Hierarchy grey relational analysis using DEA and AHP

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.