the ndea–mop model in the presence of negative data using fuzzy method

in this study, the multi-objective programming (mop) method was used to solve network dea (ndea) models with assumption that, negative data is considered for the proposed ndea model which consists of seminegative and semipositive input and output. at first, two stage and then k-stage production models were formulated with consideration of negative data. in the multi-objective programming, two separate objective functions including the divisional efficiencies and the overall efficiency of the organization are modeled.  in comparison to conventional dea with negative data, the advantage of the proposed ndea models is consideration of intermediate processes and products, in order to calculate the organization’s overall efficiency. however, in conventional dea, substages of the organizations are neglected. to measure the efficiencies of an organization regarding interactive internal process, two case studies were investigated by application of the ndea-mop method with negative data. case study 1 is focused on units with two stages having seminegative and semipositive indexes. in case study 2, units with three stages are evaluated. these units also have seminegative and semipositive indexes. the overall efficiency of each unit is calculated using the proposed models. fuzzy approach as a solution procedure is applied.