Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis

16NON‐RADIAL APPROACH FOR UNIFIED EFFICIENCY MEASURES

16.1 INTRODUCTION

This chapter¹ discusses the three types of non‐radial models for DEA environmental assessment, all of which originate from the range‐adjusted measure (RAM) discussed in Chapter 5. See the properties of RAM in Chapter 6. This study utilizes RAM as a basic model because it produces positive multipliers, or dual variables, related to all production factors. The analytical feature implies that all production factors are fully utilized in RAM‐based assessment. Furthermore, as discussed in Chapter 6, the non‐radial model has the property of “translation invariance.” This property indicates that an efficiency measure should be not influenced even if inputs and/or outputs are shifted toward the same direction by adding or subtracting a specific real number. The desirable property makes it possible to evaluate the performance of various organizations (i.e., DMUs), whose production factors contain zeros and negative values in a data set. See Chapter 26 for a detailed description on how to use the desirable property for DEA environmental assessment. The two unique features indicate the important methodological benefits of RAM. However, it is necessary for this chapter to reorganize RAM for environmental assessment because it cannot directly handle the existence of undesirable outputs in the original formulation, as discussed in Chapter 5.

To measure the performance of DMUs whose production activities are characterized by ...