How to assess sustainability of countries via inverse data envelopment analysis?

In this paper, two input-oriented and output-oriented inverse semi-oriented radial measures are presented. Such models are applied to determine resource allocation and investment strategies for assessing sustainability of countries. Our proposed models can deal with both positive and negative data. In our proposed inverse input-oriented data envelopment analysis (DEA) model, optimal inputs are suggested while outputs and efficiency score of decision-making unit (DMU) under evaluation are unchanged. Similarly, in our proposed inverse output-oriented DEA model, optimal outputs are proposed while inputs and efficiency score of DMU under evaluation are kept unchanged. For the first time, we propose two new inverse DEA models to handle resource allocation and investment analysis problems given sustainable development aspects in the presence of negative data. A case study is given for assessing sustainability of countries.