Efficiency Evaluation on Series Structure Production

The knowledge of the internal structure of decision making units (DMUs) gives further insights with respect to the "black box" perspective when considering data envelopment analysis models. We present series structure of the DMUs under evaluation. Each unit is composed of several divisions with constant returns to scale. We discuss the relationship between system efficiency and division efficiency in series structures. We find that if the system is efficient, each of its division may not be efficient, but there must exist a path from the original input to the final output along which every division is efficient. Especially, for the series structure, it means if the system is efficient, then all of its divisions are efficient. Examples are given in the last section.