Hierarchy grey relational analysis using DEA and AHP

Abstract

Purpose This paper aims to apply an integrated data envelopment analysis (DEA) and analytic hierarchy process (AHP) approach to a multi-hierarchy grey relational analysis (GRA) model. Consistent with the most real-life applications, the authors focus on a two-level hierarchy in which the attributes of similar characteristics can be grouped into categories. Nevertheless, the proposed approach can be easily extended to a three-level hierarchy in which attributes might also belong to different sub-categories and further be linked to categories. Design/methodology/approach The procedure of incorporating the DEA and AHP methods in a two-level GRA may be broken down into a series of steps. The first three steps are under the heading of attributes and the latter three steps are under the heading of categories as follows: computing the grey relational coefficients of attributes for each alternative using the basic GRA model which further provides the required (output) data for an additive DEA model; computing the priority weights of attributes and categories using the AHP method which provides a priori information on the adjustments of attributes and categories in additive DEA models; computing the grey relational grades of attributes in each category for alternatives using an additive DEA model; converting the grey relational grades of attributes to the grey relational coefficients of categories; computing the grey relational grades of categories for alternatives using an additive DEA model; computing the dissimilarity grades of categories for the tied alternatives using an additive DEA exclusion model. Findings The proposed approach provides a more reasonable and encompassing measure of performance in a hierarchy GRA, based on which the overall ranking position of alternatives is obtained. A case study of a wastewater treatment technology selection verifies the effectiveness of this approach. Originality/value This research is a step forward to overcome the current shortcomings in a hierarchy GRA by extracting the benefits from both the objective and subjective weighting methods.

Evaluation of the Efficiencies of Public High Schools in Izmir/Turkey Using Deahp Approach

“…The activities of 8 financial years were evaluated by using the CCR model; [10] in another study conducted to evaluate the efficiency of 12 faculties in Serbia, constant returns to scale model was used, which identified 2 input variables and 3 input variables; [11] the export efficiency of 30 textile and pret a porter companies was assessed with DEA model, which included data from 2012 by using 4 input and 1 output variables. AHP model was used to determine the factors of efficiency for those with 100% efficiency; [12] 8 non-life insurance companies in Turkey conducted performance evaluation tests for financial rates by using ratio analysis based on DEA and AHP models; [13] in another study, the researchers performed an analysis by integrating grey relational analysis (GRA) into DEA and AHP models in a multi-hierarchical structure; and [14] in a relevant study, the researchers proposed a integrated model of DEA and AHP to evaluate efficiency in higher education in Greece.…”

Editorial

“…The next paper by Pakkar (2017) proposes the application of additive data envelopment analysis models in hierarchy grey relational analysis (GRA). He finds that the proposed approach provides a more reasonable and encompassing measure of performance in a hierarchy GRA based on which the overall ranking position of alternatives is obtained.…”