The general form of a mathematical model is
E ¼ f x i , y j
À
Á
,
where E ¼ objective function,
x i ¼ decision variables,
y j ¼ uncontrollable variables,
and f ¼ relationships between E and x i , y j
It must be remembered that a model is only an approximation of the reality (real
situation), and thus, may not include all the variables.
Model construction will be followed by data collection for inputting into the
model. This may be obtained from records, from ongoing tests and experiments or
eventually from hunches based on experience.
13.2.3 Deriving a Solution from the Model
The model will provide a solution either by simulation or by mathematical analysis.
Some cases may require the use of a combination of both, depending upon the nature
and complexity of the system.
Since a model is an approximation of the real system or problem, the optimum
solution for the model does not guarantee an optimum solution for the real problem.
However, if the model is well formulated and tested, the solution from the model will
provide a good estimate to the solution of the actual problem.
13.2.4 Testing the Model and the Solution Derived from It
As already explained, a model can never represent the real problem perfectly.
However, when correctly framed and properly operated, the model will help in
forecasting the effect of fluctuations in decision variables on the overall system
response. The effectiveness of a model is tested by determining how accurately it
forecasts the impact of these fluctuations. This analysis is also called a sensitivity
analysis. If the results obtained without using the solution are compared against the
results obtained with using the solution, this will indicate the validity or utility of the
solution.
13.2.5 Establishing Controls over the Solution
The universe is subjected to continuous, unceasing change. Yesterday’s optimum
solution may no longer be so tomorrow, because parameter values have changed,
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E ¼ f x i , y j
À
Á
,
where E ¼ objective function,
x i ¼ decision variables,
y j ¼ uncontrollable variables,
and f ¼ relationships between E and x i , y j
It must be remembered that a model is only an approximation of the reality (real
situation), and thus, may not include all the variables.
Model construction will be followed by data collection for inputting into the
model. This may be obtained from records, from ongoing tests and experiments or
eventually from hunches based on experience.
13.2.3 Deriving a Solution from the Model
The model will provide a solution either by simulation or by mathematical analysis.
Some cases may require the use of a combination of both, depending upon the nature
and complexity of the system.
Since a model is an approximation of the real system or problem, the optimum
solution for the model does not guarantee an optimum solution for the real problem.
However, if the model is well formulated and tested, the solution from the model will
provide a good estimate to the solution of the actual problem.
13.2.4 Testing the Model and the Solution Derived from It
As already explained, a model can never represent the real problem perfectly.
However, when correctly framed and properly operated, the model will help in
forecasting the effect of fluctuations in decision variables on the overall system
response. The effectiveness of a model is tested by determining how accurately it
forecasts the impact of these fluctuations. This analysis is also called a sensitivity
analysis. If the results obtained without using the solution are compared against the
results obtained with using the solution, this will indicate the validity or utility of the
solution.
13.2.5 Establishing Controls over the Solution
The universe is subjected to continuous, unceasing change. Yesterday’s optimum
solution may no longer be so tomorrow, because parameter values have changed,
358
13 Modelling in Infrastructure Planning