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A linear programming approach to efficiency evaluation in nonconvex metatechnologies

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journal contribution
posted on 2018-01-11, 16:30 authored by Mohsen Afsharian, Victor PodinovskiVictor Podinovski
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.

Funding

The financial support of the Deutsche Forschungsgemeinschaft (DFG) in the context of the research fund AH 90/5-1 is gratefully acknowledged.

History

School

  • Business and Economics

Department

  • Business

Published in

European Journal of Operational Research

Volume

268

Issue

1

Pages

268-280

Citation

AFSHARIAN, M. and PODINOVSKI, V.V., 2018. A linear programming approach to efficiency evaluation in nonconvex metatechnologies. European Journal of Operational Research, 268(1), pp. 268-280.

Publisher

© Elsevier

Version

  • AM (Accepted Manuscript)

Publisher statement

This paper was accepted for publication in the journal European Journal of Operational Research and the definitive published version is available at https://doi.org/10.1016/j.ejor.2018.01.013

Acceptance date

2018-01-03

Publication date

2018-08-18

Copyright date

2018

ISSN

0377-2217

Language

  • en