Theoretical developments in balance model and models with virtual weight restrictions

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.

Randomizing Efficiency Scores in DEA Using Beta Distribution

Data Envelopment Analysis (DEA) has come under criticism that it is capable of handling only the deterministic input/output data, and therefore, efficiency scores reported by DEA may not be realistic when the data contain random error. Several researchers in the past have addressed this issue by proposing Stochastic DEA models. Some others, citing imprecise data, have proposed Fuzzy DEA models. This paper proposes a method to randomize efficiency scores in DEA by treating each score as an ‘order statistic' that follows a Beta distribution, and it uses Thompson et al.'s (1996) DEA model appended with Assurance Regions (AR) randomized by our “uniform sampling”. In an application to a set of banks, the work demonstrates the randomization and derives some statistical results.

Nonlinear Efficiency in DEA Relative to “Ideal Reference”

Several researchers in the past have emphasized the importance of computing efficiency measures in Data Envelopment Analysis (DEA) relative to a best-practice benchmark. Thompson et al. (1995) introduced a nonlinear efficiency measure with linked-cone (LC) assurance-regions (AR) in DEA. In this paper, we compute Thompson-Thrall's measure vis-à-vis linear efficiency measures of CCR (Charnes et al., 1978), BCC (Banker et al., 1984), CCR/AR and BCC/AR (Thompson et al., 1992), relative to “ideal reference”- an industry average. We demonstrate the computations in an application to a set of banks and show that the nonlinear measure is stricter than the linear measures.