Optimal solutions of multiplier DEA models

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.