Marginal rates in DEA using defining hyperplanes of PPS with CRS technology
Data envelopment analysis (DEA) was proposed in a highly influential paper by Charnes et al. (J Oper Res 2:429–444, 1978), who developed the Farrell seminal research (J R Stat Soc 120:253–290, 1957). The aim of the present research is calculating marginal rates for strong and weak efficient decision...
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| Veröffentlicht in: | Operational research Jg. 23; H. 1; S. 11 |
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| Abstract | Data envelopment analysis (DEA) was proposed in a highly influential paper by Charnes et al. (J Oper Res 2:429–444, 1978), who developed the Farrell seminal research (J R Stat Soc 120:253–290, 1957). The aim of the present research is calculating marginal rates for strong and weak efficient decision making units (DMUs) using the defining hyperplanes of the production possibility set (PPS). Toward this end, there are three essential objectives in the current study: (1) Implement Farrell’s idea to construct a new PPS called the Farrell PPS. In doing so, important relationships were discovered between the PPSs with constant returns to scale (CRS), non-increasing returns to scale, and non-decreasing returns to scale technologies. (2) Apply the newly constructed Farrell PPS as a catalyst to obtain strong and weak efficient DMUs and explicit form equations of strong and weak defining hyperplanes for the PPS with CRS technology. In order to do this task, a multiple objective linear programming problem is proposed whose structure for the decision space of the criterion space is similar to the proposed Farrell PPS. (3) Calculate the marginal rates for strong and weak efficient DMUs using the obtained explicit form equations of strong and weak defining hyperplanes for the PPS with CRS technology. Finally, an empirical study in the Iranian banking sector is used to show the applicability of the proposed methods. |
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| AbstractList | Data envelopment analysis (DEA) was proposed in a highly influential paper by Charnes et al. (J Oper Res 2:429–444, 1978), who developed the Farrell seminal research (J R Stat Soc 120:253–290, 1957). The aim of the present research is calculating marginal rates for strong and weak efficient decision making units (DMUs) using the defining hyperplanes of the production possibility set (PPS). Toward this end, there are three essential objectives in the current study: (1) Implement Farrell’s idea to construct a new PPS called the Farrell PPS. In doing so, important relationships were discovered between the PPSs with constant returns to scale (CRS), non-increasing returns to scale, and non-decreasing returns to scale technologies. (2) Apply the newly constructed Farrell PPS as a catalyst to obtain strong and weak efficient DMUs and explicit form equations of strong and weak defining hyperplanes for the PPS with CRS technology. In order to do this task, a multiple objective linear programming problem is proposed whose structure for the decision space of the criterion space is similar to the proposed Farrell PPS. (3) Calculate the marginal rates for strong and weak efficient DMUs using the obtained explicit form equations of strong and weak defining hyperplanes for the PPS with CRS technology. Finally, an empirical study in the Iranian banking sector is used to show the applicability of the proposed methods. |
| ArticleNumber | 11 |
| Author | Ghazi, A. Hosseinzadeh Lotfi, F. |
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| Cites_doi | 10.1016/j.eneco.2016.01.017 10.1016/j.ejor.2012.02.035 10.1016/0377-2217(78)90138-8 10.1016/j.apm.2010.02.023 10.1287/mnsc.30.9.1078 10.1016/j.measurement.2015.02.020 10.1057/jors.1996.127 10.2307/2982329 10.1007/s10100-008-0071-1 10.1057/jors.1977.147 10.1016/j.jsis.2006.10.002 10.1016/j.econmod.2013.09.042 10.1023/A:1013519902012 10.1023/A:1018382904489 10.1016/j.ejor.2011.09.002 10.1016/j.measurement.2014.09.019 10.1016/S0377-2217(96)00349-9 10.1016/j.aml.2011.09.068 10.1287/mnsc.42.2.205 10.1023/A:1027303901017 10.1287/inte.29.3.1 10.1016/j.ejor.2008.04.036 10.1016/0022-247X(75)90189-4 10.1023/A:1007896629828 10.1016/j.cam.2010.08.007 10.1016/j.ejor.2005.11.031 10.1016/0304-4076(90)90045-U 10.1057/jors.2008.185 10.1016/j.ejor.2004.07.043 10.1016/j.eswa.2007.09.001 10.1007/BF02125452 10.1016/j.amc.2004.09.092 10.1016/0377-2217(95)00304-5 |
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| Keywords | Marginal rates Defining hyperplane Farrell efficiency measure Multiple objective linear programming Data envelopment analysis |
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| SubjectTerms | Business and Management Computational Intelligence Data envelopment analysis Decision making Empirical analysis Hyperplanes Linear programming Management Science Mathematical analysis Operations Research Operations Research/Decision Theory Original Paper |
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| Title | Marginal rates in DEA using defining hyperplanes of PPS with CRS technology |
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