Limitation and optimization of inputs and outputs in the inverse data envelopment analysis under variable returns to scale

As an important component of data envelopment analysis (DEA), the inverse DEA method often has no feasible solution under variable returns to scale (VRS). By analyzing the reason of this problem, the limitation of inputs and outputs in the inverse DEA method under VRS is identified. Then the outputs possible set and the inputs possible set are defined for different inverse DEA models; and some models are thus developed to determine the change range of outputs/inputs. Sequentially, by determining the optimal given outputs/inputs, the inverse DEA model under VRS is used to estimate the optimal inputs increment or outputs diminution for the optimal given efficiency, and the problem that the inverse DEA method has no feasible solution is avoided. In addition, the effects of efficiency change and technological change on the optimization of inputs and outputs are further discussed in this paper. Finally, two examples are provided to illustrate the validity and effectiveness of our methods.