Abstract
We provide a unifying framework synthesizing the dual spaces of production and value used in DEA efficiency measurement with some well-known linear programming (LP) problems. Specifically, we make use of the technology matrix to map intensity variables into input–output space, and the adjoint transformation of the technology matrix to map input–output prices into prices of intensity variables. We show how the diet problem, a classical LP problem, is related to DEA and also use the adjoint matrix to demonstrate a procedure for pricing efficient decision-making units. We further illustrate the relationship between benefit-of-the-doubt aggregation and the diet problem.
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Notes
Charnes et al. (1978).
This is one of our interpretations of Magill and Quinzii (1996), Figure 13.1.
In the profit maximization problem we may want to restrict the intensity variables to satisfy \(\sum _{k=1}^Kz_k\leqq 1\) or \(=1\) in order for the maximum to exist.
Originally developed by Färe et al. (2013).
Färe et al. (2011) have shown by means of formulating a Langrangian–Kuhn–Tucker problem that the diet problem can be considered to be dual to the DEA profit maximization problem in the sense that the intensity variables in the profit maximization model are shadow prices in the diet problem.
The importance of the BoD model in constructing composite performance indicators is emphasized by the OECD (2008).
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We thank two anonymous referees for their comments.
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Färe, R., Grosskopf, S., Karagiannis, G. et al. Data envelopment analysis and its related linear programming models. Ann Oper Res 250, 37–43 (2017). https://doi.org/10.1007/s10479-015-2042-y
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DOI: https://doi.org/10.1007/s10479-015-2042-y