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management in highland catchments. A scenario modeling approach was used in the toolbox which translated policy and uncontrollable drivers into scenario inputs
to the biophysical toolbox, a component of the integrated modeling toolbox. A sensitivity analysis of the model to changes in various input assumptions was
conducted which showed plausible levels and patterns of sensitivity. The sensitivity analysis used in this study was that of parameter sensitivity
which determine how sensitive the model developed to changes in the value of the parameters Jourdan et al. 1991; Pannell 1997; Breierova Choudhari 2001.
This was done as a series of tests in which different parameters values were set to see how a change in the parameter causes a change in the behavior of the yield.
Aside from that, the model can be used to determine the maximum profit that can be obtained by using optimization technique. The objective of this study was to
make sensitivity analysis of the production model based on Cobb-Douglas production function and used the model for the calculation of the optimum profit
that could be obtained through optimization process.
5.2. Method
5.2.1. Definition of Sensitivity Analysis
In general, sensitivity analysis can be defined as the investigation of the potential changes and errors of the parameter values of a model and their impacts
on conclusions to be drawn from the model. Many possible uses of sensitivity analysis are within the categories of decision support, communication, increased
understanding or quantification of the system, and model development Pannell, 1997. Sensitivity analysis can be used to determine how sensitive a model is to
changes in the value of the parameters of the model and to changes in the structure of the model. It helps to build confidence in the model by studying the
uncertainties that are often associated with parameters in models. Sensitivity analysis is a useful tool in model building as well as in model evaluation
Breierova Choudhari 2001. Parameters are usually uncertain in all models. The current values might be
unsure and the future values are even more uncertain. This applies to things such as prices, costs, productivity, and technology. Uncertainty is one of the primary
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reasons why sensitivity analysis is helpful in making decisions or recommendations. If parameters are uncertain, sensitivity analysis can give
information such as the robustness of optimal solution in the face of different parameter values, change in optimal solution under certain circumstances, and
change in optimal solution in different circumstances Pannell 1997. Parameter sensitivity analysis was used in this study where a productivity
model on organic rice farming was developed. A series of tests was conducted by setting different parameter values to see how a change in the parameter causes a
change in the behavior of the productivity model 5.2.2.
Sensitivity Analysis for Production Model
A study on the productivity of organic rice farming using SRI method was conducted with the study area in the District of Sukabumi, West Java, Indonesia
Gardjito et al. 2010. A production or productivity models was developed based on Cobb-Douglas production function. Four production inputs of seed S, organic
fertilizer F, labors L and irrigation water W were used in the model. The developed productivity model had the following form:
W L
F AS
Y
LD
1
where A, , , , are parameters or constants. The values of the constants A, , ,
, and were determined through optimization process. The optimization process resulted in values of
A, , , , and of 2.664, -0.002, 0.00019, 0.002, and 0.94, respectively Gardjito et. al. 2010. By applying the parameter values, the model
could be expressed as:
94 .
002 .
00019 .
002 .
664 .
2 W
L F
S Y
LD
2
The fitting process resulted in a regression curve of data vs. model with an error of 2.295E-05 and R
2
of 0.9990 see Table 5.1. Sensitivity analysis was conducted by applying analysis of errors of a linear
function with more than one component Jourdan et al. 1991. It should be noted
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here that in this analysis the errors were treated as the change in the yield due to changes in the production components of seed, fertilizer, labor and water. The
equation is in the form of Taylor’s series expansion that in general can be stated as
follows:
.... 2
2 1
2 2
2 2
2 2
2
dy
y F
dxdy y
x F
dx x
F dy
y F
dx x
F F
dF F
3
where F is the linear function and dF is the errors. The higher order involving the error usually can be neglected. In the case of the productivity model expressed in
Equation 1, the terms of the series are then can be expressed as:
dW W
Y dL
L Y
dF F
Y S
Y Y
dY Y
4
The maximum possible value of the error can be obtained by summing the absolute values of the error. Combining the terms by a root-mean square and
changing to the finite difference form, however, gives a more realistic value of the error when the errors are independent as stated below:
2 2
2 2
W
W Y
L L
Y F
F Y
S S
Y Y
5 where:
W L
F S
A S
Y
1
6
W L
F AS
F Y
1
7
W L
F AS
L Y
1
8
1
W L
F AS
W Y
9
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5.2.3. Profit Calculation
