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Sequential data envelopment analysis

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Abstract

We consider a new class of Data Envelopment Analysis (DEA) modeling, which we call ‘sequential DEA’. This new approach is a relatively simple generalization of the standard and popular in practice DEA. It allows for analyzing efficiency of the decision making units that consist of a sequence of sub-DMUs (e.g., branches of banks, hospital holding company running a number of hospitals at different locations, hotel chains, etc.). The approach is embedded in the Hilbert sequence space (\(\ell ^{2}\)) and therefore it allows for potentially different numbers of the sub-DMUs as well as different numbers of inputs and outputs used by different decision making units. We hope this approach will open up a new stream of literature in the sense that many existing variations from the already rich literature on DEA can be adapted to this approach.

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Notes

  1. See Luenberger (1969) on Banach spaces in the context of optimization theory. Also see Shephard and Färe (1980).

  2. See Luenberger (1969) on this topic in the context of optimization theory.

  3. Also see Debreu (1951) for the economic theory roots of this measure and Färe et al. (2019) for various generalizations.

  4. Shephard and Färe (1978) describe their theory as having inputs and outputs in Banach spaces and their theoretical foundation can be potentially used (with some adaptation) to further generalize our approach, to represent DEA models in sequences of the Banach space.

  5. Also see Sickles and Zelenyuk (2019) for related discussions.

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Acknowledgements

The authors also acknowledge the financial support from ARC Grant (FT170100401). We also thank Bao Hoang Nguyen, Zhichao Wang, and Evelyn Smart for their proofreading feedback.

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Correspondence to Valentin Zelenyuk.

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Färe, R., Zelenyuk, V. Sequential data envelopment analysis. Ann Oper Res 300, 307–312 (2021). https://doi.org/10.1007/s10479-020-03924-x

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