Two-stage network DEA: When intermediate measures can be treated as outputs from the second stage

This paper investigates efficiency measurement in a two-stage data envelopment analysis (DEA) setting. Since 1978, DEA literature has witnessed the expansion of the original concept to encompass a wide range of theoretical and applied research areas. One such area is network DEA, and in particular two-stage DEA. In the conventional closed serial system, the only role played by the outputs from Stage 1 is to behave as inputs to Stage 2. The current paper examines a variation of that system. In particular, we consider settings where the set of final outputs comprises not only those that result from Stage 2, but can include, in addition, certain outputs from the previous (first) stage. The difficulty that this situation creates is that such outputs are attempting to play both an input and output role in the same stage. We develop a DEA-based methodology that is designed to handle what we term 'time-staged outputs'. We then examine an application of this concept where the DMUs are schools of business.