Proper and Consistent Production Tradeoffs in Models of Data Envelopment Analysis

In data envelopment analysis, value judgements expressed as weight restrictions in multiplier models correspond to production tradeoffs in the dual envelopment models. Such tradeoffs are interpretable as simultaneous changes to the inputs and outputs that are assumed to be technologically possible for all decision-making units (DMUs) in the technology. The specification of production tradeoffs leads to the creation of additional DMUs, expansion of technology, and improved discriminating power of the model. A known requirement to production tradeoffs is that they should be consistent with the set of observed DMUs; that is, they should not generate free and unlimited production of a nonzero vector of outputs. In this paper, we define a new principle of proper production tradeoffs and weight restrictions that should be verified in their assessment. No combination of proper tradeoffs can lead to an improvement of some inputs and outputs without simultaneously making at least some of the other inputs and outputs worse. It is possible that the tradeoffs are consistent but not proper and that they are proper but inconsistent. If the tradeoffs are not proper or are inconsistent, or both, they cannot be used in applications and should be reassessed. In this paper, we develop analytical and computational tests of proper tradeoffs, which are significantly simpler than the known tests of their consistency. We prove that, for a very large class of tradeoffs, the fact that they are proper implies that they are also consistent, which further simplifies the testing. The notion of proper tradeoffs and approaches to its testing are also applicable in decision analysis with imprecise information about the preferences of the decision-maker, stated as a set of linear inequalities in terms of criterion weights. We illustrate the new theoretical results and their use by examples and an application in the context of higher education.