Input Estimation in Two-Stage Systems with Undesirable Outputs Based on Cost Efficiency

In the Inverse Data Envelopment Analysis (InvDEA) models, inputs and outputs of Decision Making Units (DMUs) are estimated while their relative efficiency scores remain unchanged. But, in some cases, the inputs cost information is available. This paper uses the inputs cost information and generalized the InvDEA concept in two-stage network structures with undesirable output in the second stage. To this end, it proposes a four-stage method to deal with the InvDEA concept for estimating the inputs of the DMUs with a two-stage network structure method, while the allocative efficiency scores of all units remain stable. Eventually, an empirical example is presented to illustrate the capability of the presented method.