Obviating some of the theoretical barriers of data envelopment analysis-discriminant analysis: an application in predicting cluster membership of customers

Abstract

Data envelopment analysis-discriminant analysis (DEA-DA) has been used for predicting cluster membership of decision-making units (DMUs). One of the possible applications of DEA-DA is in the marketing research area. This paper uses cluster analysis to cluster customers into two clusters: Gold and Lead. Then, to predict cluster membership of new customers, DEA-DA is applied. In DEA-DA, an arbitrary parameter imposing a small gap between two clusters (η) is incorporated. It is shown that different η leads to different prediction accuracy levels since an unsuitable value for η leads to an incorrect classification of DMUs. We show that even the data set with no overlap between two clusters can be misclassified. This paper proposes a new DEA-DA model to tackle this issue. The aim of this paper is to illustrate some computational difficulties in previous DEA-DA approaches and then to propose a new DEA-DA model to overcome the difficulties. A case study demonstrates the efficacy of the proposed model.

Keywords:

• data envelopment analysis
• discriminant analysis
• data envelopment analysis-discriminant analysis (DEA-DA)
• cluster analysis

Acknowledgements

The authors wish to thank the two anonymous reviewers for valuable suggestions and comments. The research was supported by the Czech Science Foundation (GACR project 14-31593S) and through the European Social Fund within the project CZ.1.07/2.3.00/20.0296.

Notes

1 This variable is a qualitative criterion. For this qualitative variable, each customer is rated on a 5-point Likert scale. Five-point scales are common for evaluation in terms of qualitative data and are often accompanied by interpretations such as: 1=very bad, 2=bad, 3=medium, 4=good, 5=very good, which are easily understood by the decision maker.

2 This variable is also a qualitative criterion.