The Efficiency Evaluation of DEA Model Incorporating Improved Possibility Theory
Abstract
:1. Introduction
2. Materials and Methods
2.1. DEA Model
2.2. Full-Ranking Models
2.3. Possibility Theory
3. Improved Model
3.1. Interval DEA Improvement Model
3.2. Improving DEA Model with Possibility Theory
3.3. Model Steps and Properties
4. Illustrations
4.1. Numerical Examples
4.2. Airline Efficiency Evaluations
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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DMU | x1 | x2 | x3 | y1 | y2 | y3 |
---|---|---|---|---|---|---|
1 | 12 | 400 | 20 | 60 | 35 | 17 |
2 | 19 | 750 | 70 | 139 | 41 | 40 |
3 | 42 | 1500 | 70 | 225 | 68 | 75 |
4 | 15 | 600 | 100 | 90 | 12 | 17 |
5 | 45 | 2000 | 250 | 253 | 145 | 130 |
6 | 19 | 730 | 50 | 132 | 45 | 45 |
7 | 41 | 2350 | 600 | 305 | 159 | 97 |
DMU | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Selfish model (13) | 1 | 1 | 1 | 0.82 | 1 | 1 | 1 |
Non-selfish model (15) | −10.1524 | 1.336643 | 5.268163 | −1.57278 | 7.280709 | 0.993284 | 7.099546 |
DMU | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Interval efficiency | [0,1] | [0.6590,1] | [0.8846,1] | [0.4291,0.82] | [1,1] | [0.6393,1] | [0.9896,1] |
DMU | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Sum |
---|---|---|---|---|---|---|---|---|
1 | 0.5 | 0.146722 | 0.046936 | 0.301884 | 0 | 0.155947 | 0.00411 | 1.1556 |
2 | 0.853278 | 0.5 | 0.159949 | 0.883573 | 0 | 0.529575 | 0.014007 | 2.940381 |
3 | 0.953064 | 0.840051 | 0.5 | 1 | 0 | 0.849512 | 0.043786 | 4.186413 |
4 | 0.698116 | 0.116427 | 0 | 0.5 | 0 | 0.139267 | 0 | 1.453811 |
5 | 1 | 1 | 1 | 1 | 0.5 | 1 | 1 | 6.5 |
6 | 0.844053 | 0.470425 | 0.150488 | 0.860733 | 0 | 0.5 | 0.013179 | 2.838878 |
7 | 0.99589 | 0.985993 | 0.956214 | 1 | 0 | 0.986821 | 0.5 | 5.424918 |
DMU | CCR | Shifted Frontier | Super-Efficiency | Ghasemi | The Proposed Method | |||
---|---|---|---|---|---|---|---|---|
Eff. Values | Eff. Values | Rank | Eff. Values | Rank | Eff. Values | Rank | Rank | |
DMU1 | 1 | 0.20683 | 7 | 1.829615 | 1 | 0.218 | 7 | 7 |
DMU2 | 1 | 0.270049 | 2 | 1.048895 | 7 | 0.145 | 5 | 4 |
DMU3 | 1 | 0.197749 | 6 | 1.198308 | 5 | 0.805 | 6 | 3 |
DMU4 | 0.82 | 0.221479 | 5 | 0.819737 | 3 | - | 2 | 6 |
DMU5 | 1 | 0.250576 | 4 | 1.219992 | 6 | 0.049 | 1 | 1 |
DMU6 | 1 | 0.25645 | 1 | 1.190642 | 2 | 0.126 | 3 | 5 |
DMU7 | 1 | 0.277708 | 3 | 1.266094 | 4 | 0.045 | 4 | 2 |
Representative Study | Input Indicators | Output Indicators |
---|---|---|
Ngo and Tsui [53] | Available seat-kilometers (ASK) Available tonne-kilometers (ATK) Operating expenses (EXPENSES) | Revenue passenger-kilometers (RPK) Revenue tonne-kilometers (RTK) Operating revenues (REVENUES) |
Lee and Worthington [54] | The average number of employees Total assets in USD Kilometers flown | Available tonne-kilometers (ATK) |
Min and Joo [55] | Underutilization Operating expenses | Passengers RPKs Operating revenue Service rating |
Barbot et al. [56] | Labor Capital (the airline’s fleet) Fuel Other operating inputs | Passenger service Cargo service Ancillary output |
Indicators | Explanation | |
---|---|---|
Input indicators | Number of take-offs (unit: aircraft) | The aggregate number of aircraft sorties within a designated period of time. |
Flight hours (unit: hours) | The duration of the aircraft flying time. | |
Output indicators | Passenger volume (unit: individuals) | The actual number of passengers transported within a specific period. |
Passenger turnover (unit: 10,000 passenger-kilometers) | The passenger turnover reflects the total volume of passenger transportation work during a specific period. | |
