This paper explores the differences in performance between two groups of grocery stores that operate with different brands. The study develops a Malmquist-type index to distinguish internal inefficiencies from those associated with the group (or brand) characteristics. A fundamental characteristic of the new index is to compare groups in a static setting. The study described in this paper combines the use of a Malmquist-type index with statistical testes. The Malmquist-type index is decomposed into sub-indexes for comparing the efficiency spread between groups and the productivity differences between the best-practice frontiers of the groups. The hypothesis tests are used to verify if the differences between groups captured by the Malmquist-type index and its components are statistically significant.
There are several methods based on DEA for comparing the performance of two groups, such as the program efficiency method, the comparison of efficiency distributions using statistical hypothesis tests, and methods based on the Malmquist index. The strengths and weaknesses of these methods are explored using data sets that represent different scenarios regarding the relative position of the frontiers and the efficiency spread within the groups. The new method used in this paper is compared with the existing approaches described in the DEA literature to highlight its potential for performance assessments.
The applicability of the method is illustrated with a case study that compares the performance of sections from stores with different brands (supermarkets versus hypermarkets). Only large supermarkets are compared with hypermarkets, such that the comparisons are only made between stores with similar scale size. The stores are organised in five different sections: grocery, perishables, light bazaar, heavy bazaar and textiles. The objective of the analysis is to determine if there is evidence that the sections of stores in hypermarkets perform better than the sections from stores in supermarkets.
The study showed that there is evidence to conclude that the frontier of the sections in hypermarkets is more productive that the frontier of the sections in supermarkets. This conclusion is valid for the five sections analysed. However, the efficiency spread among sections within the same group did not differ between supermarkets and hypermarkets for all sections except for the heavy bazaar section. If the best practices of the heavy bazaar section are followed by the other sections in the same group, the scope for efficiency improvements is larger in hypermarkets than in supermarkets.
In conclusion, we recommend changing the brand of large supermarket to the brand of hypermarkets, whenever this is compatible with the organisation requirements to label a store as an hypermarket. Hypermarkets seem to be more appealing to customers and to allow the attainment of higher productivity levels
