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In conventional data envelopment analysis (DEA) models, data are usually considered as continuous measures while the role of measures from input and/or output aspects is known. However, there are situations in the real world that a measure can play either input or output roles, a flexible measure, while it can only take integer values (e.g., nurse trainees and medical interns in assessing the performance of hospitals). In the current paper, integer DEA models with flexible measures from two individual DMUs and aggregate efficiency perspectives are proposed to determine the relative efficiency of units and the role of flexible measures. Indeed, slacks are addressed and a slacks-based measure (SBM) of efficiency is defined for calculating the performance of decision making units (DMUs) in the presence of flexible and integer factors. The majority decision rule is also used to specify the role of flexible measures from the individual DMU point of view. Two examples including banks and hospitals are utilized to clarify and demonstrate the suggested approach.

Data envelopment analysis (DEA) is an approach to measure the relative efficiency of a set of decision-making units (DMUs) which uses multiple inputs to produce multiple outputs. In real world situations, due to uncertainty, DEA is sometimes faced with imprecise inputs and/or outputs. Therefore, performance measurement must often be performed under uncertainty conditions. Generally, the performance of DMUs can be evaluated from two perspectives—optimistic and pessimistic. As a result, two different evaluations are obtained for each DMU. In this article, we first obtain the efficiencies of the DMUs under evaluation from both optimistic and pessimistic views. The optimistic view evaluates each DMU with a set of the most desirable weights; the efficiencies measured by the optimistic approach are called optimistic efficiencies. The pessimistic view evaluates each DMU with a set of the most undesirable weights; the efficiencies measured by the pessimistic approach are called pessimistic efficiencies. Then it is shown that the outcomes of these two evaluations are conflicting with each other, being undoubtedly biased, unrealistic, and unconvincing. To overcome this problem, we propose a new measure of overall performance which is used for integrating the measures obtained from optimistic and pessimistic views and we will use it to identify the DMU with the best performance under uncertainty conditions. Also, we propose new fuzzy DEA models that evaluate a DMU from the pessimistic perspective in a fuzzy context. The proposed measure will be shown with two numerical examples, including the selection of a flexible manufacturing system.

Data Envelopment Analysis (DEA) has gained a wide range of applications in measuring the relative performance of a set of comparable operational units with multiple in-commensurate inputs and outputs. One research issue which has received widespread attention in the rapidly growing field of DEA deals with the problem of determining marginal rates or elasticities of substitution of the production units. This paper uses a DEA-based procedure to calculate group marginal rates of substitution. To this end, the envelopment form of BCC model is directly applied to analyze the trade-offs and marginal rates of substitution. The contribution of this paper is the calculation of the directional marginal rates of a group of variables to another group. In order to illustrate the applicability of the proposed approach a real application on US power plants is presented.

Marginal rates of substitution are important quantities for analysts and managers. The current paper focuses on estimating these quantities in the presence of nondiscretionary factors in performance measurement of a group of production units. We propose a DEA framework to verify how an efficient unit would perform in two different environments and find out how the efficiency scores depends on locating the units in a more or less favorable environment. An empirical study in banking is then used to illustrate the applicability of the proposed approach.

The non-parametric Data Envelopment Analysis (DEA) literature on network-structured performance analysis normally considers desirable intermediate measures. These measures are the outputs from the first stage and are used as inputs to the second stage. In many real situations, the intermediate measures consist of desirable and undesirable outputs. This subject has recently attracted considerable attention among DEA researchers. The motivation of this study is the application of the weak disposability to modeling network DEA with undesirable intermediate measures. Undesirable products in this paper are studied in two different cases: either as final outputs or as intermediate measures. In both cases, cooperative and non-cooperative game theories are proposed to assess the relative performance of the operational units. A real case on 39 Spanish Airports in 2008 has been illustrated to verify the applicability of the proposed approaches.

Data envelopment analysis (DEA) has gained a wide range of applications in measuring comparative efficiency of decision making units (DMUs) with multiple incommensurate inputs and outputs. The standard DEA method requires that the status of all input and output variables be known exactly. However, in many real applications, the status of some measures is not clearly known as inputs or outputs. These measures are referred to as flexible measures. This paper proposes a flexible slacks-based measure (FSBM) of efficiency in which each flexible measure can play input role for some DMUs and output role for others to maximize the relative efficiency of the DMU under evaluation. Further, we will show that when an operational unit is efficient in a specific flexible measure, this measure can play both input and output roles for this unit. In this case, the optimal input/output designation for flexible measure is one that optimizes the efficiency of the artificial average unit. An application in assessing UK higher education institutions used to show the applicability of the proposed approach.