Theoretical developments in balance model and models with virtual weight restrictions

Abstract

The balance model (BM) is a unit invariant model in which takes into account the imposed strategies for DMUs through adding some balance constraints to the basic DEA models in general and the CCR model in particular. Also, balance factor is calculated along with efficiency, effectiveness and similar concepts. The mentioned balance constraints belong to the virtual weight restrictions (VWRs) category. However, to date, the consequences of incorporating weight restrictions (e.g. absolute weight restrictions, assurance regions type I (ARI), assurance regions type II (ARII)) within the classical DEA models have been explored by scholars, but are not considered for virtual weight restrictions. This paper analyses properties of the balance model and subsequently the models with VWRs by an illustrative example. The results show that models with such restrictions correctly maximize the relative efficiency (RE) of the assessed DMU despite the fact that none of the DMUs might be fully efficient (i.e. with efficiency score of 1). In addition, feasibility conditions are discussed. Finally, the proposed method will be applied to assess the branches of a specialized bank of Iran as a real application.