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 ramain unchanged. but, in some cases, the inputs/outputs cost/price information is available. this paper uses the inputs/output cost/price information and generalized the invdea concept in tow-stage structures. to this end, it proposes a four-stage method to deal with the invdea concept for estimating the inputs/outputs 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.