Hierarchy grey relational analysis using DEA and AHP

Mohammad Sadegh Pakkar

doi:10.1108/prr-05-2017-0028

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.

Highlights

Grey relational analysis (GRA) is a multi-attribute decision-making (MADM) tool that provides a single measure of performance for each alternative with respect to a set of incommensurate attributes
2.1 Step 1: Computations at the level of attributes Computing the grey relational coefficients of attributes for each alternative using the basic GRA model which further provides the required data for an additive data envelopment analysis (DEA) model; Computing the priority weights of attributes and categories using the analytic hierarchy process (AHP) method which provides a priori information on the adjustments of attributes and categories in additive DEA models; and Computing the grey relational grades of attributes in each category for alternatives using an additive DEA model
One should notice that the additive DEA models bounded by AHP does not necessarily yield results that are different from those obtained from the original additive DEA models (Charnes et al, 1985)

Summary

Introduction

Grey relational analysis (GRA) is a multi-attribute decision-making (MADM) tool that provides a single measure of performance for each alternative with respect to a set of incommensurate attributes. By noting the problematic contradiction between objective weights in DEA and subjective weights in AHP, this research is intended to develop an integrated DEA and AHP approach in a multi-level GRA framework It can provide more reasonable and encompassing results for ranking alternatives in GRA. Pakkar (2016b) applies a pair of additive DEA models in a fuzzy multi-attribute GRA methodology to assess the overall performance of alternatives from both the optimistic and pessimistic perspectives In this approach, the attribute weights obtained by additive DEA models are bounded by AHP. The procedure of incorporating DEA and AHP in a two-level GRA may be broken down into the following steps (Figure 2)

Step 1

Step 2

The analytic hierarchy process

Additive DEA models

C11 C12 C13 C24 C25 C26 C27 C38

Conclusions