A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design
Abstract
:1. Introduction
2. Two-Stage Process
3. Geometric Properties of Pareto Front
4. Rank-Based Efficiency Decomposition Approach
5. Comparison of Different Efficiency Decomposition Methods
5.1. Priority Decomposition Method
5.2. Uniform Efficiency Decomposition Method
6. Empirical Tests
6.1. Performance Evaluation of Banking
6.2. Performance Evaluation of Sustainable Designs
7. Concluding Remarks
Author Contributions
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. Proofs
Appendix A.1.1. The Proof of the Lemma
Appendix A.1.2. The Proof of the Theorem
Appendix A.2. Datasets
DMU | Branch | EM (103) | FA (¥108) | EX (¥108) | CR (¥108) | IL (¥108) | LO (¥108) | PR (¥108) |
---|---|---|---|---|---|---|---|---|
1 | Maanshan | 0.4775 | 0.526 | 0.3848 | 49.9174 | 5.4613 | 34.9897 | 0.843 |
2 | Anqing | 1.2363 | 0.713 | 0.5547 | 37.4954 | 4.0825 | 20.6013 | 0.4864 |
3 | Huangshan | 0.446 | 0.443 | 0.3419 | 20.9846 | 0.6897 | 8.6332 | 0.1288 |
4 | Fuyang | 1.2481 | 0.638 | 0.4574 | 45.0508 | 1.7237 | 9.2354 | 0.3019 |
5 | Suzhou | 0.705 | 0.575 | 0.4036 | 38.1625 | 2.2492 | 12.0171 | 0.3138 |
6 | Chuzhou | 0.6446 | 0.432 | 0.4012 | 30.1676 | 2.3354 | 13.813 | 0.3772 |
7 | Luan | 0.7239 | 0.51 | 0.3709 | 26.5391 | 1.3416 | 5.0961 | 0.1453 |
8 | Chizhou | 0.3363 | 0.322 | 0.2334 | 16.1235 | 0.4889 | 5.9803 | 0.0928 |
9 | Chaozhou | 0.6678 | 0.423 | 0.3471 | 22.1848 | 1.1767 | 9.2348 | 0.2002 |
10 | Bozhou | 0.3418 | 0.256 | 0.1594 | 13.4364 | 0.4064 | 2.5326 | 0.0057 |
Vehicle Manufacturer Name | Test Vehicle ID | Cid | Rhp | n/v Ratio | Axle | Etw | Mpg | Hc | CO | CO2 | Nox |
---|---|---|---|---|---|---|---|---|---|---|---|
Land Rover | LBDVP001 | 122.04749 | 240 | 30.6 | 3.75 | 4500 | 21.8 | 0.04564 | 0.6178 | 406.99 | 0.0012 |
Land Rover | 0AVP0002 | 305.11872 | 375 | 31 | 3.54 | 6000 | 15.3 | 0.01596 | 0.2238 | 576.48 | 0.0181 |
Land Rover | LKDTT066 | 305.11872 | 375 | 23.9 | 3.21 | 5500 | 16.8 | 0.01342 | 0.1923 | 531.45 | 0.0114 |
Land Rover | 3CTTP036 | 122.04749 | 240 | 30.5 | 3.75 | 4250 | 24.6 | 0.0169 | 0.1359 | 362.42 | 0.0078 |
Land Rover | VX10HWS | 305.11872 | 375 | 32.5 | 3.54 | 6000 | 15.6 | 0.014 | 0.17 | 570.95 | 0.012 |
Land Rover | 0AVP0049 | 305.11872 | 510 | 32.5 | 3.54 | 6000 | 14.4 | 0.01689 | 0.3361 | 612.43 | 0.0066 |
Land Rover | LKDTT065 | 305.11872 | 510 | 24.1 | 3.21 | 6000 | 15.7 | 0.02768 | 0.2859 | 565.05 | 0.0112 |
Maserati | 48675 | 286.8116 | 444 | 32.1 | 3.73 | 4750 | 15.75 | 0.0405 | 0.6305 | 566.841 | 0.017 |
Maserati | 45367 | 286.8116 | 454 | 30.5 | 3.54 | 4500 | 15.8 | 0.018 | 0.469 | 564.07 | 0.008 |
