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Step 3: Determining the minimum quantities for each input criterion in the input matrix normalized using Eq. (7) and the maximum quantities for each output criterion in the output matrix normalized using Eq. (8). a; in Eq. (7) represents the minimum quantity of input criterion j and ¢ in Eq. (8) represents the maximum quantity of output criterion k. In Eq. (1), gj represents the quantity of input j of DMU i. In Eq. (2), cx represents the quantity of output k of DMU i. Step 2: Normalization of the input quantities using the formula shown in Eq. (3) and of the output quantities using the formula it Eq. (4). Composing the normalized input matrix represented by Gin Eq. (5) and the normalized output matrix represented by Cin Eq (6). In these equations, g;, stands for the normalized quantity of DMUi on the basis of input j criterion and ¢j stands for the normalize: quantity of DMU i on the basis of output k.

Figure 4 Step 3: Determining the minimum quantities for each input criterion in the input matrix normalized using Eq. (7) and the maximum quantities for each output criterion in the output matrix normalized using Eq. (8). a; in Eq. (7) represents the minimum quantity of input criterion j and ¢ in Eq. (8) represents the maximum quantity of output criterion k. In Eq. (1), gj represents the quantity of input j of DMU i. In Eq. (2), cx represents the quantity of output k of DMU i. Step 2: Normalization of the input quantities using the formula shown in Eq. (3) and of the output quantities using the formula it Eq. (4). Composing the normalized input matrix represented by Gin Eq. (5) and the normalized output matrix represented by Cin Eq (6). In these equations, g;, stands for the normalized quantity of DMUi on the basis of input j criterion and ¢j stands for the normalize: quantity of DMU i on the basis of output k.

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A brief outline of what was done to determine the productivity of airports. Table 1
A brief outline of what was done to determine the productivity of airports. Table 1
Fig. 1. Methods used in literature for airports efficiency.
Fig. 1. Methods used in literature for airports efficiency.
A brief outline of studies using MCDM methods for airports.
A brief outline of studies using MCDM methods for airports.
Fig. 2. Outputs used for airports efficiency in literature. above used 185 different inputs and 147 different outputs. Looking at Fig. 2, it is apparent that the inputs used in these studies are more varied than the outputs and the outputs generally include variables such as passenger traffic, cargo traffic, aircraft traffic, sales, and revenues.
Fig. 2. Outputs used for airports efficiency in literature. above used 185 different inputs and 147 different outputs. Looking at Fig. 2, it is apparent that the inputs used in these studies are more varied than the outputs and the outputs generally include variables such as passenger traffic, cargo traffic, aircraft traffic, sales, and revenues.
Fig. 3. Inputs used for airports efficiency in literature.
Fig. 3. Inputs used for airports efficiency in literature.
Airports operating in 2018. *IATA Codes: International Air Transport Association Codes. Table 3
Airports operating in 2018. *IATA Codes: International Air Transport Association Codes. Table 3
Decision making units from 2014 to 2018. Table 4
Decision making units from 2014 to 2018. Table 4
The decision matrix represented by G in Eq. (1) was used to calculate the input weights and the decision matrix represented b in Eq. (2) was used to calculate the output weights. In the next step, normalized input quantities (zj) were calculated using formula in Eq. (11) and a normalized input matrix represented by Z in Eq. (12) was formed. Normalized output quantities (fj) w calculated using the formula in Eq. (13) and a normalized output decision matrix represented by F in Eq. (14) was formed. Once normalized input and output quantities are calculated and the normalized input and output decision matrices are formed the entropy of each input criterion (B,) is calculated using the formula in Eq. (15) and the entropy of each output criterion (D,) i calculated using the formula in Eq. (16). determined only through a decision matrix including the quantities that the alternatives take from criteria (Cati et al., 2014). A decision matrix in entropy is regarded as a pure source of information (G6k and Yigit, 2017). The use of entropy eliminates the subjectivity in subjective weight determination methods and provides researchers with considerable ease in mathematical operations (istanbullu Dincer and Goral, 2017). The entropy method consists of four basic steps outlined below (Wang and Lee, 2009; Shemshadi et al., 2011):
