realworld applications that the efficiency of firms must be assessed while bounded elements, discrete values, and flexible measures are present. For this purpose, the current study proposes DEA-based approaches to estimate the relative efficiency of DMUs where bounded factors, integer values, and flexible measures exist. To illustrate it, radial models based on two aspects, individual and aggregate, are introduced to measure the performance of entities and to handle the status of the flexible measure such that there are bounded components and discrete data. Applications of approaches proposed in the areas of quality management, highway maintenance patrols, and university performance measurement are given to clarify the issue and to show their practicability. It was found that the introduced procedure can determine practical projection points for bounded measures and integer values (from the individual DMU viewpoint) and can classify flexible measures along with evaluation of DMUs relative efficiency.

series components are considered, in which the first component or parallel section consists of the shared inputs, and the second component or series section consists of undesirable factors. By considering the weak disposability assumption for undesirable factors, a DEA approach as based on network slackbased measure (NSBM) is introduced to evaluate the performance of processes with mixed structures. The proposed model is illustrated with a real case study. Then, the model is developed to discriminate efficient units.

as the inputs for the first stage. The existing approach did not consider undesirable products and from experience though we know that in real applications, network structures may consist of desirable and undesirable products outputs in which undesirable products can be used in the systems. The present paper proposes a DEA-based method for evaluating the relative efficiency of such a two-stage-feedback network structure with undesirable factors. Directional distance function along with weak disposability assumption for undesirable outputs has been used to analyse the performance of the network. A real case on ecological system of 31 regions in China is used to illustrate the applicability of the proposed approach.

(DEA) models require that the status of all inputs and outputs measures be precisely specified in advance. However, there are situations where a performance measure can play input role for some DMUs and output role for the others. This paper introduces an approach to determine the situation of such flexibility where in the presence of resource sharing among subunits, the partial input will impact output in DEA. As a result, DMUs have a fair evaluation when compared to each other. Likewise, the maximum improvement is obtained in aggregate efficiency due to partial input to output impacts. The proposed approach is applied to a set of real data collected from 30 branches of an Iranian bank.