An extended inequality approach for evaluating decision making units with a single output
Abstract In this work, an extended evaluation approach for decision making units (DMUs) with a single output is proposed. Firstly, the input and output data for each DMU are changed in the same proportion until all the outputs are equal, and then the coordinate system is established with input i as...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1459-z |
| _version_ | 1819113495867686912 |
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| author | Xiao-Li Meng Fu-Gui Shi |
| author_facet | Xiao-Li Meng Fu-Gui Shi |
| author_sort | Xiao-Li Meng |
| collection | DOAJ |
| description | Abstract In this work, an extended evaluation approach for decision making units (DMUs) with a single output is proposed. Firstly, the input and output data for each DMU are changed in the same proportion until all the outputs are equal, and then the coordinate system is established with input i as the ith coordinate axis. Secondly, in the coordinate system, the production possibility set, which is spanned by all the DMUs without the evaluated DMU, is expressed by inequalities. Moreover, the mathematical expression of the line segment joining the origin to the evaluated DMU is given. Thirdly, the efficiency measure of the evaluated DMU is obtained from the relationship between the production possibility set and the line segment. In order to distinguish the weak efficiency and efficiency, the partially ordered set and minimal element are introduced in the paper. Finally, an example is provided to illustrate the proposed approach. |
| first_indexed | 2024-12-22T04:30:19Z |
| format | Article |
| id | doaj.art-74624c6c852549a58c5ce0ef79ae3164 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-22T04:30:19Z |
| publishDate | 2017-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-74624c6c852549a58c5ce0ef79ae31642022-12-21T18:39:02ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-08-012017111010.1186/s13660-017-1459-zAn extended inequality approach for evaluating decision making units with a single outputXiao-Li Meng0Fu-Gui Shi1School of Mathematics and Statistics, Beijing Institute of TechnologySchool of Mathematics and Statistics, Beijing Institute of TechnologyAbstract In this work, an extended evaluation approach for decision making units (DMUs) with a single output is proposed. Firstly, the input and output data for each DMU are changed in the same proportion until all the outputs are equal, and then the coordinate system is established with input i as the ith coordinate axis. Secondly, in the coordinate system, the production possibility set, which is spanned by all the DMUs without the evaluated DMU, is expressed by inequalities. Moreover, the mathematical expression of the line segment joining the origin to the evaluated DMU is given. Thirdly, the efficiency measure of the evaluated DMU is obtained from the relationship between the production possibility set and the line segment. In order to distinguish the weak efficiency and efficiency, the partially ordered set and minimal element are introduced in the paper. Finally, an example is provided to illustrate the proposed approach.http://link.springer.com/article/10.1186/s13660-017-1459-zdata envelopment analysisdecision making unitinequalitypartially ordered setminimal element |
| spellingShingle | Xiao-Li Meng Fu-Gui Shi An extended inequality approach for evaluating decision making units with a single output Journal of Inequalities and Applications data envelopment analysis decision making unit inequality partially ordered set minimal element |
| title | An extended inequality approach for evaluating decision making units with a single output |
| title_full | An extended inequality approach for evaluating decision making units with a single output |
| title_fullStr | An extended inequality approach for evaluating decision making units with a single output |
| title_full_unstemmed | An extended inequality approach for evaluating decision making units with a single output |
| title_short | An extended inequality approach for evaluating decision making units with a single output |
| title_sort | extended inequality approach for evaluating decision making units with a single output |
| topic | data envelopment analysis decision making unit inequality partially ordered set minimal element |
| url | http://link.springer.com/article/10.1186/s13660-017-1459-z |
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