MONTE CARLO ANALYSIS

28  Monte Carlo analysis allows an assessment of the consequences of simultaneous uncertainty about key inputs, and can take account of correlations between these inputs. It involves replacing single entries with probability distributions of possible values for key inputs. Typically, the choice of probabilistic inputs will be based on prior sensitivity testing. The calculation is then repeated a large number of times randomly (using a computer program) to combine different input values selected from the probability distributions specified. The results consist of a set of probability distributions showing how uncertainties in key inputs might impact on key outcomes.

29  Box 4.5 provides an example illustrating the use of Monte Carlo analysis.7

BOX 4.5:ALLOWING FOR UNCERTAINTY IN AN ANALYSIS OF COSTS

The table below gives the costs of various parts of a construction project, broken down into excavation (E), foundations (F), structure (S), roofing (R), and decorations (D). All costs are independent of each other. The model for total cost is as follows:

Total cost = E + F + S + R + D

Costs for construction project (£)

 

Minimum

Best Guess

Maximum

Excavation (E)

30,500

33,200

37,800

Foundations (F)

23,500

27,200

31,100

Structure (S)

172,000

178,000

189,000

Roofing (R)

56,200

58,500

63,700

Decoration (D)

29,600

37,200

43,600

From this information we can produce a best guess of £334,100 for the total cost of the project. However, we can also conclude a possible range from £311,800 to £365,200. Suppose the project would not go ahead unless the total cost is unlikely to exceed £350,000; how much assurance can we take from these figures that the total cost will be less than £350,000?

By undertaking a Monte Carlo analysis, we can simulate many possible values of the input variables, weighted so that the 'best guess' value is more likely than the extreme values. The total cost is calculated for each simulation, giving a distribution of values for total cost. The precise weighting depends on the probability distributions specified for each variable.

Using triangular distributions, it can be concluded that the most likely total cost is £334,000; and that the chance of total cost exceeding £350,000 is less than 1%.




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7  This example was adapted from 'Measuring costs and benefits - a guide on cost benefit and cost effectiveness analysis', National Audit Office (NAO) and Vose, D (1996)