An inverse network DEA model for two-stage processes in the presence of undesirable factors

The inverse Data Envelopment Analysis (DEA) problem has been one of the most critical issues in the last decade. The inverse DEA permits the chief manager to increase (or decrease) outputs (or inputs) of Decision-Making Units (DMUs) in such a way that the level of the relative efficiency of the under–observed DMU is preserved. Due to the importance of network-structured production systems in real life, the primary purpose of the present research is to provide an inverse DEA model for a two-stage network-structured production system in the presence of undesirable factors. The weak disposability assumption is used to handle undesirable outputs in the proposed model. The focus of the proposed model is on estimating the amount of change in one or more indicators of one stage of the process by changing the indicators of another stage to preserve the level of efficiency. The most important advantage of the proposed procedure is that it can increase the level of outputs and simultaneously reduce the level of inputs. To demonstrate its practical use, the model is applied to a real-life example in poultry farming.