The two-stage data envelopment analysis models are among the widely used mathematical programming approaches to evaluate the performance of two-stage structures. In this paper, a two-stage structure with shared inputs and feedback is studied. To reduce undesirable outputs, an additive slack-based measure model is proposed to evaluate the stages and overall efficiencies, while undesirable outputs are weakly disposable. As it does not require determining the weights for combining stages’ efficiencies, all Pareto optimal stages’ efficiencies can be gained. In addition, the proposed approach can identify desirable outputs from undesirable outputs, thereby avoiding the need for weighting. This advantage from the aspect of multiobjective programming helps internal evaluation of the network model to match priorities of managers. The proposed nonlinear model is reformulated as a second-order cone program, which is a convex optimization problem that can be solved to global optimality. This is a computational improvement over the parametric models in the literature. Furthermore, the proposed model is applied for country-wise and area-wise performance evaluations of a real industrial application dataset in mainland China. Results show that the efficiency of the overall system relies between the efficiencies of the two stages and for all DMUs, the first stage’s efficiency scores are always higher than the second stage ones in both evaluations. Also, the Pearson correlation coefficient test results show that the overall efficiency is more correlated with the waste disposal stage. Finally, to show the effect of the decision maker’s preference, a detailed sensitivity analysis is performed.

The slacks-based measure (SBM) and additive SBM (ASBM) models are two widely used DEA models acting based on inputs and outputs slacks and giving efficiency scores between zero and unity. In this paper, we use both models with the application of the weak disposability axiom for outputs to evaluate efficiency in a two-stage structure in the presence of undesirable outputs. In the external evaluation, the SBM model is reformulated as a linear program and the ASBM model is reformulated as a second-order cone program (SOCP) that is a convex programming problem. In the internal evaluation, the SBM model for a specific choice of weights is linearized while the ASBM model is presented as an SOCP for arbitrary choice of weights. Finally, the proposed models are applied on a real dataset for which efficiency comparison and Pearson correlation coefficients analysis show advantages of the ASBM model to the SBM model.