Advances In Data Envelopment Analysis

Rolf Färe, Shawna Grosskopf, Dimitris Margaritis

• Publisher: WSPC
• Year: 2015
• eBook ISBN: 9789814644563
• Topic: Ciencias biológicas
• Subtopic: Ciencias en general

Data Envelopment Analysis (DEA) is often overlooked in empirical work such as diagnostic tests to determine whether the data conform with technology which, in turn, is important in identifying technical change, or finding which types of DEA models allow data transformations, including dealing with ordinal data.

Advances in Data Envelopment Analysis focuses on both theoretical developments and their applications into the measurement of productive efficiency and productivity growth, such as its application to the modelling of time substitution, i.e. the problem of how to allocate resources over time, and estimating the "value" of a Decision Making Unit (DMU).

Contents:

• Acknowledgements
• Preface
• Introduction:
  • The DEA Technology and Its Representation
  • (Axiomatic) Properties of the DEA Model
  • Appendix
• Looking at the Data in DEA:
  • Data Diagnostics
  • Technical Change
  • Data Translation
  • Appendix: Distance Functions
• DEA and Intensity Variables:
  • On Shephard's Duality Theory
  • Adjoint Transformations in DEA
  • The Diet Problem
  • Pricing Decision Making Units
• DEA and Directional Distance Functions:
  • Directional Vectors
  • Aggregation and Directional Vectors
  • Endogenizing the Directional Vector
  • Appendix
• DEA and Time Substitution:
  • Theoretical Underpinning
  • Reassessing the EU Stability and Growth Pact
  • Method
• Some Limitations of Two DEA Models:
  • The Non-Archimedean and DEA
  • Super-Efficiency and Zeros
• References
• Advanced postgraduate students and researchers in operations research and economics with a particular interest in production theory and operations management.

Chapter 1

Introduction

The purpose of our first chapter is to review the basic building blocks used as the foundation for the rest of this monograph. These will be familiar to the Data Envelopment Analysis (DEA) audience, although our notation and orientation toward axiomatic production theory may be less familiar.

We begin with the DEA technology constructed from data generated by activities of DMUs (Decision Making Units). To transform sample data points into a technology set, intensity variables, familiar from Activity Analysis are introduced. These allow us to form the basic DEA technology satisfying strong disposability of inputs and outputs as well as constant returns to scale (CRS). We start with three variations of the technology: (i) the (input–output) technology set, (ii) the output sets, and (iii) the input sets. These three equivalent representations allow us to highlight or focus on various features of production such as returns to scale, or substitution among outputs or inputs.

To provide a more direct link to the early work using Activity Analysis Models and linear programming associated with Koopmans (1951), Dorfman, Samuelson and Solow (1958), we also introduce a technology matrix M, and show how this is linked to the DEA framework.

In Section 2 we discuss properties satisfied by the DEA technology. We also show how the conditions proposed by Kemeny, Morgenstern and Thompson (1956) are essential to prove some fundamental economic and mathematical properties: (i) no free lunch, (ii) scarcity, and (iii) closedness.

An appendix of proofs concludes the chapter.

1.1The DEA Technology and Its Representation

In this section we introduce the different formulations of the DEA technology we use in this monograph. In terms of notation we assume that there are

inputs used to produce

outputs. Each input and output is a nonnegative real number; thus we are assuming that inputs and outputs are divisible.¹ This is a simplifying assumption which may be modified if required. For example, it is difficult to think of producing π number of cars.

Our three basic specifications of the technology are

•T = {(x, y) : x can produce y} Technology Set

•P(x) = {y : x can produce y} Output Set

•L(y) = {x : x can produce y} Input Set

The equivalence relationship among the sets may be summarized as Lemma 1:1 (x, y) ∈ T ⇔ y ∈ P(x) ⇔ x ∈ L(y).²

To provide some intuition concerning the relationships among these three representations of technology assume that we have one input employed to produce one output. Our three sets are illustrated in Figure 1.1.

Fig....

Table of contents

• Cover page
• Title page
• Copyright page
• Acknowledgements
• Preface
• Contents
• Chapter 1 Introduction
• Chapter 2 Looking at the Data in DEA
• Chapter 3 DEA and Intensity Variables
• Chapter 4 DEA and Directional Distance Functions
• Chapter 5 DEA and Time Substitution
• Chapter 6 Some Limitations of Two DEA Models
• References
• Index