Sensitivity analysis and simulation provide alternatives to the methods used above to deal with risk and uncertainty in decision-making.

　　1 Sensitivity Analysis

　　Sensitivity analysis calculates how responsive a decision is to changes in any of the variables used to calculate it.

　　It looks at one variable at a time and measures how much the variable can change by (in percentage terms) before the decision changes.

　　Advantages

　　It gives an idea of how sensitive the decision taken is to changes in any of the original estimates.

　　It can be readily adapted for use in spreadsheet packages.

　　Limitations

　　Although it can be adapted to deal with multi-variable changes, sensitivity is usually only used to examine what happens when one variable changes and others remain constant.

　　Without a computer, it can be time consuming.

　　2 Simulation

　　Simulation—a mathematical model constructed to represent the operation of a real-life process or situation.

　　Simulation is a technique which allows more than one variable to change at the same time.

　　Most real-life problems are complex as there is more than one uncertain variable. Models can be generated which "simulate" the real-world environment within which the decision must be made.

　　Although a simulation is not likely to be used in such a simple situation (as alternative models are available), it may be the only suitable method of analysing more complex situations where there are many variables which could change.

　　One example of a mathematical model used in simulation is the "Monte Carlo" method.

　　2.1 Stages

　　1. Specify the major variables (excessive detail will overcomplicate).

　　2. Specify the relationship between the variables.

　　3. Attach probability distributions to each variable and assign random numbers to reflect the distribution.

　　4. Simulate the environment by generating random numbers.

　　5. Record the outcome of each simulation.

　　6. Repeat each simulation many times to obtain a probability distribution of the likely outcomes.

　　2.2 Advantages and Limitations

　　Advantages

　　It overcomes the limitations of sensitivity analysis by examining the effects of all possible combinations of variables and their realisations.

　　It therefore provides more information about the possible outcomes and their relative probabilities.

　　It is useful for problems which cannot be solved analytically by other means.

　　Limitations

　　It is not a technique for making a decision, only for getting more information about the possible outcomes.

　　It can be very time consuming without a computer.

　　It could prove expensive in designing and running the simulation on a computer.

　　It relies on reliable estimates of the probability distributions of the underlying variables.