Hierarchical groups DEA super-efficiency and group TOPSIS technique: Application on mobile money agents locations

We consider the problem of ranking two-level efficient decision-making units (DMUs) in a hierarchical group structure. Traditionally, the radial hierarchical data envelopment analysis (DEA) models were used, but these are based on the assumption that there are proportional changes in inputs or outputs. To address this shortcoming, non-radial DEA models, capable of dealing with slacks directly are commonly used. To minimise the bias associated with using a single super-efficiency (SE) model, seven diversified SE models are extended to suit an environment with DMUs structured as hierarchical groups. The seven SE ratings of the suburb and district locations as potential locations of mobile money agents reveal wide variations. A proposed group technique for order preference by similarity to ideal solution (TOPSIS) ranking method is applied for harmonising the ratings and ensuring a complete ranking of efficient suburb locations. A complete ranking is achieved for all the district and suburb locations. The TOPSIS results are moderately well-verified and validated by the principal component analysis and Spearman correlation analysis methods. The accuracy of the district location TOPSIS rankings on the final suburb location TOPSIS rankings was discovered to be moderate at 61 percent.