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Construction planning and operations

Opportunity and risk management

How schedule and cost risks can be quantified: terms, approach and Monte Carlo simulation on the example project.

Updated on September 29, 2026Contact: Robert Hagmann

Opportunity, risk, uncertainty

Not every uncertainty is a risk. Deviations can be assessed when their impact and probability can be estimated: positive ones as opportunities, negative ones as risks.1, 2 This distinction is the starting point of every robust risk analysis.

Uncertainty
deviation unknownpositive deviation expectednegative deviation expected
IgnoranceAmbiguityOpportunityRisk
Impact knownnonot fullyyesyes
Probability of occurrence knownnonoyes (objective or subjective)yes (objective or subjective)
Fig. 1 Terminology of uncertainty.Adapted from Hofstadler and Kummer (2017)2

Approach

We work in four steps, following the risk management process of ISO 31000.3

  1. Identify

    Capture opportunities and risks for schedule, cost and quality with the project team.

  2. Assess

    Estimate impact and probability, qualitatively or through distributions.

  3. Simulate

    Aggregate individual risks in the schedule or estimate into an overall statement.

  4. Control

    Define measures and contingencies and monitor their effect as the project progresses.

Probabilistic simulation

In Monte Carlo simulation4 every activity receives a range instead of a single value. Many simulated construction sequences yield the distribution of the result and with it a statement on how likely a date or budget will be met. In the simulation below every duration follows a PERT distribution between half and twice its most likely value.5 It can be re-run directly in your browser.

Initial data: example project.

Frequency distribution of total effort

Number of simulation runs per class (class width 500 h)

010020030016,000 h20,000 h24,000 h28,000 h32,000 h36,000 hPlan valueP50P80P90
≤ P80 > P80

Cumulative distribution (probability of not exceeding)

Probability that total effort does not exceed a value

0 %25 %50 %75 %100 %16,000 h20,000 h24,000 h28,000 h32,000 h36,000 hPlan valueP50P80P90

Convergence of the median

Running median over the first 1,000 simulation runs

21k23k25k27k02505007501,000
Show values as table
Class [h]Runscumulative
15,500 - 16,00010 %
16,000 - 16,50010 %
16,500 - 17,000160 %
17,000 - 17,500291 %
17,500 - 18,000682 %
18,000 - 18,500814 %
18,500 - 19,0001246 %
19,000 - 19,5001399 %
19,500 - 20,00016913 %
20,000 - 20,50018316 %
20,500 - 21,00023121 %
21,000 - 21,50021325 %
21,500 - 22,00023030 %
22,000 - 22,50024835 %
22,500 - 23,00027440 %
23,000 - 23,50025745 %
23,500 - 24,00027251 %
24,000 - 24,50025256 %
24,500 - 25,00022260 %
25,000 - 25,50021565 %
25,500 - 26,00020569 %
26,000 - 26,50019973 %
26,500 - 27,00022177 %
27,000 - 27,50017080 %
27,500 - 28,00016584 %
28,000 - 28,50014987 %
28,500 - 29,00012289 %
29,000 - 29,50010891 %
29,500 - 30,0009193 %
30,000 - 30,5008195 %
30,500 - 31,0006996 %
31,000 - 31,5004397 %
31,500 - 32,0004698 %
32,000 - 32,5003499 %
32,500 - 33,0002399 %
33,000 - 33,5001899 %
33,500 - 34,00014100 %
34,000 - 34,5008100 %
34,500 - 35,0006100 %
35,000 - 35,5002100 %
35,500 - 36,0001100 %
Fig. 2 Interactive Monte Carlo simulation with frequency distribution, cumulative curve and convergence.Source: rheonda, example project

Schedule risks in the network

We apply the same principle directly to the network. Besides ranges per activity we model project-specific risks as events of their own, such as late preceding work or deliveries, and show their effect on the completion date.

Risk definition dialog of an activity in the scheduling software
Fig. 3 Definition of a project-specific risk event in the schedule.Source: rheonda
Histogram and cumulative curve of the completion date
Fig. 4 Probability distribution of the completion date.Source: rheonda