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Traditional data envelopment analysis (DEA) models evaluate two-stage decision making unit (DMU) as a black box and neglect the connectivity may exist among the stages. This paper looks inside the system by considering the intermediate activities between the stages where the first stage uses inputs to produce outputs which are the inputs to the second stage along with its own inputs. Additionally, some of the inputs and outputs values may not be completely available because of uncertainty. Data can be interval e.g. when the missing values are replaced by intervals in which the unknown values are likely to belong. We introduce models to optimize two-stage DMU with interval data. Numerical example is applied to clarify the models.

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Data envelopment analysis is a non-parametric approach for evaluating efficiency score of peer decision making units which consume multiple inputs to produce multiple outputs. The conventional data envelopment analysis models consider decision making units as black-boxes by ignoring internal sub-processes of the production units, while network-data envelopment analysis models have been proposed for determining the efficiency score of network systems. The current paper develops a network-data envelopment analysis super efficiency model to rank and compare the performance of network systems. The proposed general network super-efficiency model can be used for ranking multi-stage production units. The new approach is then applied for evaluating wheat productions in Iran provinces. Traditional models are used as well as the new network data envelopment analysis model to calculate a set of super-efficiency scores for provinces under the investigation. The research extends the application of data envelopment analysis method to judgment and decision making in wheat farming as a network production process.

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The inverse data envelopment analysis (InvDEA) technique is an applicable method in order to estimate the input/output levels of decision-making units (DMUs) to preserve predetermined technical efficiency scores. In the managerial atmosphere, the decision maker (DM) aims to merge two or more units and needs to know the input/output levels of the merged unit, while the efficiency score of the new unit is set, however, in some cases, the units have two-stage network structures. The main purpose of this paper is merging DMUs with two-stage network structures. To reach this goal, in this paper, an InvDEA method is presented in order to estimate inputs and the intermediate products of two-stage DMUs, to achieve the different predetermined efficiency scores which have been set by the DM.