Stochastic Benchmarking: Theory and Applications

✍ Scribed by Alireza Amirteimoori, Biresh K. Sahoo, Vincent Charles, Saber Mehdizadeh

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 154
• Series: International Series in Operations Research & Management Science
• Category: Library

✦ Synopsis

This book introduces readers to benchmarking techniques in the stochastic environment, primarily stochastic data envelopment analysis (DEA), and provides stochastic models in DEA for the possibility of variations in inputs and outputs. It focuses on the application of theories and interpretations of the mathematical programs, which are combined with economic and organizational thinking. The book’s main purpose is to shed light on the advantages of the different methods in deterministic and stochastic environments and thoroughly prepare readers to properly use these methods in various cases. Simple examples, along with graphical illustrations and real-world applications in industry, are provided for a better understanding. The models introduced here can be easily used in both theoretical and real-world evaluations.

This book is intended for graduate and PhD students, advanced consultants, and practitioners with an interest in quantitative performance evaluation.

✦ Table of Contents

Preface
Introduction
Benchmarking
An Introduction to DEA
Probability Theory
Stochastic DEA
Stochastic Network DEA
Stochastic Scale Elasticity
Contents
Chapter 1: Benchmarking
1.1 What Is Benchmarking?
1.2 Key Performance Indicator
1.3 Efficiency and Productivity
1.4 Efficiency Analysis
1.4.1 Technical Efficiency
1.4.2 (Input) Allocative Efficiency
1.4.3 (Output) Allocative Efficiency
References
Chapter 2: An Introduction to Data Envelopment Analysis
2.1 Symbols and Notations
2.2 Technology (Production Possibility) Set
2.3 Basic DEA Programs
2.3.1 CCR Program
2.3.2 BCC Program
2.3.3 Additive Program
2.3.4 Allocative Efficiency Programs
2.4 Returns-to-Scale
2.5 Network DEA
2.5.1 Non-cooperative Models (Leader-Follower)
2.5.2 Centralized Model
References
Chapter 3: Probability Theory
3.1 Probability Space
3.2 Random Variable
3.3 Mathematical Expectation
3.4 Discrete Distributions
3.5 Continuous Distributions
3.6 The Normal Distribution
3.7 The Chi-Square Distribution
3.8 Sampling Distributions
3.8.1 Limit Theorems
3.9 Estimation Theory
3.9.1 The Method of Maximum Likelihood
3.9.2 Linear Regression Model
3.9.3 General Linear Model
3.9.4 Ordinary Least Square Method (OLS)
References
Chapter 4: Stochastic Data Envelopment Analysis
4.1 Stochastic Technology Set
4.2 Chance-Constrained Empirical Technology Set
4.3 Stochastic Data Envelopment Analysis Models
4.3.1 Chance-Constrained DEA Model (E-Model)
4.3.2 Error Structure
4.3.3 Chance-Constrained DEA Model (P-Model)
4.3.4 Satisficing Model
4.3.5 Transformation to a Linear Programming Problem
References
Chapter 5: Stochastic Network Data Envelopment Analysis
5.1 Stochastic Two-Stage Network DEA Models
5.2 The Non-cooperative Model
5.2.1 Stage 1 as the Leader and Stage 2 as the Follower
5.2.2 Transformation to Linear Programming
5.2.3 Stage 2 as the Leader and Stage 1 as the Follower
5.2.4 An Illustrative Application
5.3 The Cooperative Models
5.3.1 Deterministic Centralized Model
5.3.2 Stochastic Centralized Network Model
5.3.3 Transformation to Deterministic Equivalent Linear Models
5.3.4 Error Structure
5.3.5 An Empirical Example
References
Chapter 6: Stochastic Scale Elasticity
6.1 A Value-Based Measure of Technical Efficiency and SE in the Deterministic Case
6.2 A Value-Based Measure of TE and SE in the Stochastic Case
6.2.1 Stochastic Value-Based TE Measure
6.2.2 Stochastic Value-Based SE Measure
6.3 The Illustrative Empirical Application
6.3.1 The Data
6.3.2 Stochastic Value-Based TE Scores
6.3.3 Stochastic Value-Based SE Scores
6.3.4 Deterministic Value-Based SE Scores of the States
6.3.5 A Comparison Between the Deterministic and Stochastic Methods
References