1. 1 3. M ODELING U NCERTAINTY IN C ONSTRUCTION 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 Uncertainty in Construction 3.2 Deterministic Analysis 3.4 PERT Network Analysis and Modeling Uncertainty 3.5 CPM Network Analysis using Monte Carlo Sampling

2. 2 3.1 U NCERTAINTY IN C ONSTRUCTION Uncertainty in construction can occur in many places: –productivity; –environmental conditions; –supply of information; –availability of labor; etc...

3. 3 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.

4. 4 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.

5. 5 3.2 D ETERMINISTIC A NALAYSIS 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:

6. 6 Probability Density Project Duration Figure 1: Different Degrees of Certainty about Expected Project Duration Likely variation from expected duration is small Likely variation from expected duration is large Both cases have the same expected duration 95% probabilities The greater uncertainty means more likely extend beyond completion deadline Planned Completion date

7. 7 Figure 2: Simple Network with Uncertain Activity Durations ‘a’ ‘c’ ‘b’ ‘d’‘e’ 1 day 5 days 10 days 5 days 10 days 3 days 5 days 10 days 15 days 20 days Observed durations from past projects Second Major Problem: optimistic bias.

8. 8 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: ActivityActivityDuration between ‘b’‘c’‘a’ and ‘d’ 5 days 10 days 5 days 10 days Therefore, on average it will take (5+10+10+10)/4 = 8.75 days

9. 9 3.4 PERT N ETWORK A NALYSIS AND M ODELING U NCERTAINTY 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.

10. 10 ‘a’ ‘b’ ‘c’ ‘d’ Each activity has three durations associated with it: 10 most likely duration 5 optimistic duration (<=0.05p) 15 pessimistic duration (<=0.95p) 9 10 11 7 9 10 1 2 3

11. 11 Project duration only takes uncertainty into account along the critical path: ‘a’ ‘b’ ‘c’ ‘d’ 9 10 11 7 9 10 1 2 3 5 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

12. 12 Probability Density Project Duration PERT derived project duration distribution Actual project duration distribution (broader) Deterministic & PERT expected project duration Actual expected project duration (longer)

13. 13 3.5 CPM N ETWORK A NALYSIS U SING M ONTE C ARLO S AMPLING 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.

14. 14 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 Computer to Process all Possibilities 120.002 m secs 1010241.024 secs 2533,554,4329.32 hours 501.12 x 10 15 35,678 years 1001.27 x 10 30 4.02 x 10 19 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

15. 15 ‘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... 12 mean duration 1.5 standard deviation 19 1.1 21 2.2 18 1.7

16. 16 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;

17. 17 Probability Density Project Duration Monte Carlo Project Duration Distribution (say 100 + samples) Actual project duration distribution