A secondary goal in DEA cross-efficiency evaluation: A “one home run is much better than two doubles” criterion

AuthorsM. Davtalab Olyaie
JournalJournal of the Operational Research Society
Page number807-816
Serial number70
Volume number5
Paper TypeFull Paper
Published At2019
Journal GradeISI
Journal TypeTypographic
Journal CountryUnited Kingdom

Abstract

Data Envelopment Analysis (DEA) is a mathematical programming approach for assessing the
relative efficiency of decision making units (DMUs). The cross-efficiency evaluation is an extension
of DEA that provides a ranking method and eliminates unrealistic DEA weighting schemes on
weight restrictions, without requiring a prior information. The cross-efficiency evaluation may
have some shortages, e.g. the cross-efficiency scores may not be unique due to the presence
of several optima. To rectify this issue, several secondary goals have been proposed in the
literature. Some scholars have proposed several cross-efficiency evaluations based onmaximising
(minimising) the total deviation from their ideal point as an aggressive (benevolent) perspective.
In some cases, minimising (maximising) the number of DMUs that achieve their target efficiencies,
is more important than maximising (minimising) the total deviation from the ideal point. We
propose some alternative models for the cross-efficiency evaluation based on the cardinality of
the set of “satisfied DMUs”, i.e. the DMUs that achieve their maximum efficiencies. For aggressive
(benevolent) cross-efficiency evaluation, among all the optimal weights for a specific unit, we
choose the weights which can maximise its efficiency, and at the same time minimise (maximise)
the number of satisfied units. We demonstrate how the proposed method can be implemented
and illustrate the method using two examples.