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3. MODELING UNCERTAINTY IN

CONSTRUCTIONObjective:

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 Uncertainty in Construction

3.2 Deterministic Analysis

3.4 PERT Network Analysis and Modeling Uncertainty

3.5 CPM Network Analysis using Monte Carlo Sampling

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3.1 UNCERTAINTY IN

CONSTRUCTION

Uncertainty in construction can occur in many places:– productivity;– environmental conditions; – supply of information;– availability of labor; etc...

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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.

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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.

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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:

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Probability Density

ProjectDuration

Figure 1: Different Degrees of Certainty about Expected Project Duration

Likely variation fromexpected durationis small

Likely variation fromexpected durationis large

Both cases have thesame expectedduration

95% probabilities

The greater uncertainty means more likely extend beyond completion deadline

PlannedCompletiondate

7Figure 2: Simple Network with Uncertain Activity Durations

‘a’

‘c’

‘b’

‘d’ ‘e’

1 day

5 days10 days

5 days10 days

3 days 5 days10 days15 days20 days

Observed durations from past projects

Second Major Problem: optimistic bias.

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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:

ActivityActivity ActivityActivity Duration betweenDuration between‘‘b’b’ ‘c’‘c’ ‘a’ and ‘d’‘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

Therefore, on average it will take (5+10+10+10)/4 = 8.75 days

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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.

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‘a’

‘b’

‘c’

‘d’

Each activity has three durations associated with it:

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most likelyduration

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optimisticduration

(<=0.05p)

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pessimisticduration

(<=0.95p)

9 10 11

7 9 10

1 2 3

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Project duration only takes uncertainty into account along the critical path:

‘a’

‘b’

‘c’

‘d’9 10 11

7 9 10

1 2 35 10 15

• The calculated project duration is therefore the same as in deterministic analysis

duration = 22 days

• The calculated variance in the project duration is also under estimated

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Probability Density

ProjectDuration

PERT derivedproject durationdistribution

Actual project duration distribution(broader)

Deterministic & PERTexpected project duration

Actual expected project duration (longer)

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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.

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activity

d1 d2

• Consider a project where each activity has just two possible durations, d1 and d2.

Number of Activities

Number of Possible Outcomes

Time for a Computerto 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

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‘a’

‘b’

‘c’

‘d’

Each activity will have some distribution of possible durations, for example:

• Normal distribution with a mean and standard deviation;• Discrete distribution; many others...

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meanduration

1.5

standarddeviation

19 1.1

21 2.2

18 1.7

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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);- probability distributions for amounts of float on each activity;

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Probability Density

ProjectDuration

Monte CarloProject DurationDistribution(say 100 + samples)

Actual project duration distribution