Consistent proportional trade-offs in data envelopment analysis

- Inconsistent proportional trade-offs may cause infinity or negative efficiency scores.
- An approach to identify the consistency of proportional trade-offs is proposed.
- An algorithm is designed to find maximal sub-sets of proportional trade-offs.
- We show how to aggregate maximal sub-sets of trade-offs to measure efficiency.

Proportional trade-offs - as an enhanced form of the conventional absolute trade-offs - have recently been proposed as a method which can be used to incorporate prior views or information regarding the assessment of decision making units (DMUs) into relative efficiency measurement systems by Data Envelopment Analysis (DEA). A proportional trade-off is defined as a percentage change of the level of inputs/outputs so that the corresponding restriction is adapted with respect to the volume of the inputs and outputs of the DMUs in the analysis. It is well-known that the incorporation of trade-offs either in an absolute form or proportional form may lead in certain cases to serious problems such as infinity or even negative efficiency scores in the results. This phenomenon is often interpreted as a result of defining the set of trade-offs carelessly by the analyst. In this paper we show that this may not always be the case. The existing framework by which the trade-offs are combined mathematically to build a corresponding production technology may cause a problem rather than the definition of the trade-offs. We therefore develop analytical criteria and formulate computational methods that allow us to identify the above-mentioned problematic situations and test if all proportional trade-offs are consistent so that they can be applied simultaneously. We then propose a novel framework for aggregating local sets of trade-offs, which can be combined mathematically. The respective computational procedure is shown to be effectively done by a suggested algorithm. We also illustrate how the efficiency can be measured against an overall technology, which is formed by the union of these local sets. An empirical illustration in the context of engineering schools will be presented to explain the properties and features of the suggested approach.