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Network data envelopment analysis with fuzzy non-discretionary factors
1. | Department of International Business, Kao Yuan University, Kaohsiung, 82151, Taiwan |
2. | Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung, 84001, Taiwan |
3. | Department of Applied Mathematics, Tunghai University, Taichung 40704, Taiwan |
4. | Department of Applied Mathematics, National Chiayi University, Chiayi, 60004, Taiwan |
Network data envelopment analysis (DEA) concerns using the DEA technique to measure the relative efficiency of a system, taking into account its internal structure. The results are more meaningful and informative than those obtained from the conventional DEA models. This work proposed a new network DEA model based on the fuzzy concept even though the inputs and outputs data are crisp numbers. The model is then extended to investigate the network DEA with fuzzy non-discretionary variables. An illustrative application assessing the impact of information technology (IT) on firm performance is included. The results reveal that modeling the IT budget as a fuzzy non-discretionary factor improves the system performance of firms in a banking industry.
References:
[1] |
R. D. Banker and R. Morey,
Efficiency analysis for exogenously fixed inputs and outputs, Oper. Res., 34 (1986), 501-653.
doi: 10.1287/opre.34.4.513. |
[2] |
M. Barat, G. Tohidi and M. Sanei,
DEA for nonhomogeneous mixed networks, Asia Pac. Manag. Rev., 24 (2018), 161-166.
doi: 10.1016/j.apmrv.2018.02.003. |
[3] |
R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Manag. Sci., 17 (1970), B141–B164.
doi: 10.1287/mnsc.17.4.B141. |
[4] |
L. Castelli, R. Pesenti and W. Ukovich,
DEA-like models for the efficiency evaluation of hierarchically structured units, Eur. J. Oper. Res., 154 (2004), 465-476.
doi: 10.1016/S0377-2217(03)00182-6. |
[5] |
J. Zhu, Data Envelopment Analysis: A Handbook of Modeling Internal Structures and Networks, International Series in Operations Research & Management Science, 238. Springer, New York, 2016.
doi: 10.1007/978-1-4899-7684-0. |
[6] |
J. M. Cordero-Ferrera, F. Pedraja-Chaparro and D. Santín-González,
Enhancing the inclusion of non-discretionary inputs in DEA, J. Oper. Res. Soc., 61 (2010), 574-584.
doi: 10.1057/jors.2008.189. |
[7] |
R. Färe and S. Grosskopf, Intertemporal Production Frontiers: With Dynamic DEA, Boston: Kluwer Academic Publishers, 1996. |
[8] |
R. Färe and S. Grosskopf,
Network DEA, Socio. Econ. Plann. Sci., 4 (2000), 35-49.
|
[9] |
D. U. A. Galagedera,
Modelling social responsibility in mutual fund performance appraisal: A two-stage data envelopment analysis model with non-discretionary first stage output, Eur. J. Oper. Res., 273 (2019), 376-389.
doi: 10.1016/j.ejor.2018.08.011. |
[10] |
B. Golany and Y. Roll,
Some extensions of techniques to handle non-discretionary factors in data envelopment analysis, J. Prod. Anal., 4 (1993), 419-432.
doi: 10.1007/BF01073549. |
[11] |
C. Kao,
Network data envelopment analysis: A review, Eur. J. Oper. Res., 239 (2014), 1-16.
doi: 10.1016/j.ejor.2014.02.039. |
[12] |
C. Kao,
Efficiency decomposition and aggregation in network data envelopment analysis, Eur. J. Oper. Res., 255 (2016), 778-786.
doi: 10.1016/j.ejor.2016.05.019. |
[13] |
C. Kao and S.-N. Hwang,
Efficiency measurement for network systems: IT impact on firm performance, Decis. Support Syst., 48 (2010), 437-446.
doi: 10.1016/j.dss.2009.06.002. |
[14] |
R. J. Kauffman and P. Weill, An evaluative framework for research on the performance effects of information technology investment, Proceedings of the 10th International Conference on Information Systems, (1989), 377–388.
