Hierarchical fuzzy DEA model with double frontiers combined with TOPSIS technique: application on mobile money agents locations

Hierarchical data envelopment analysis (DEA) models evaluate the efficiency of decision-making units (DMUs) with a hierarchical group structure, where sub-DMUs are grouped into main DMUs. Contrary to early hierarchical DEA models, which were based on crisp input and output data, the model adopted in this study considers fuzziness attributes in the input and output data. The efficiency analysis was mainly based on the optimistic frontier in the early conventional fuzzy DEA models. To get a full view of the efficiency of the DMUs, we incorporated a second frontier based on the pessimistic assumption. In this study, two levels of analysis were implemented for the sub-DMUs and main DMUs. A combination of the optimistic and pessimistic efficiency ratings for both levels of analysis was done to get the overall performance measures. We applied the proposed approach to analyse the mobile money agents’ locations. Aggregating sub-DMUs with ratings of the main DMUs improved the segregation of sub-DMUs in different groups. However, within groups, most sub-DMUs had similar ratings, making it difficult to distinguish the performance of the DMUs. To further improve the segregation of the DMUs, we applied the technique for order preference by similarity to the ideal solution (TOPSIS) based on the overall performance measures. The performance of 75% of the sub-DMUs was completely segregated, whilst 100% was achieved for the main DMUs. The final TOPSIS results were validated using the principal component analysis (PCA). A Spearman correlation of 50% was observed between the TOPSIS and the PCA results. The accuracy of the district location TOPSIS rankings on the final suburb location TOPSIS rankings was 72%.