Network DEA based on DEA-ratio

Dariush Akbarian

doi:10.1186/s40854-021-00278-6

Abstract

Data envelopment analysis (DEA) is a technique to measure the performance of decision-making units (DMUs). Conventional DEA treats DMUs as black boxes and the internal structure of DMUs is ignored. Two-stage DEA models are special case network DEA models that explore the internal structures of DMUs. Most often, one output cannot be produced by certain input data and/or the data may be expressed as ratio output/input. In these cases, traditional two-stage DEA models can no longer be used. To deal with these situations, we applied DEA-Ratio (DEA-R) to evaluate two-stage DMUs instead of traditional DEA. To this end, we developed two novel DEA-R models, namely, range directional DEA-R (RDD-R) and (weighted) Tchebycheff norm DEA-R (TND-R). The validity and reliability of our proposed approaches are shown by some examples. The Taiwanese non-life insurance companies are revisited using these proposed approaches and the results from the proposed methods are compared with those from some other methods.

Highlights

Data envelopment analysis (DEA) is an approach used to measure the relative efficiency of a set of : Decision making unit (DMU) with multiple inputs and outputs, first introduced into the operations research and management science literature by Charnes et al (1978)
Considering the advantage of DEA-R models over the : Charnes (CCR)-based models, we evaluate the efficiency of two-stage DMUs by DEA-R models
In network DEA, if all data are expressed as ratio output/input or if in the production process an input is not used for producing a particular output or if data ratio is important to managers, traditional two-stage DEA models can no longer be used

Summary

Introduction

Data envelopment analysis (DEA) is an approach used to measure the relative efficiency of a set of DMUs with multiple inputs and outputs, first introduced into the operations research and management science literature by Charnes et al (1978). Chen et al (2009) revealed that Kao and Hwang’s (2008) two-stage DEA model assumed constant returns to scale (CRS) and did not Akbarian Financ Innov (2021) 7:73 apply the variable returns to scale (VRS) assumption They developed an additive efficiency decomposition approach in which the overall efficiency is expressed as a weighted average of the efficiency of the individual stages under VRS technology. Olesen et al (2015) showed that the use of ratio inputs and outputs in the variable returns-to-scale (VRS) and constant returns-to-scale (CRS) models generally violates the stated production assumptions. The DEA-R is an approach to apply expert’s opinions in performance evaluationn of DMUs. For example, if a certain output cannot be produced by a certain input, the corresponding ratio “output/input” can be deleted from the model.

Literature review

Proposed methodology

21 Royal Sunalliance

Conclusion