Using a MACBETH based multicriteria approach for virtual weight restrictions in each stage of a DEA multi-stage ranking process

Abstract

This paper proposes a new approach for fully ranking decision-making units (DMUs) in the context of Data Envelopment Analysis (DEA) models, in the presence of restrictions on virtual weights, which reflect the relative importance of certain inputs or outputs. The proposed approach is a multi-stage process involving the solution of a super-efficiency DEA model at each stage. The key idea behind our approach lies in the fact that decision-makers are allowed to apply different weight bounds at each stage of the process, taking into account the particular conditions concerning the DMUs under assessment at that stage. The different bounds of each stage are obtained using the MACBETH methodology. Our proposed approach enriches the discrimination power of the underlying super-efficiency model since it provides decision-makers with more control over the importance of inputs and outputs at each stage of the ranking process. Empirical results concerning 33 general hospitals of the Greek NHS reveal that the final rankings, as obtained by our approach, can indeed increase the discrimination power of the conventional super-efficiency DEA model and improve the DMUs’ ranking. This improvement may have serious implications in decisions related to the allocation of funds or other resources and is particularly relevant from a decision-making perspective.