project duration;
In turn, this complicates management tasks
such as the following:
– determining an appropriate bid;
– budgetary control;
– comparison of the cost or time efficiency of
alternative construction methods.
3
Uncertainty is a lack of knowledge about the
likely outcome or requirement of some
aspect of a project:
– can reduce uncertainty by analyzing the
situation in more detail, however, this is
limited:
• limited theory defining cause-effect relationships
between key project variables;
• performance of computing hardware and software;
• limited resources available to undertake the study,
such as money, time and expertise.
4
3.2 DETERMINISTIC ANALAYSIS
Usually, uncertainty is ignored, and a
deterministic stand is adopted:
– two major problems:
• no indication as to whether actual performance
will vary much from expected performance;
• leads to optimistic bias in performance
assessment.
Will discuss these points in turn:
5
Probability Density
Likely variation from
expected duration
is small
Both cases have the
same expected
duration
95% probabilities
Likely variation from
expected duration
is large
Project
Duration
The greater uncertainty means more
likely extend beyond completion deadline
Planned
Completion
date
6
Figure 1: Different Degrees of Certainty about Expected Project Duration
Second Major Problem: optimistic bias.
‘b’
‘a’
5 days
10 days
1 day
‘d’
‘e’
3 days
5 days
10 days
15 days
20 days
‘c’
5 days
10 days
Observed durations from past projects
Figure 2: Simple Network with Uncertain Activity Durations 7
If use deterministic analysis:
– ‘b’ takes 7.5 days (mean)
– ‘c’ takes 7.5 days (mean)
– thus the duration between ‘a’ and ‘d’ = 7.5 days
In reality, there are four possible outcomes:
Activity
‘b’
Activity
‘c’
Duration between
‘a’ and ‘d’
5 days
5 days
5 days
5 days
10 days
10 days
10 days
5 days
10 days
10 days
10 days
10 days
8
Therefore, on average it will take (5+10+10+10)/4 = 8.75 days
3.4 PERT NETWORK ANALYSIS
AND MODELING UNCERTAINTY
PERT (Program Evaluation and Review
Technique):
– a method (similar to deterministic CPM)
developed to take account of uncertainty;
– quite popular in construction;
– it includes an incorrect assumption that
makes it only slightly more useful than the
deterministic approach.
9
‘b’
9 10 11
‘a’
5
10 15
most likely
duration
optimistic
duration
(<=0.05p)
‘d’
‘c’
1 2 3
7 9 10
pessimistic
duration
(<=0.95p)
Each activity has three durations associated with it:
10
‘b’
9 10 11
‘a’
‘d’
5 10 15
1 2 3
‘c’
duration = 22 days
7 9 10
Project duration only takes uncertainty into
account along the critical path:
• The calculated project duration is therefore the same
as in deterministic analysis
• The calculated variance in the project duration is
also under estimated
11
Probability Density
PERT derived
project duration
distribution
Deterministic & PERT
expected project duration
Actual project
duration distribution
(broader)
Project
Duration
Actual expected
project duration (longer)
12
3.5 CPM NETWORK ANALYSIS
USING MONTE CARLO SAMPLING
Monte Carlo based CPM
– a method where a random sample of
possible outcomes are considered;
– increasing popularity in construction;
– its accuracy increases with an increase in
the number of samples considered
– will accurately estimate expected duration
and variance.
13
• Consider a project where each activity has
just two possible durations, d1 and d2.
activity
d1 d2
Number of
Activities
Number of
Possible Outcomes
Time for a Computer
to Process all Possibilities
1
2
0.002 m secs
10
1024
1.024 secs
25
33,554,432
9.32 hours
50
1.12 x 1015
35,678 years
100
1.27 x 1030
4.02 x 1019 years
>>> age of universe
• Clearly, evaluating all possible outcomes is not feasible!
• So just select a random sample of possible outcomes.
• The most popular way of selecting the samples is Monte
Carlo sampling
14
‘b’
19 1.1
‘a’
12 1.5
standard
mean
duration deviation
‘d’
‘c’
18 1.7
21 2.2
Each activity will have some distribution of possible
durations, for example:
• Normal distribution with a mean and standard deviation;
• Discrete distribution; many others...
15
The approach recognizes that different paths could be critical
in different samples:
• Consequently, the estimate of project duration is accurate;
• Also, the estimate of variance in project duration is accurate;
• We have additional information:
- probabilities of activities becoming critical (critical indices);
16
- probability distributions for amounts of float on each activity;
Probability Density
Actual project
duration distribution
Monte Carlo
Project Duration
Distribution
(say 100 +
samples)
Project
Duration
17