Performance analysis of two-stage network processes with feedback flows and undesirable factors

Network data envelopment analysis (NDEA) is a non-parametric technique to evaluate the relative efficiency of decision-making units (DMUs) with network structures. An interesting and important network structure is a two-stage feedback process in which the outputs of the second stage are used as the inputs for the first stage. The existing approach did not consider undesirable products and from experience though we know that in real applications, network structures may consist of desirable and undesirable products outputs in which undesirable products can be used in the systems. The present paper proposes a DEA-based method for evaluating the relative efficiency of such a two-stage-feedback network structure with undesirable factors. Directional distance function along with weak disposability assumption for undesirable outputs has been used to analyse the performance of the network. A real case on ecological system of 31 regions in China is used to illustrate the applicability of the proposed approach.