In data envelopment analysis (DEA), multiplier and envelopment CCR models evaluate the decision-making units (DMUs) under optimal conditions. Therefore, the best prices are allocated to the inputs and outputs. Thus, if a given DMU was not efficient under optimal conditions, it would not be considered efficient by any other models. In the current study, using common weights in DEA, a number of decision-making units are evaluated under the same conditions, and a number of Two-Stage neTwork DEA models are proposed within the framework of multi-objective linear programming (MOLP) for finding common weights. Furthermore, using the infinity norm, common weight sets are determined in Two-Stage neTwork models with MOLP structures.

Standard Data Envelopment Analysis (DEA) supposes that the performance measure status from the point of view of input or output is known. Nevertheless, in some situations, determining the status of a performance measure in Two-Stage neTwork is not easy. Measures with unknown status of input/output are called exible measures. In all of the previous studies did not point to classify exible measures in Two-Stage neTwork DEA. In this paper we propose FNDEA models based on the multiplier model under constant returns to scale (CRS) and variable returns to scale (VRS) in general Two-Stage neTwork structures. Our models classify exible measures, in which each one of the exible measure is treated as either input or output to maximize the overall neTwork e, ciency of the DMU under evaluation. The current paper develops an additive e, ciency decomposition approach wherein the overall e, ciency is expressed as a (weighted) sum of the e, ciencies of the individual Stages. This approach can be applied under both CRS and (VRS) assumptions. Numerical examples are used to illustrate the procedures.

Data Envelopment Analysis (DEA) has been applied in many studies in the banking sector. Conventional DEA models consider the system as a single-process black box. There are however a number of so-called neTwork DEA approach that consider the system as composed by distinct processes or Stages, each one with its own inputs and outputs and with intermediate flows among the Stages. In this paper some of these approaches that have been applied to banking sector are reviewed and in particular applications of Two-Stage DEA to Iranian banking branches are presented and discussed. The conclusions of this research are that Two-Stage DEA models have a greater discrimination power than conventional, single-process DEA and since they allow a more fine-grained analysis their results are generally more valid and useful. The main drawback is the need for more detailed data (i.e. at the process level) and the greater complexity of the resulting models, especially if there are inputs or outputs that are shared among the processes.

In the present world, there are many Two-Stage systems which provide information of inputs, outputs and intermediate measures which are imprecise, such as, (stochastic, fuzzy, interval etc). In these conditions, a Two-Stage data envelopment analysis or a (Two-Stage DEA method) cannot evaluate the e, ciencies of these systems. In several Two-Stage systems, the simultaneous presence of Stages is necessary for the , nal product. Hence, in this paper, we shall propose the stochas-tic multiplicative model and the deterministic equivalent, to measure the e, ciencies of these systems, primarily, in the presence of stochastic data, under the constant returns to scale (CRS) assumption, by using the non-compensatory property of the multiplication operator. Then, we will use the reparative property of the additive operation to propose the additive models as well as the deterministic equivalents, to calculate the e, ciencies of Two-Stage systems, in presence of stochastic data, under the constant returns to scale (CRS) and variable returns to scale (VRS) assumptions. This is to illustrate that a simultaneous presence of the Stages is not necessary for the , nal product and one Stage compen-sates the shortcomings of another Stage. Likewise, we shall convert each of these deterministic equivalents to quadratic programming prob-lems. Based on the proposed stochastic models, the whole system is e, cient if and only if, the , rst and the second Stages are e, cient. Ul-timately, in the proposed multiplicative model, we will illustrate the proposed multiplicative model, by employing the data of the Taiwanese non-life insurance companies, which has been extracted from the extant literature.

Enterprise resources planning (ERP) systems attract many attentions from industry sector because of their ability to facilitate and integrate the enterprise operations. However, many expenses accompany the implementation of these systems and consecutive changes which doing a precise and comprehensive performance evaluation a necessary part of this process. These evaluations should consider operational and technical aspects of ERP systems to reflect the effectiveness of them toward the organization's requirements. In this paper, a Two-Stage data envelopment analysis model (DEA) is presented in order to evaluate the efficiency of ERP systems in such a way that the operational and the technical aspect are evaluated in the first Stage and the second Stage of DEM model, respectively. Based on the obtained results the ERP systems’ functionality and customizability to the client processes are the Two key features that need to be considered by the providers. Furthermore, the findings of parameter sensitivity analysis of the proposed model provide deep and managerial insights into the further usability improvements of ERP systems.