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@RISK Models

When submitting a budget proposal for a project, two key questions that you are likely to be interested in are:

a. What is the probability that the project will actually be delivered within this budget?
b. How much contingency (i.e. extra budget) should be included in order for this new revised budget level to be achieved with a certain degree of confidence?

This model shows how one might answer these questions through simulation: It is assumed that each item's actual cost will be within a min-max range, and uses Pert distributions to describe the possible costs of each item in practice.

The user may change any of the light blue colored cells, which are the model's inputs. The answers to the key questions can be found by appropriate interrogation of the output in the Results Summary window. Alternatively, as shown here, the results can in fact be built into the model automatically, using the @RISK Statistics functions.

In many circumstances one wishes to calculate the aggregate impact of many possible yes/no type events. For example, it is often important to answer questions such as "What is the loss amount that will not be exceeded in 95% of cases?" Simulation is usually required to answer such questions. In this model, the "yes/no" events are modeled using Binomial distributions. The results profile shows a multi-peaked distribution, which is typical when there are discrete-type inputs. It can be seen that a provision level of around \$700,000 is necessary to cover 95% of the cases.

This model illustrates the RiskResultsGraph function for creating (non-interactive) graphs of specified inputs or outputs when a simulation is run.

The RiskSimtable feature can be used to run multiple simulations to test the sensitivity of the model, for example to changes in the parameters of a distribution. This model is of a business with a base case expected revenue of 100 and cost of 80, giving a profit of 20.

The risk model assumes that the revenue and cost distributions are determined from a mean and standard deviation. The RiskSimtable feature is used to test the sensitivity of the distribution of profit to changes in the standard deviation of the revenues. Three values are tested of which the first is our original @RISK model. The number of simulations is therefore set at 3. A RiskSimtable can be set up either by directly typing in the required format, or by inserting it as for other Excel functions via the Insert Function menu option. The model also uses some @RISK Statistics functions to report the probability for each simulation that the profit exceeds 50.

This model simulates the daily expenses of a business traveler who faces uncertainty each day on whether he makes a trip, and if so, the miles, miles per hour, miles per gallon, and price per gallon for the trip. Its outputs are total cost and total hours driven for a month, and it uses the RiskCollect function to enable sensitivity analysis of these outputs to "inputs" of interest, such as the average miles per gallon per trip.

This model demonstrates the use of the alternate, percentile parameter formulation. In this case we assume that we have decided to use a Normal distribution to represent the arrival time of someone at work. The use of traditional parameters would require knowledge of the standard deviation of the arrival time, which may be hard to estimate. The use of the alternative parameter formulation allows data to be estimated by others in a more natural way. In the first case, the traditional parameters are used (mean and standard deviation). In the second case, the mean is still used, and the P90 is used in place of the standard deviation, i.e. the time before which the person arrives in 90% of cases. In the second case, the P10 and the P90 is used in place of the standard deviation i.e. the time before which the person arrives in 10% of cases, and in 90% of cases respectively.

Evolver Models

This model uses Evolver to check whether a chess knight can make 64 consecutive moves and hit each square exactly once. It doesn't optimize anything. It only tries to find a solution with the desired characteristic.

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