An inverse Free Disposal Hull model for the inputs/outputs estimation

Inverse data envelopment analysis (IDEA) is a method for estimatingthe expected input(output) variation level while their relative efficiencyscores remain unchanged. However, the IDEA underestimates(overestimates)the input variation in a non-convex situation of the reference technology. Inthis paper, we employ the inverse Free Disposal Hull (FDH) technique whichrelies only on the free disposability assumption and removes the convexity.Estimating the input(output) variation for FDH technology requires solvinglinear/nonlinear mixed integer programs which are computationally expensive.In this paper, we provide the enumeration method for estimating theinput(output) variations without changing the efficiency of the unit and bycalculating some simple ratios. Furthermore, the inverse convex DEA and nonconvexFDH models are extended in such a way as to estimate the expectedinput price variation level while preserving their cost efficiency scores.