Inverse DEA in two-stage systems based on allocative efficiency

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