Abstract
Conventional models of data envelopment analysis (DEA) are based on the constant and variable returns-to-scale production technologies. Any optimal input and output weights of the multiplier DEA models based on these technologies are interpreted as being the most favorable for the decision making unit (DMU) under the assessment when the latter is benchmarked against the set of all observed DMUs. In this paper we consider a very large class of DEA models based on arbitrary polyhedral technologies, which includes almost all known convex DEA models. We highlight the fact that the conventional interpretation of the optimal input and output weights in such models is generally incorrect, which raises a question about the meaning of multiplier models. We address this question and prove that the optimal solutions of such models show the DMU under the assessment in the best light in comparison to the entire technology, but not necessarily in comparison to the set of observed DMUs. This result allows a clear and meaningful interpretation of the optimal solutions of multiplier models, including known models with a complex constraint structure whose interpretation has been problematic and left unaddressed in the existing literature.
Highlights
The two conventional models of data envelopment analysis (DEA) are based on the assumption that the production technology is characterized by either constant or variable returns to scale (CRS and VRS), respectively
Complexity of their statements, the optimal solutions of the multiplier model based on any polyhedral technology, including the hybrid returns-to-scale (HRS) technology, are the most favorable for decision making unit (DMU) (Xo, Yo) when it is compared not to the finite set of observed DMUs but to the infinite set of all DMUs in the technology. (We further illustrate the difference between the two interpretations using an example in Section 8.) This new universal interpretation cannot be observed from the standard multiplier model such as (2), and we need to develop alternative multiplier statements that make this new interpretation clear
A clear and rigorous interpretation of optimal input and output weights is important for explaining the meaning of multiplier DEA models and the efficiency of DMUs obtained from them
Summary
The two conventional models of data envelopment analysis (DEA) are based on the assumption that the production technology is characterized by either constant or variable returns to scale (CRS and VRS), respectively. In Appendix B, we show the usefulness of our results for the interpretation of multiplier models based on three different polyhedral technologies
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