A double-frontier analysis approach for measuring the efficiency of dynamic systems

Measuring intertemporal efficiency variations (such as window analysis and the Malmquist index) has always been an interesting topic in the field of Data Envelopment Analysis (DEA). However, these methods overlook carry-over activities across two consecutive periods. Instead, they focus independently on individual time periods while also taking the time variation effect into account. In the real world of commerce, long planning and investment times can be a source of concern. To adapt to the long-time view, dynamic DEA integrates carry-over activities into the model and allows us to measure the special function of the period based on the long-term optimization during the whole period. Accordingly, dynamic analysis is needed when the data are available.

The present paper proposes the double-frontier dynamic DEA for simultaneously measuring system efficiency and period efficiency for multitemporal systems in which quasi-fixed input or interstitial periods are the source of intertemporal dependence between consecutive periods.

To illustrate this approach, an example is presented from the forests of Taiwan where the forest entity acts as the quasi-fixed input.

Originality/Value: 

In addition to the optimistic efficiency of the decision-making unit, this approach also considers its pessimistic efficiency. Compared with the traditional dynamic DEA, the double-frontier dynamic DEA approach has a higher differential power in identifying better-performing systems.