The decision matrix represented by G in Eq. (1) was used to calculate the input weights and the decision matrix represented b in Eq. (2) was used to calculate the output weights. In the next step, normalized input quantities (zj) were calculated using formula in Eq. (11) and a normalized input matrix represented by Z in Eq. (12) was formed. Normalized output quantities (fj) w calculated using the formula in Eq. (13) and a normalized output decision matrix represented by F in Eq. (14) was formed. Once normalized input and output quantities are calculated and the normalized input and output decision matrices are formed the entropy of each input criterion (B,) is calculated using the formula in Eq. (15) and the entropy of each output criterion (D,) i calculated using the formula in Eq. (16). determined only through a decision matrix including the quantities that the alternatives take from criteria (Cati et al., 2014). A decision matrix in entropy is regarded as a pure source of information (G6k and Yigit, 2017). The use of entropy eliminates the subjectivity in subjective weight determination methods and provides researchers with considerable ease in mathematical operations (istanbullu Dincer and Goral, 2017). The entropy method consists of four basic steps outlined below (Wang and Lee, 2009; Shemshadi et al., 2011):
The first group airports in 2018 (DMUs in 2018).
The first group airports in 2018 (DMUs in 2018).
Input decision matrix for first group airports in 2018.
Input decision matrix for first group airports in 2018.
Output decision matrix for first group airports in 2018. Table 7
Output decision matrix for first group airports in 2018. Table 7
Weights of inputs under the entropy method (W,) for first group airports in 2018. Table 8
Weights of inputs under the entropy method (W,) for first group airports in 2018. Table 8
Weights of outputs under the entropy method (V;) for first group airports in 2018.
Weights of outputs under the entropy method (V;) for first group airports in 2018.
Total weighted input distance measures (Ej), and total weighted output (L;) distance measures, and pro- ductivity scores (P;) for first group airports in 2018.
Total weighted input distance measures (Ej), and total weighted output (L;) distance measures, and pro- ductivity scores (P;) for first group airports in 2018.
Productivity and efficiency scores of first group airports in 2018.
Productivity and efficiency scores of first group airports in 2018.
Productivity and efficiency scores of second group airports in 2018.
Productivity and efficiency scores of second group airports in 2018.
Productivity and efficiency scores of first group airports in 2017.
Productivity and efficiency scores of first group airports in 2017.
Productivity and efficiency scores of second group airports in 2017.
Productivity and efficiency scores of second group airports in 2017.
Productivity and efficiency scores of first group airports in 2016.
Productivity and efficiency scores of first group airports in 2016.
Productivity and efficiency scores of second group airports in 2016.
Productivity and efficiency scores of second group airports in 2016.
Productivity and efficiency scores of first group airports in 2015. Table 17
Productivity and efficiency scores of first group airports in 2015. Table 17
Productivity and efficiency scores of second group airports in 2015. Table 18
Productivity and efficiency scores of second group airports in 2015. Table 18
Productivity and efficiency scores of first group airports in 2014.
Productivity and efficiency scores of first group airports in 2014.
Productivity and efficiency scores of second group airports in 2014.
Productivity and efficiency scores of second group airports in 2014.
Fig. 4. Inputs weights for the first and second group airports from 2014 to 2018 (%). Inputs weights for the first and second group airports
Fig. 4. Inputs weights for the first and second group airports from 2014 to 2018 (%). Inputs weights for the first and second group airports
Fig. 5. Outputs weights for the first and second group airports from 2014 to 2018 (%).
Fig. 5. Outputs weights for the first and second group airports from 2014 to 2018 (%).
Inputs and Outputs for The First Group Airports in 2014
Inputs and Outputs for The First Group Airports in 2014
Inputs and Outputs for The First Group Airports in 2015
Inputs and Outputs for The First Group Airports in 2015
Appendix D
Appendix D
Inputs and Outputs for 2017
Inputs and Outputs for 2017
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