A unified classification of two-stage DEA models

Standard Data Envelopment Analysis (DEA) is used to evaluate the efficiency of Decision Making Units (DMUs) and treats its internal structures as a “black box”. The aim of this paper is twofold. The first task is to survey and classify the two-stage DEA models and to present the applications of these models across the literature. The second aim is to point out the significance of these models for the decision maker of a supply chain. We analyze the simple case of these models which is the two-stage models and a few more general models such as network DEA models. Furthermore, we study some variations of these models such as models with only intermediate measures between the first and second stages and models with exogenous inputs in the second stage. We define four categories: independent, connected, relational and game theoretic two-stage DEA models. We present each category along with its mathematical formulations, main applications and possible connections with other categories. Finally, we present some concluding remarks and a number of policy implications and opportunities for the decision maker.