Variable Return to Scale VRS DEA Model
Referring to Koopmans definition about technical efficiency, the study used two requirements that both requirements must achieved by rice milling industry to
determine efficiency of rice milling, namely: 1.
Rice milling industry must have efficiency score equal to one. 2.
Rice milling industry must achieve zero slack condition for all variables used.
DEA was created as a tool to evaluate the performance of an activity in a unit entity organization Charnes, Cooper, Rhodes, 1978. DEA calculates the
efficiency of a DMU in one group of observation. The working principle of the DEA model is to compare the data input and output of an organizations data
decision-making unit DMU with other input and output data on the same DMU. This comparison is performed to obtain an efficiency score.
Assumptions of DEA: 1.
Entities evaluated by using a set of the same input to produce likewise set of the same output.
2. The data is positive and the weight is limited on positive values.
3. Input and output are variable.
4. In the presentation of Hayes, 2005, there are strengths and weaknesses of
DEA. DEA model used as a device to measure the performance has several advantages over other models, including:
5. DEA model can measure many input and output variables.
6. It does not require an assumption of a functional relationship between the
variables measured input and output. 7.
DMU is directly compared with one another. 8.
Input and output variable can have different measurement units. Meanwhile, limitation of DEA model, including:
1. It has sample specific.
2. It is an extreme point technique so that measurement error can be fatal.
3. It just measures the relative efficiency of DMU, not absolute efficiency.
4. Hypothesis testing is statistically difficult to be done. Using linear
programming formulation separately for each DMU calculations is manually difficult, especially for large-scale problems.
Research working steps on DEA method, including: 1.
Identify the DMU or unit that will be observed with inputs and outputs constituent.
2. Form the efficiency frontier from the available data.
3. Calculate the efficiency of each DMU to obtain input and output targets
needed to achieve optimal performance. Model used was output orientation. There were two reasons of this. First,
rice miller was a business, which was produces multi output. Second, the owner manager has control over the output produced compared to the input used. This
was used to cover makloon type that did not provide grain in production. This study also assumed VRS DEA model. This study has no a priori reason
to believe that the rice milling industry in study site achieves optimal scale. Thus, using of VRS DEA model is more appropriate than using of CRS DEA model for
this study. Model used in this study were consists of input and output variables. Input
variables used were amount of harvest dry grain, fuel, and working hour of machine. Meanwhile, output variable were amount of rice, broken rice, rice bran,
and chaff. Variables used in this study were: 1.
Grain, amount of grain is generated from the harvest and then dried through a process of drying kg.
2. Fuel, amount of solar is used to operate the machine in rice milling litter.
3. Working hour of machine hour. Working hours approach was done because
it was difficult to exactly determine the number of labor used by rice miller. Most of rice miller used labor in term of group borongan. Thus, rice miller
was not knows exactly the number of labor used. They only paid a specified amount to person who responsible in the group. Then, this person was
responsible for group. 4.
Rice, amount of rice is main result of rice milling machine kg. 5.
Broken rice is amount of broken rice, which is a byproduct of the milling fractions of rice grain kg.
6. Rice bran, amount of rice bran is byproduct of the rice milling process the
conversion of brown rice to white rice in the form of powder kg.
7. Chaff, amount of chaff is a byproduct of rice milling process in the form of
grain leather kg. Based on explanation above, variables both of output and of input described
below: 1.
The output 1 is amount of rice kg. 2.
The output 2 is amount of broken rice kg 3.
The output 3 is amount of rice bran kg 4.
The output 4 is amount of chaff kg 5.
The input 1 is amount of grain kg. 6.
The input 2 is number of working hour hour. 7.
The input 3 is amount of fuel liter. The amount of output and input variable used depicted in Appendix 2. In
order to calculate efficiency scores of rice millers, this study used computer program, namely DEAP 2.1 version. This program calculated efficiency score
both each rice miller and a set of rice millers as an industry.