doi: 10.1145/75034.75066. |
[15] |
M. A. Muniz, J. Paradi, J. Ruggiero and Z. Yang,
Evaluating alternative DEA models used to control for non-discretionary inputs, Comput. Oper. Res., 33 (2006), 1173-1183.
|
[16] |
L. Simar and P. W. Wilson,
Estimation and inference in two-stage, semi-parametric models of production processes, J. Econom., 136 (1997), 31-64.
doi: 10.1016/j.jeconom.2005.07.009. |
[17] |
M. Taleb, R. Ramli and R. Khalid,
Developing a two-stage approach of super efficiency slack-based measure in the presence of non-discretionary factors and mixed integer-valued data envelopment analysis, Expert. Syst. Appl., 103 (2018), 14-24.
doi: 10.1016/j.eswa.2018.02.037. |
[18] |
C. H. Wang, R. Gopal and S. Zionts,
Use of data envelopment analysis in assessing information technology impact on firm performance, Ann. Oper. Res., 73 (1997), 191-213.
|
[19] |
M. Zerafat Angiz L and A. Mustafa,
Fuzzy interpretation of efficiency in data envelopment analysis and its application in a non-discretionary model, Knowl.-Based Syst., 49 (2013), 145-151.
|
show all references
References:
[1] |
R. D. Banker and R. Morey,
Efficiency analysis for exogenously fixed inputs and outputs, Oper. Res., 34 (1986), 501-653.
doi: 10.1287/opre.34.4.513. |
[2] |
M. Barat, G. Tohidi and M. Sanei,
DEA for nonhomogeneous mixed networks, Asia Pac. Manag. Rev., 24 (2018), 161-166.
doi: 10.1016/j.apmrv.2018.02.003. |
[3] |
R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Manag. Sci., 17 (1970), B141–B164.
doi: 10.1287/mnsc.17.4.B141. |
[4] |
L. Castelli, R. Pesenti and W. Ukovich,
DEA-like models for the efficiency evaluation of hierarchically structured units, Eur. J. Oper. Res., 154 (2004), 465-476.
doi: 10.1016/S0377-2217(03)00182-6. |
[5] |
J. Zhu, Data Envelopment Analysis: A Handbook of Modeling Internal Structures and Networks, International Series in Operations Research & Management Science, 238. Springer, New York, 2016.
doi: 10.1007/978-1-4899-7684-0. |
[6] |
J. M. Cordero-Ferrera, F. Pedraja-Chaparro and D. Santín-González,
Enhancing the inclusion of non-discretionary inputs in DEA, J. Oper. Res. Soc., 61 (2010), 574-584.
doi: 10.1057/jors.2008.189. |
[7] |
R. Färe and S. Grosskopf, Intertemporal Production Frontiers: With Dynamic DEA, Boston: Kluwer Academic Publishers, 1996. |
[8] |
R. Färe and S. Grosskopf,
Network DEA, Socio. Econ. Plann. Sci., 4 (2000), 35-49.
|
[9] |
D. U. A. Galagedera,
Modelling social responsibility in mutual fund performance appraisal: A two-stage data envelopment analysis model with non-discretionary first stage output, Eur. J. Oper. Res., 273 (2019), 376-389.
doi: 10.1016/j.ejor.2018.08.011. |
[10] |
B. Golany and Y. Roll,
Some extensions of techniques to handle non-discretionary factors in data envelopment analysis, J. Prod. Anal., 4 (1993), 419-432.
doi: 10.1007/BF01073549. |
[11] |
C. Kao,
Network data envelopment analysis: A review, Eur. J. Oper. Res., 239 (2014), 1-16.
doi: 10.1016/j.ejor.2014.02.039. |
[12] |
C. Kao,
Efficiency decomposition and aggregation in network data envelopment analysis, Eur. J. Oper. Res., 255 (2016), 778-786.
