Traditional DEA models cannot determine the source of inefficiency for structures with more than one stage (network structures). Continuous two-stage structures are one of the most applicable and basic network structures, and one of their main challenges is determining the relationship between the total efficiency and the efficiency of the stage and also determining the optimum amount of intermediate variables. The available models in solving the challenges and calculating the efficiency have orib or aren’t applicable for all two-stage structures. The purpose of this study is developing a multi-objective network DEA model that doesn’t have the weaknesses of the previous model.
In this study, it is attempted to develop a multi-objective model with a composition approach that considers the efficiency of the stages simultaneously, and also to interpret the results geometrically and compare it with the available models. The presented model was developed to multi-optimal and VRS conditions.
In all the models, efficiencies are between zero to one and a unit is network efficient only and only when it is efficient in both stages.
The presented model was used in an applicable example to evaluate the sustainability of 17 supply chains and the results showed that the model does a realistic evaluation in comparison to the traditional models. In the end, the model priority over the literature review models was mentioned with examples.