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Assessing inputs and outputs is a significant aspect of taking decisions while there are complex and multistage processes in many examinations. Due to the presence of interval performance measures in various real-world studies, the purpose of this study is to address the changes of interval inputs of two-stage processes for the perturbations of interval outputs of two-stage systems, given that the overall efficiency scores are maintained.

Actually, an interval inverse two-stage data envelopment analysis (DEA) model is proposed to plan resources. To illustrate, an interval two-stage network DEA model with external interval inputs and outputs and also its inverse problem are suggested to estimate the upper and lower bounds of the entire efficiency and the stages efficiency along with the variations of interval inputs.

An example from the literature and a real case study of the banking industry are applied to demonstrate the introduced approach. The results show the proposed approach is suitable to estimate the resources of two-stage systems when interval measures are presented.

To the best of the authors’ knowledge, there is no study to estimate the fluctuation of imprecise inputs related to network structures for the changes of imprecise outputs while the interval efficiency of network processes is maintained. Accordingly, this paper considers the resource planning problem when there are imprecise and interval measures in two-stage networks.