analysis

1. MODEL SENSITIVITY
ANALYSIS
Yuli Dwi Astanti, ST, MT

2. DEFINITION
The parameter values and assumptions of any model are
subject to change and error. Sensitivity analysis (SA), broadly
defined, is the investigation of these potential changes and
errors and their impacts on conclusions to be drawn from the
model (e.g. Baird, 1989)
Sensitivity analysis methods can be classified in a variety of
ways. In this article, they are classified as:
(1) mathematical; (2) statistical; or (3) graphical.

3. MATHEMATICAL METHODS FOR
SENSITIVITY ANALYSIS
Mathematical methods assess sensitivity of a model output to the
range of variation of an input. These methods typically involve
calculating the output for a few values of an input that represent the
possible range of the input (e.g., Salehi et al., 2000). These methods
do not address the variance in the output due to the variance in the
inputs, but they can assess the impact of range of variation in the
input values on the output (Morgan and Henrion, 1990). In some
cases, mathematical methods can be helpful in screening the most
important inputs (e.g., Brun et al., 2001). These methods also can be
used for verification and validation (e.g., Wotawa et al., 1997), and to
identify inputs that require further data acquisition or research (e.g.,
Ariens et al., 2000). Mathematical methods evaluated here include
nominal range sensitivity analysis, break-even analysis, difference in
log-odds ratio, and automatic differentiation.

4. STATISTICAL METHODS FOR
SENSITIVITY ANALYSIS
which inputs are assigned probability distributions and assessing the
effect of variance in inputs on the output distribution (e.g.,
Andersson et al., 2000; Neter et al., 1996). Depending on the
method, one or more inputs are varied at a time. Statistical methods
allow one to identify the effect of interactions among multiple inputs.
The range and relative likelihood of inputs can be propagated using a
variety of techniques such as Monte Carlo simulation, Latin hypercube
sampling, and other methods. Sensitivity of the model results to
individual inputs or groups of inputs can be evaluated by a variety of
techniques (Cullen and Frey, 1999). Greene and Ernhart (1993),
Fontaine and Jacomino (1997), and Andersson et al. (2000) give
examples of the application of statistical methods. The statistical
methods evaluated here include regression analysis, analysis of
variance, response surface methods, Fourier amplitude sensitivity
test, and mutual information index.

5. GRAPHICAL METHODS FOR
SENSITIVITY ANALYSIS
Graphical methods give representation of sensitivity in the form of
graphs, charts, or surfaces. Generally, graphical methods are used to
give visual indication of how an output is affected by variation in
inputs (e.g., Geldermann and Rentz, 2001). Graphical methods can be
used as a screening method before further analysis of a model or to
represent complex dependencies between inputs and outputs (e.g.,
McCamley and Rudel, 1995). Graphical methods can be used to
complement the results of mathematical and statistical methods for
better representation (e.g., Stiber et al., 1999; Critchfield and Willard,
1986).

8. WHAT-IF OR SENSITIVITY ANALYSIS
1. How is the preferred or optimal solution affected by
individual or simultaneous changes of uncontrollable inputs
into the system?
2. How costly are errors in inputs in terms of reduced benefits
achieved if a solution based on incorrect inputs is
implemented?
Both are referred to as sensitivity analysis.
The insights gained from it may be more valuable than finding a good
or even the optimal solution. Extensive sensitivity and error analysis
are also an integral part of checking external validity.

9. ONCE THE OPTIMAL SOLUTION HAS
BEEN FOUND, TWO FURTHER
ISSUES NEED ADDRESSING:
1. How does the optimal solution respond to changes in
the input parameters?
2. What is the error, in terms of loss of benefits or savings,
incurred for using the
model based on wrong values for input parameters?
Although both may be called sensitivity analysis, we reserve this term for the
first,
while the second is more appropriately referred to as error analysis.
Sensitivity analysis explores how the optimal solution responds to changes
in a given
input parameter, keeping all other inputs unchanged.

10. USES OF
SENSITIVIT
Y
ANALYSIS
The Uses Are Grouped
Into Four Main
Categories: Decision
Making Or Development
Of Recommendations
For Decision Makers,
Communication,
Increased
Understanding Or
Quantification Of The
System, And Model
Development.

11. Uncertainty is one of the primary reasons why sensitivity
analysis is helpful in making decisions or recommendations. If
parameters are uncertain, sensitivity analysis can give
information such as:
1. How robust the optimal solution is in the face of different
parameter values (use 1.1 from Table 1),
2. Under what circumstances the optimal solution would
change (uses 1.2, 1.3, 1.5),
3. How the optimal solution changes in different
circumstances (use 3.1),
4. How much worse off would the decision makers be if they
ignored the changed circumstances and stayed with the
original optimal strategy or some other strategy (uses 1.4,
1.6),

12. In Principle, Sensitivity Analysis Is A Simple Idea: Change The
Model And Observe Its Behaviour. In Practice There Are Many
Different Possible Ways To Go About Changing And Observing The
Model.
One might choose to vary any or all of the following:
1. the contribution of an activity to the objective,
2. the objective (e.g. minimise risk of failure instead of maximising profit),
3. a constraint limit (e.g. the maximum availability of a resource),
4. the number of constraints (e.g. add or remove a constraint designed to
express personal preferences of the decision maker for or against a
particular activity),
5. the number of activities (e.g. add or remove an activity), or
6. technical parameters.

13. Whichever items the modeller chooses to vary,
there are many different aspects of a model
output to which attention might be paid:
1. the value of the objective function for the optimal strategy,
2. the value of the objective function for sub-optimal strategies (e.g. strategies
which are optimal for other scenarios, or particular strategies suggested by
the decision maker),
3. the difference in objective function values between two strategies (e.g.
between the optimal strategy and a particular strategy suggested by the
decision maker),
4. the values of decision variables,
5. in an optimisation model, the values of shadow costs, constraint slacks or
shadow prices, or
6. the rankings of decision variables, shadow costs, etc.

14. LET SEE THE EXAMPLES,
FROM ME, AND YOU…