Data envelopment analysis efficiency in two-stage networks with feedback

Conventional applications of data envelopment analysis generally treat the Decision-Making Unit (DMU) as a black box in that the internal processes are not examined in detail. In some situations, such as the measurement of performance of a set of supply chains, the DMU can be viewed as exhibiting a network structure. A significant body of recent literature has examined a particular form of network structure, namely, where the DMU is a two-stage serial process in which the outputs from the first stage are intermediate variables that serve as inputs to the second stage. The current article extends this idea to include those situations where outputs from the second stage can be fed back as inputs to the first stage. Such feedback variables thus serve a dual role. Models are developed for examining performance in this feedback setting and are illustrated using an application involving the measurement of performance of a set of Chinese universities.