Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis

5NON‐RADIAL MEASUREMENT

5.1 INTRODUCTION

This chapter¹ discusses non‐radial models based upon the Pareto–Koopmans measurement to determine the level of operational efficiency (OE). The DEA assessment is generally separated into two groups of models. One of the two groups is referred to as “radial measures,” or input and desirable output‐oriented RM(v) and RM(c), as discussed in Chapter 4. The other group of models includes “non‐radial measures,” most of which are discussed in this chapter. The radial models, belonging to “Debreu–Farrell measures,” can determine the level of OE regarding DMUs by examining an efficiency score, along with slacks, in the objective function of their linear programming formulations². In contrast, the non‐radial measures (e.g., an additive model: Charnes et al., 1985), discussed in this chapter determine the OE level by examining the total amount of slacks, because they do not have any efficiency score in these objective functions. This type of measure belongs to the “Pareto–Koopmans measure” (Koopmans, 1951; Russell, 1985).

In addition to these OE measurement criteria, it is important to note that the proposed non‐radial measures can avoid specifying the non‐Archimedean small number (ε_n). The unique feature is important because none knows what it is in reality. See Chapter 7 for a discussion on another approach to avoid specifying such a small number even in the radial measures.

This chapter is concerned with descriptions on five non‐radial models in terms ...