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The related research uses a variety of variables. Based on the nature of DEA, the number of variables in the model affects the results. Given imperfect data, researchers often must make tradeoffs in selecting input and output variables. In this research, in order to verify the stability of the DEA model, a stability test is conducted by changing the number of inputs and outputs. To get a fuller picture, four models are developed for this test. Spearman correlation coefficients are calculated to assess the impact of the variation.

DEA is a linear programming methodology measuring the relative performance and efficiency of multiple DMUs when the production process is composed of a difficult structure of multiple inputs and outputs [38]. A
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Details of the linear form of a CRS model may be found in Chapter 2 of Cooper [39]. The dual of the linear model reduces the number of constraints and makes the linear problem easier to solve. It is given below [39, 40]: where is the measure of the efficiency of DMUo, the DMU in the set of DMUs rated relative to the others; and is the dual weight assigned to DMUs. Constant returns to scale are assumed in the above model. When the constraint is added, we have a variable return to scale model [6].

The DEA estimates of is an indicator of efficiency. It measures the distance between the observed input/output combination and the efficiency frontier. The Malmquist Productivity Index (MPI) is based on ideas similar to the DEA, but MPI allows comparisons between two periods. Assume the technology at is implied in a set , where all feasible are included, i.e., .The output distance function, based on , is . The distance function increases output as much as possible for given input and technology at time . Following Färe et al. [41] and Boisso et al. [42], MPI is defined as:

Rearranging the terms in formula (4), following Färe et al. [41], we obtain the subsequent formula:

The MPI is thus decomposed into two elements, efficiency change , and technological change . The distance functions in the MPI can be calculated by linear programming methods similar to those used in the DEA. DEA constructs a production

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