An SOCP approach to a two-stage network DEA with feedbacks and shared resources

For performance evaluation, it is necessary to first build an appropriate assessment system based on real situations before extracting any technical measurement approach. This paper proposes a set of additive and multiplicative data envelopment analysis models in the cooperative context to decompose the efficiency of a two-stage system, composed of a production stage and a disposal stage. Furthermore, using shared resources, the current paper seeks to evaluate production efficiency, when undesirable outputs are recycled and reused in the production process that is called feedback variables. Since the proposed models cannot be linearized using the classical Charnes–Cooper technique, their conic relaxation formulations are presented that are convex problems. Finally, an industrial production process application dataset is used to compare the proposed models with the existing ones.