doi: 10.1016/j.ejor.2016.05.019. |
[13] |
C. Kao and S.-N. Hwang,
Efficiency measurement for network systems: IT impact on firm performance, Decis. Support Syst., 48 (2010), 437-446.
doi: 10.1016/j.dss.2009.06.002. |
[14] |
R. J. Kauffman and P. Weill, An evaluative framework for research on the performance effects of information technology investment, Proceedings of the 10th International Conference on Information Systems, (1989), 377–388.
doi: 10.1145/75034.75066. |
[15] |
M. A. Muniz, J. Paradi, J. Ruggiero and Z. Yang,
Evaluating alternative DEA models used to control for non-discretionary inputs, Comput. Oper. Res., 33 (2006), 1173-1183.
|
[16] |
L. Simar and P. W. Wilson,
Estimation and inference in two-stage, semi-parametric models of production processes, J. Econom., 136 (1997), 31-64.
doi: 10.1016/j.jeconom.2005.07.009. |
[17] |
M. Taleb, R. Ramli and R. Khalid,
Developing a two-stage approach of super efficiency slack-based measure in the presence of non-discretionary factors and mixed integer-valued data envelopment analysis, Expert. Syst. Appl., 103 (2018), 14-24.
doi: 10.1016/j.eswa.2018.02.037. |
[18] |
C. H. Wang, R. Gopal and S. Zionts,
Use of data envelopment analysis in assessing information technology impact on firm performance, Ann. Oper. Res., 73 (1997), 191-213.
|
[19] |
M. Zerafat Angiz L and A. Mustafa,
Fuzzy interpretation of efficiency in data envelopment analysis and its application in a non-discretionary model, Knowl.-Based Syst., 49 (2013), 145-151.
|
DMU j |
IT | Fixed | No. of | Deposits | Profit | Fraction |
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Fuzzy non-discretionary input | ||||||
Rank | ||||||
1 | 0.1102 | 0.5236 | 9.6335 | 0.2654 | 0.7346 | 18 |
2 | 0.1260 | 0.7723 | 12.4259 | 0.2589 | 0.7411 | 17 |
3 | 0.1586 | 0.8079 | 16.1328 | 0.3253 | 0.6747 | 25 |
4 | 0.1506 | 0.2564 | 10.9013 | 0.2864 | 0.7136 | 21 |
5 | 0.0921 | 0.2793 | 11.2165 | 0.3077 | 0.6923 | 23 |
6 | 0.4008 | 4.6342 | 45.4289 | 0.1936 | 0.8064 | 10 |
7 | 0.0600 | 0.9180 | 56.4200 | 0.0000 | 1.0000 | 1 |
8 | 0.0485 | 0.7677 | 8.0988 | 0.3173 | 0.6827 | 24 |
9 | 1.0908 | 13.1471 | 64.8529 | 0.2728 | 0.7272 | 20 |
10 | 0.0798 | 1.0715 | 12.8295 | 0.3351 | 0.6649 | 26 |
11 | 0.0797 | 1.0997 | 12.7416 | 0.3358 | 0.6642 | 27 |
12 | 0.0376 | 0.6544 | 9.7883 | 0.2490 | 0.7510 | 14 |
13 | 0.3519 | 5.3291 | 11.8900 | 0.0488 | 0.9512 | 5 |