Maserati | ZAMJK39A690027157 | 286.8116 | 424 | 31.4 | 3.54 | 4750 | 14.25 | 0.017 | 0.346 | 621.803 | 0.008 |
VPG | 523MF1163BM000007 | 194.78779 | 240 | 33.3 | 4.06 | 5000 | 19.8 | 0.018 | 0.27 | 441 | 0.022 |
VPG | 523MF1267BT000001 | 280.70922 | 248 | 28.4 | 3.45 | 5250 | 15.55 | 0.12011 | 2.17351 | 565.85 | 0.0341 |
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Stage 1 | Stage 2 | Stage 1 | Stage 2 | ||||
---|---|---|---|---|---|---|---|
DMU | Overall | CCR | CCR | ||||
1 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
2 | 0.4344 | 0.5526 | 0.5541 | 0.7838 | 0.7861 | 0.5541 | 0.7861 |
3 | 0.2930 | 0.2930 | 0.4991 | 0.5869 | 1.0000 | 0.4991 | 1.0000 |
4 | 0.3013 | 0.3209 | 0.7593 | 0.3968 | 0.9389 | 0.7593 | 0.9699 |
5 | 0.3549 | 0.4304 | 0.7289 | 0.4869 | 0.8246 | 0.7289 | 0.8334 |
6 | 0.5448 | 0.5448 | 0.7359 | 0.7404 | 1.0000 | 0.7359 | 1.0000 |
7 | 0.1788 | 0.2881 | 0.5516 | 0.3242 | 0.6206 | 0.5516 | 0.6316 |
8 | 0.2818 | 0.3052 | 0.5325 | 0.5291 | 0.9232 | 0.5325 | 1.0000 |
9 | 0.3282 | 0.3845 | 0.5526 | 0.5939 | 0.8535 | 0.5526 | 1.0000 |
10 | 0.1747 | 0.3722 | 0.6498 | 0.2689 | 0.4695 | 0.6498 | 0.4979 |
Stage 1 | Stage 2 | Stage 1 | Stage 2 | |
---|---|---|---|---|
DMU | CCR | CCR | BG model | BG model |
1 | 1(1) | 1(1) | 1.0000(1) | 1(1) |
2 | 0.5541(6) | 0.7861(8) | 0.5534(4) | 0.785(3) |
3 | 0.4991(10) | 1(1) | 0.3824(10) | 0.7661(4) |
4 | 0.7593(2) | 0.9699(6) | 0.4936(5) | 0.6104(8) |
5 | 0.7289(4) | 0.8334(7) | 0.5601(3) | 0.6337(7) |
6 | 0.7359(3) | 1(1) | 0.6332(2) | 0.8605(2) |
7 | 0.5516(8) | 0.6316(9) | 0.3987(9) | 0.4485(9) |
8 | 0.5325(9) | 1(1) | 0.4032(8) | 0.6989(6) |
9 | 0.5526(7) | 1(1) | 0.461(7) | 0.749(5) |
10 | 0.6498(5) | 0.4979(10) | 0.4918(6) | 0.3553(10) |
RD = 10 | RD = 20 |
Stage 1 | Stage 2 | Stage 1 | Stage 2 | Stage 1 | Stage 2 | |
---|---|---|---|---|---|---|
DMU | M = 1 | M = 1 | M = 2 | M = 2 | M = 3 | M = 3 |
1 | 1(1) | 1(1) | 1(1) | 1(1) | 1(1) | 1(1) |
2 | 0.5534(5) | 0.7848(4) | 0.5535(5) | 0.7848(5) | 0.5536(6) | 0.7847(6) |
3 | 0.3484(10) | 0.841(3) | 0.3326(10) | 0.8808(3) | 0.3237(10) | 0.905(3) |
4 | 0.5633(4) | 0.5349(8) | 0.6062(3) | 0.497(8) | 0.6343(2) | 0.475(8) |
5 | 0.5905(3) | 0.601(7) | 0.6123(2) | 0.5796(7) | 0.6284(3) | 0.5648(7) |
6 | 0.6081(2) | 0.8959(2) | 0.5939(4) | 0.9173(2) | 0.5848(4) | 0.9316(2) |
7 | 0.4068(8) | 0.4396(9) | 0.4142(8) | 0.4317(9) | 0.421(7) | 0.4247(9) |
8 | 0.3659(9) | 0.7702(5) | 0.3486(9) | 0.8084(4) | 0.3388(9) | 0.8316(4) |
9 | 0.4345(7) | 0.7553(6) | 0.4214(7) | 0.7788(6) | 0.4137(8) | 0.7934(5) |
10 | 0.5242(6) | 0.3333(10) | 0.5463(6) | 0.3199(10) | 0.562(5) | 0.3109(10) |
RD | 6 | 18 | 6 | 16 | 4 | 17 |
Stage 1 | Stage 2 | Stage 1 | Stage 2 | Stage 1 | Stage 2 | |