Cargo volume (unit: tons) | The freight transport volume represents the actual quantity of goods transported during a specific period. | |
Cargo turnover (unit: 10,000 ton-kilometers) | The freight turnover reflects the total volume of goods transportation work during a specific period. |
Airlines | Before Normalization | After Normalization | ||
---|---|---|---|---|
Efficiency Upper Bound | Efficiency Lower Bound | Efficiency Upper Bound | Efficiency Lower Bound | |
China Southern Airlines | 1 | 7605.413 | 0.421488 | 1 |
Air China | 0.977608 | 7602.522 | 0.421484 | 0.977608 |
China Eastern Airlines | 0.858185 | 7603.034 | 0.421485 | 0.858185 |
Sichuan Airlines | 0.905655 | 7593.871 | 0.421475 | 0.905655 |
Xiamen Air | 0.857561 | 7594.547 | 0.421476 | 0.857561 |
Shenzhen Airlines | 0.816271 | 7595.956 | 0.421477 | 0.816271 |
Hainan Airlines | 0.989872 | 7589.414 | 0.42147 | 0.989872 |
Spring Airlines | 1 | 7588.01 | 0.421468 | 1 |
Shandong Airlines | 0.892908 | 7589.532 | 0.42147 | 0.892908 |
Juneyao Airlines | 0.899937 | 7577.694 | 0.421457 | 0.899937 |
Beijing Capital Airlines | 1 | 7567.888 | 0.421446 | 1 |
Zhejiang Loong Airlines | 0.864505 | 7564.184 | 0.421442 | 0.864505 |
China Eastern Airlines Yunnan Limited | 0.738032 | 7573.442 | 0.421452 | 0.738032 |
Shanghai Airlines | 0.774332 | 7568.362 | 0.421447 | 0.774332 |
China Eastern Airlines Jiangsu Limited | 0.780659 | 7566.109 | 0.421444 | 0.780659 |
Lucky Air | 0.957777 | 7549.363 | 0.421426 | 0.957777 |
Tianjin Airlines | 0.825296 | 7558.067 | 0.421436 | 0.825296 |
West Air | 1 | 7539.486 | 0.421415 | 1 |
Chengdu Airlines | 0.825793 | 7549.955 | 0.421427 | 0.825793 |
Suparna Airlines | 1 | 7454.055 | 0.421321 | 1 |
China Express | 0.592403 | 7565.231 | 0.421443 | 0.592403 |
China Xinhua Airlines Group | 0.8613 | 7526.507 | 0.421401 | 0.8613 |
China United | 0.684278 | 7546.518 | 0.421423 | 0.684278 |
Hebei Airlines | 0.836645 | 7516.756 | 0.42139 | 0.836645 |
China Southern Airlines Henan Limited | 0.84781 | 7518.408 | 0.421392 | 0.84781 |
Tibet Airlines | 0.785782 | 7520.074 | 0.421394 | 0.785782 |
Shenzhen Donghai Airlines | 0.910002 | 7500.322 | 0.421372 | 0.910002 |
Kunming Airlines | 0.829705 | 7508.146 | 0.421381 | 0.829705 |
9 Air | 1 | 7484.573 | 0.421355 | 1 |
Qingdao Airlines | 0.839825 | 7499.946 | 0.421372 | 0.839825 |
Okay Airways | 0.944351 | 7477.43 | 0.421347 | 0.944351 |
Ruili Airlines | 0.921448 | 7479.333 | 0.421349 | 0.921448 |
Chongqing Airlines | 0.733775 | 7504.117 | 0.421376 | 0.733775 |
Air Guizhou | 0.865709 | 7474.284 | 0.421344 | 0.865709 |
China Eastern Airlines Wuhan Limited | 0.919896 | 7469.817 | 0.421339 | 0.919896 |
Guangxi Airlines | 0.764911 | 7463.234 | 0.421331 | 0.764911 |
Urumqi Air | 1 | 7330.962 | 0.421186 | 1 |
Zhuhai Airlines | 0.792984 | 7418.66 | 0.421282 | 0.792984 |
Fuzhou Airlines | 0.857159 | 7402.27 | 0.421264 | 0.857159 |
Shantou Airlines | 0.821189 | 7420.001 | 0.421284 | 0.821189 |
Air Changan | 0.951132 | 7358.437 | 0.421216 | 0.951132 |
Dalian Airlines | 0.773927 | 7370.418 | 0.42123 | 0.773927 |
Air Travel | 0.91094 | 7290.883 | 0.421142 | 0.91094 |
Jiangxi Airlines | 0.855918 | 7303.761 | 0.421156 | 0.855918 |
Air China Inner Mongolia | 0.820033 | 7350.895 | 0.421208 | 0.820033 |
Air Guilin | 0.855987 | 7283.549 | 0.421134 | 0.855987 |
Colorful Guizhou Airlines | 0.618158 | 7380.347 | 0.42124 | 0.618158 |
Grand China Air | 0.924141 | 6267.371 | 0.420019 | 0.924141 |
Longjiang Airlines | 0.804375 | 6227.493 | 0.419975 | 0.804375 |
Beijing Airlines | 0.950829 | 6511.255 | 0.420286 | 0.950829 |
Joyair | 0.421488 | 7020.024 | 0.420845 | 0.421488 |
Genghis Khan Airlines | 0.541277 | 5500.45 | 0.419177 | 0.541277 |
