Knowledge Discovery Process and Methods to Enhance Organizational Performance

215

Chapter 11

Determining Sources of

Relative Inefciency in

Heterogeneous Samples

Using Multiple Data

Analytic Techniques

Sergey Samoilenko

andKweku-Muata Osei-Bryson

Contents

Introduction ......................................................................................................216

DEA with CA and NNs .................................................................................... 219

CA and DEA ................................................................................................ 219

NNs and DEA ............................................................................................. 220

Description of the Methodology ...................................................................... 220

Description of Steps 3–5 of the Methodology ...............................................223

Step 3: Generate a Black Box Model of Transformative Capacity of

Each Cluster.............................................................................................223

Step 4: Obtain Simulated Sets of the Outputs for Each DMU in Each

Cluster .....................................................................................................223

Step 5: Determine the Sources of the Relative Ineciency of the

DMUs in the Sample ...............................................................................223

216 ◾ Sergey Samoilenko and Kweku-Muata Osei-Bryson

Abstract: Data envelopment analysis (DEA) is widelyusedbyresearchers and prac-

titioners alike to assess relative performance of decision-making units (DMUs).

Commonly, the dierence in the scores of relative performance of DMUs in the

sample is considered to reect their dierences in the eciency of conversion of

inputs into outputs. In the presence of scale heterogeneity, however, the source of

the dierence in scores becomes less clear, for it is also possible that the dierence in

scores is caused by heterogeneity of the levels of inputs and outputs of DMUs in the

sample. In this chapter, we present and demonstrate a hybrid ve-step methodology

that involves the use of DEA, cluster analysis, and neural networks, and that allows

an investigator to determine the source of relative heterogeneity.

Keywords: Cluster Analysis, neural nets, data envelopment analysis, relative eciency,

heterogeneous samples.

Introduction

Data envelopment analysis (DEA) is a widely used nonparametric analytic tool (e.g.,

Asmild et al. 2007; Chen and van Dalen 2010; Doyle and Green 1994; Gillen and

Lall 1997; Khalili et al. 2010; Khouja 1995; Shao and Lin 2001), which is com-

monly applied in the research and practitioner communities to determine the rela-

tive eciencies of the decision-making units (DMUs). Any entity that receives a

set of inputs and produces a set of outputs could be designated as a DMU; thus,

any group of such entities could be subjected to DEA. As a result, this method

has been applied to evaluate productivity and performance of airports (Gillen and

Lall 1997; Martin and Roman 2001; Pels et al. 2001), eciency of US Air Force

maintenance units (Charnes et al. 1985), hospitals (Grosskopf et al. 2001; Gruca

Motivation for Steps 3 and 5 of the Methodology .........................................223

Motivation for Step 3 ...............................................................................223

Motivation for Step 5 ...............................................................................224

Illustrative Example ...........................................................................................225

Description of the Illustrative Dataset ........................................................... 225

Application of the Methodology to the Illustrative Dataset .......................... 226

Results of Step 1: Evaluate the Scale Heterogeneity Status of the Dataset ..... 227

Results of Step 2: Determine the Relative Eciency Status of Each DMU .... 228

Results of Steps 3 and 4: Generate Simulated Sets of the Outputs for

Each Cluster Based on Black Box Models of Transformative Capacity

Processes ................................................................................................. 228

Results of Step 5 .......................................................................................229

Discussion and Conclusion ...............................................................................230

References .........................................................................................................231

Appendix: Results of Cluster Analysis ................................................................236