14 | 0.3116 | 3.1047 | 29.5929 | 0.2918 | 0.7082 | 22 |
15 | 0.3212 | 3.2772 | 30.4969 | 0.2547 | 0.7453 | 16 |
16 | 0.0824 | 0.8943 | 10.7729 | 0.2512 | 0.7488 | 15 |
17 | 0.0413 | 0.3509 | 5.8871 | 0.2202 | 0.7798 | 11 |
18 | 0.3450 | 5.8920 | 15.5000 | 0.0000 | 1.0000 | 1 |
19 | 0.1080 | 0.8154 | 10.6151 | 0.1565 | 0.8435 | 7 |
20 | 0.0421 | 0.3349 | 4.4948 | 0.2343 | 0.7657 | 13 |
21 | 0.0441 | 0.3904 | 4.3686 | 0.2268 | 0.7732 | 12 |
22 | 0.0813 | 0.3043 | 11.6775 | 0.1707 | 0.8293 | 8 |
23 | 0.0853 | 0.3216 | 11.9554 | 0.1802 | 0.8198 | 9 |
24 | 0.1925 | 2.4125 | 18.3176 | 0.0654 | 0.9346 | 6 |
25 | 0.0488 | 0.5448 | 7.5342 | 0.2717 | 0.7283 | 19 |
26 | 0.1000 | 0.8720 | 12.1000 | 0.0000 | 1.0000 | 1 |
27 | 0.0106 | 1.7570 | 12.7000 | 0.0000 | 1.0000 | 1 |
Fuzzy non-discretionary input | ||||||
Rank | ||||||
1 | 0.1102 | 0.5236 | 9.6335 | 0.2654 | 0.7346 | 18 |
2 | 0.1260 | 0.7723 | 12.4259 | 0.2589 | 0.7411 | 17 |
3 | 0.1586 | 0.8079 | 16.1328 | 0.3253 | 0.6747 | 25 |
4 | 0.1506 | 0.2564 | 10.9013 | 0.2864 | 0.7136 | 21 |
5 | 0.0921 | 0.2793 | 11.2165 | 0.3077 | 0.6923 | 23 |
6 | 0.4008 | 4.6342 | 45.4289 | 0.1936 | 0.8064 | 10 |
7 | 0.0600 | 0.9180 | 56.4200 | 0.0000 | 1.0000 | 1 |
8 | 0.0485 | 0.7677 | 8.0988 | 0.3173 | 0.6827 | 24 |
9 | 1.0908 | 13.1471 | 64.8529 | 0.2728 | 0.7272 | 20 |
10 | 0.0798 | 1.0715 | 12.8295 | 0.3351 | 0.6649 | 26 |
11 | 0.0797 | 1.0997 | 12.7416 | 0.3358 | 0.6642 | 27 |
12 | 0.0376 | 0.6544 | 9.7883 | 0.2490 | 0.7510 | 14 |
13 | 0.3519 | 5.3291 | 11.8900 | 0.0488 | 0.9512 | 5 |
14 | 0.3116 | 3.1047 | 29.5929 | 0.2918 | 0.7082 | 22 |
15 | 0.3212 | 3.2772 | 30.4969 | 0.2547 | 0.7453 | 16 |
16 | 0.0824 | 0.8943 | 10.7729 | 0.2512 | 0.7488 | 15 |
17 | 0.0413 | 0.3509 | 5.8871 | 0.2202 | 0.7798 | 11 |
18 | 0.3450 | 5.8920 | 15.5000 | 0.0000 | 1.0000 | 1 |
19 | 0.1080 | 0.8154 | 10.6151 | 0.1565 | 0.8435 | 7 |
20 | 0.0421 | 0.3349 | 4.4948 | 0.2343 | 0.7657 | 13 |
21 | 0.0441 | 0.3904 | 4.3686 | 0.2268 | 0.7732 | 12 |
22 | 0.0813 | 0.3043 | 11.6775 | 0.1707 | 0.8293 | 8 |
23 | 0.0853 | 0.3216 | 11.9554 | 0.1802 | 0.8198 | 9 |
24 | 0.1925 | 2.4125 | 18.3176 | 0.0654 | 0.9346 | 6 |
25 | 0.0488 | 0.5448 | 7.5342 | 0.2717 | 0.7283 | 19 |
26 | 0.1000 | 0.8720 | 12.1000 | 0.0000 | 1.0000 | 1 |
27 | 0.0106 | 1.7570 | 12.7000 | 0.0000 | 1.0000 | 1 |
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