One Two Three | 0.50545 | -376311 | 0 | 0.50545 |
China Southern Airlines | Air China | China Eastern Airlines | Sichuan Airlines | Xiamen Air | Shenzhen Airlines | Hainan Airlines | |
---|---|---|---|---|---|---|---|
China Southern Airlines | 0.5 | 0.519367 | 0.622623 | 0.58159 | 0.623171 | 0.658865 | 0.508774 |
Air China | 0.480633 | 0.5 | 0.607416 | 0.56473 | 0.607986 | 0.645117 | 0.489219 |
China Eastern Airlines | 0.377377 | 0.392584 | 0.5 | 0.450968 | 0.500726 | 0.548017 | 0.384124 |
Sichuan Airlines | 0.41841 | 0.43527 | 0.549032 | 0.5 | 0.549687 | 0.592338 | 0.425888 |
Xiamen Air | 0.376829 | 0.392014 | 0.499274 | 0.450313 | 0.5 | 0.547357 | 0.383566 |
Shenzhen Airlines | 0.341135 | 0.354883 | 0.451983 | 0.407662 | 0.452643 | 0.5 | 0.347238 |
Hainan Airlines | 0.491226 | 0.510781 | 0.615876 | 0.574112 | 0.616434 | 0.652762 | 0.5 |
Airlines | Possibility Accumulation | Ranking |
---|---|---|
China Southern Airlines | 33.7404 | 1 |
Air China | 32.96998 | 9 |
China Eastern Airlines | 27.95349 | 25 |
Sichuan Airlines | 30.1364 | 19 |
Xiamen Air | 27.92244 | 26 |
Shenzhen Airlines | 25.82609 | 38 |
Hainan Airlines | 33.39712 | 8 |
Spring Airlines | 33.73934 | 2 |
Shandong Airlines | 29.57464 | 21 |
Juneyao Airlines | 29.88564 | 20 |
Beijing Capital Airlines | 33.73813 | 3 |
Zhejiang Loong Airlines | 28.25687 | 23 |
China Eastern Airlines Yunnan Limited | 21.53633 | 46 |
Shanghai Airlines | 23.56419 | 43 |
China Eastern Airlines Jiangsu Limited | 23.91198 | 42 |
Lucky Air | 32.24218 | 10 |
Tianjin Airlines | 26.29467 | 35 |
West Air | 33.73641 | 4 |
Chengdu Airlines | 26.31985 | 34 |
Suparna Airlines | 33.73121 | 6 |
China Express | 12.92083 | 50 |
China Xinhua Airlines Group | 28.09983 | 24 |
China United | 18.4483 | 48 |
Hebei Airlines | 26.87465 | 32 |
China Southern Airlines Henan Limited | 27.43652 | 30 |
Tibet Airlines | 24.18898 | 41 |
Shenzhen Donghai Airlines | 30.31785 | 18 |
Kunming Airlines | 26.51913 | 33 |
9 Air | 33.73307 | 5 |
Qingdao Airlines | 27.03476 | 31 |
Okay Airways | 31.72312 | 13 |
Ruili Airlines | 30.80009 | 15 |
Chongqing Airlines | 21.2903 | 47 |
Air Guizhou | 28.30871 | 22 |
China Eastern Airlines Wuhan Limited | 30.73475 | 16 |
Guangxi Airlines | 23.03551 | 45 |
Urumqi Air | 33.72369 | 7 |
Zhuhai Airlines | 24.57313 | 40 |
Fuzhou Airlines | 27.89012 | 27 |
Shantou Airlines | 26.07175 | 36 |
Air Changan | 31.97793 | 11 |
Dalian Airlines | 23.52835 | 44 |
Air Travel | 30.34448 | 17 |
Jiangxi Airlines | 27.82282 | 29 |
Air China Inner Mongolia | 26.00671 | 37 |
Air Guilin | 27.82484 | 28 |
Colorful Guizhou Airlines | 14.49835 | 49 |
Grand China Air | 30.83279 | 14 |
Longjiang Airlines | 25.10228 | 39 |
Beijing Airlines | 31.91201 | 12 |
Joyair | 1.358619 | 53 |
Genghis Khan Airlines | 9.517831 | 51 |
One Two Three | 1.570545 | 52 |
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Yang, S.; Zhao, G.; Li, F. The Efficiency Evaluation of DEA Model Incorporating Improved Possibility Theory. Mathematics 2024, 12, 3116. https://doi.org/10.3390/math12193116
Yang S, Zhao G, Li F. The Efficiency Evaluation of DEA Model Incorporating Improved Possibility Theory. Mathematics. 2024; 12(19):3116. https://doi.org/10.3390/math12193116
Chicago/Turabian StyleYang, Shenzi, Guoqing Zhao, and Fan Li. 2024. "The Efficiency Evaluation of DEA Model Incorporating Improved Possibility Theory" Mathematics 12, no. 19: 3116. https://doi.org/10.3390/math12193116
APA StyleYang, S., Zhao, G., & Li, F. (2024). The Efficiency Evaluation of DEA Model Incorporating Improved Possibility Theory. Mathematics, 12(19), 3116. https://doi.org/10.3390/math12193116