STRICT VS WEAK ORDINAL RELATIONS FOR MULTIPLIERS IN DATA ENVELOPMENT ANALYSIS

In a recent paper, Golany (1988) proposes an interesting extension of Data Envelopment Analysis to the situation where ordinal relations among weights corresponding to certain dimensions exist. However, the development of the extended model contains mathematical errors and the proposed equivalence is incorrect. We establish the correct model equivalence and prove that weak ordinal relations require a nonstandard DEA model. We also show that the case of strict ordinal relations can be handled with the standard DEA model. These results hold for the CCR, BCC, additive, and multiplicative models and for relations involving both input and output multipliers.