DEA for Two-Stage Networks: Efficiency Decompositions and Modeling Techniques

Data envelopment analysis (DEA) is a method for identifying best practices among peer decision making units (DMUs). An important area of development in recent years has been that devoted to applications wherein DMUs represent network processes. One particular subset of such processes is those in which all the outputs from the first stage become inputs to the second stage. We call these types of DMU structures “two-stage networks”. Existing approaches in modeling efficiency of two-stage networks can be categorized as using either Stackelberg (leader-follower), or cooperative game concepts. There are two types of efficiency decomposition; multiplicative and additive. In multiplicative efficiency decomposition, the overall efficiency is defined as a product of the two individual stages’ efficiency scores, whereas in additive efficiency decomposition, the overall efficiency is defined as a weighted average of the two individual stages’ efficiency scores. We discuss modeling techniques used for solving two-stage network DEA models in linear programs.