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A linear programming approach to efficiency evaluation in nonconvex metatechnologies
The notions of metatechnology and metafrontier arise in applications of data envelopment analysis (DEA) in which decision making units (DMUs) are not sufficiently homogeneous to be considered as operating in the same technology. In this case, DMUs are partitioned into different groups, each operatin...
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| Main Authors: | , |
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| Format: | Default Article |
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2018
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| Online Access: | https://hdl.handle.net/2134/28051 |
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| _version_ | 1818167741203349504 |
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| author | Mohsen Afsharian Victor Podinovski |
| author_facet | Mohsen Afsharian Victor Podinovski |
| author_sort | Mohsen Afsharian (7197755) |
| collection | Figshare |
| description | The notions of metatechnology and metafrontier arise in applications of data envelopment analysis (DEA) in which decision making units (DMUs) are not sufficiently homogeneous to be considered as operating in the same technology. In this case, DMUs are partitioned into different groups, each operating in the same technology. In contrast, the metatechnology includes all DMUs and represents all production possibilities that can in principle be achieved in different production environments. Often, the metatechnology cannot be assumed to be a convex set. In such cases benchmarking a DMU against the common metafrontier requires implementing either an enumeration algorithm and solving a linear program at each of its steps, or solving an equivalent mixed integer linear program. In this paper we show that the same task can be accomplished by solving a single linear program. We also show that its dual can be used for the returns-to-scale characterization of efficient DMUs on the metafrontier. |
| format | Default Article |
| id | rr-article-9497915 |
| institution | Loughborough University |
| publishDate | 2018 |
| record_format | Figshare |
| spelling | rr-article-94979152018-08-14T00:00:00Z A linear programming approach to efficiency evaluation in nonconvex metatechnologies Mohsen Afsharian (7197755) Victor Podinovski (1256964) Other commerce, management, tourism and services not elsewhere classified Data envelopment analysis Nonconvex metatechnology Metafrontier Returns to scale Business and Management not elsewhere classified The notions of metatechnology and metafrontier arise in applications of data envelopment analysis (DEA) in which decision making units (DMUs) are not sufficiently homogeneous to be considered as operating in the same technology. In this case, DMUs are partitioned into different groups, each operating in the same technology. In contrast, the metatechnology includes all DMUs and represents all production possibilities that can in principle be achieved in different production environments. Often, the metatechnology cannot be assumed to be a convex set. In such cases benchmarking a DMU against the common metafrontier requires implementing either an enumeration algorithm and solving a linear program at each of its steps, or solving an equivalent mixed integer linear program. In this paper we show that the same task can be accomplished by solving a single linear program. We also show that its dual can be used for the returns-to-scale characterization of efficient DMUs on the metafrontier. 2018-08-14T00:00:00Z Text Journal contribution 2134/28051 https://figshare.com/articles/journal_contribution/A_linear_programming_approach_to_efficiency_evaluation_in_nonconvex_metatechnologies/9497915 CC BY-NC-ND 4.0 |
| spellingShingle | Other commerce, management, tourism and services not elsewhere classified Data envelopment analysis Nonconvex metatechnology Metafrontier Returns to scale Business and Management not elsewhere classified Mohsen Afsharian Victor Podinovski A linear programming approach to efficiency evaluation in nonconvex metatechnologies |
| title | A linear programming approach to efficiency evaluation in nonconvex metatechnologies |
| title_full | A linear programming approach to efficiency evaluation in nonconvex metatechnologies |
| title_fullStr | A linear programming approach to efficiency evaluation in nonconvex metatechnologies |
| title_full_unstemmed | A linear programming approach to efficiency evaluation in nonconvex metatechnologies |
| title_short | A linear programming approach to efficiency evaluation in nonconvex metatechnologies |
| title_sort | linear programming approach to efficiency evaluation in nonconvex metatechnologies |
| topic | Other commerce, management, tourism and services not elsewhere classified Data envelopment analysis Nonconvex metatechnology Metafrontier Returns to scale Business and Management not elsewhere classified |
| url | https://hdl.handle.net/2134/28051 |