The extension and integration of the inverse DEA method

The inverse DEA (Data Envelopment Analysis) method is primarily used to analyse the changing relationship between the inputs and outputs of a DMU (Decision-Making Unit) when its efficiency is kept constant or set to a target value. However, the existing inverse DEA method cannot be applied directly to estimate all the changing relationships. For example, the existing DEA models fail to estimate the input variations when the supervisor wants to maintain the DMU’s output-oriented efficiency during the downscaling of production. This paper analyses all the possible changing relationships that need to be solved by the inverse DEA method and develops different models for both the output and input orientations, accomplishing the extension and integration of the inverse DEA model. For illustration of our results, a numerical example is given.