---|---|---|---|---|---|---|
DMU | M = 4 | M = 4 | M = 5 | M = 5 | M = 6 | M = 6 |
1 | 1(1) | 1(1) | 1(1) | 1(1) | 1(1) | 1(1) |
2 | 0.5536(6) | 0.7846(6) | 0.5536(6) | 0.7846(6) | 0.5537(6) | 0.7845(6) |
3 | 0.3181(10) | 0.9211(3) | 0.3141(10) | 0.9326(3) | 0.3113(10) | 0.9412(3) |
4 | 0.6539(2) | 0.4608(8) | 0.6682(2) | 0.4509(8) | 0.6792(2) | 0.4436(8) |
5 | 0.6407(3) | 0.5539(7) | 0.6504(3) | 0.5456(7) | 0.6583(3) | 0.5392(7) |
6 | 0.5785(4) | 0.9417(2) | 0.574(5) | 0.9492(2) | 0.5705(5) | 0.955(2) |
7 | 0.4272(7) | 0.4186(9) | 0.433(7) | 0.413(9) | 0.4382(7) | 0.4081(9) |
8 | 0.3326(9) | 0.8471(4) | 0.3284(9) | 0.8582(4) | 0.3252(9) | 0.8664(4) |
9 | 0.4086(8) | 0.8033(5) | 0.405(8) | 0.8104(5) | 0.4023(8) | 0.8157(5) |
10 | 0.5737(5) | 0.3046(10) | 0.5827(4) | 0.2999(10) | 0.5899(4) | 0.2962(10) |
RD | 4 | 14 | 6 | 14 | 6 | 14 |
Stage 1 | Stage 2 | Stage 1 | Stage 2 | ||||
---|---|---|---|---|---|---|---|
DMU | Overall | CCR | CCR | ||||
1 | 0.8891 | 0.9475 | 0.9633 | 0.9229 | 0.9383 | 0.9475 | 1 |
2 | 0.8127 | 0.9295 | 0.9295 | 0.8742 | 0.8742 | 0.9735 | 1 |
3 | 0.9171 | 0.9171 | 0.9171 | 1 | 1 | 1 | 0.9951 |
4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
5 | 0.8791 | 0.9295 | 0.9295 | 0.9457 | 0.9457 | 1 | 1 |
6 | 0.8134 | 1 | 1 | 0.8134 | 0.8134 | 1 | 1 |
7 | 0.7593 | 0.9413 | 0.9413 | 0.8067 | 0.8067 | 1 | 0.99 |
8 | 0.7119 | 1 | 1 | 0.7119 | 0.7119 | 1 | 0.9787 |
9 | 0.7579 | 1 | 1 | 0.7579 | 0.7579 | 1 | 0.986 |
10 | 0.7134 | 0.9734 | 0.9734 | 0.7328 | 0.7328 | 0.9741 | 0.996 |
11 | 0.9291 | 0.98 | 0.98 | 0.9481 | 0.9481 | 1 | 1 |
12 | 0.6552 | 0.8958 | 0.8958 | 0.7314 | 0.7314 | 0.9456 | 0.9924 |
R-B model | |||
---|---|---|---|
DMU1 | Stage 1 | Stage 2 | RD |
M = 1 | 0.9529 | 0.9330 | 8 |
M = 2 | 0.9517 | 0.9343 | 8 |
M = 3 | 0.9509 | 0.9350 | 8 |
M = 4 | 0.9503 | 0.9356 | 8 |
BG model | 0.9554 | 0.9306 | 8 |
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Li, H.; Xiong, J.; Xie, J.; Zhou, Z.; Zhang, J. A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design. Sustainability 2019, 11, 4401. https://doi.org/10.3390/su11164401
Li H, Xiong J, Xie J, Zhou Z, Zhang J. A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design. Sustainability. 2019; 11(16):4401. https://doi.org/10.3390/su11164401
Chicago/Turabian StyleLi, Haitao, Jie Xiong, Jianhui Xie, Zhongbao Zhou, and Jinlong Zhang. 2019. "A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design" Sustainability 11, no. 16: 4401. https://doi.org/10.3390/su11164401
APA StyleLi, H., Xiong, J., Xie, J., Zhou, Z., & Zhang, J. (2019). A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design. Sustainability, 11(16), 4401. https://doi.org/10.3390/su11164401