Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis

8RETURNS TO SCALE

8.1 INTRODUCTION

This chapter¹ discusses the concept and type of returns to scale (RTS) that serve as a methodological basis for examining useful scale‐related measures by DEA. The measure provides us with information on not only a change of desirable outputs due to a unit increase of inputs but also the shape of an efficiency frontier. The first research effort on RTS was discussed by Banker (1984) and then followed by many other studies (e.g., Chang and Guh, 1991). At an early stage of this type of research, the previous efforts were interested in how to measure the type of RTS on the specific k‐th DMU. In a conventional framework of DEA, the measurement looks for the type of “local” RTS. Hereafter, this chapter and the others related to scale measures do not use the term “local” because we clearly understand the implication.

After the research of Banker and Thrall (1992), the central theme moved to the RTS measurement under an occurrence of multiple solutions on an intercept (σ) of a supporting hyperplane although their measurements need to assume a unique projection and a unique reference set. They discussed how to handle multiple solutions on σ, but not considering the other types of multiple solutions such as multiple projections and multiple reference sets. See Chapter 7 on such an occurrence of multiple projections and multiple reference sets.

To intuitively describe the concept and type of RTS, this chapter starts with a description on the measurement on ...