A general inverse DEA model for non-radial DEA

•We analyze the weakness of inverse DEA models based on radial efficiency measures.•We propose an integrated framework of inverse DEA based on non-radial DEA by multi-objective programming.•We give the concrete mathematical formula of inverse SBM and some properties.•An algorithm for inverse DEA based on non-radial DEA is given. Traditional inverse DEA models could be called inverse radial DEA because they are based on radial efficiency measures. Due to the neglect of slacks in evaluating the efficiency score, inverse radial DEA may mislead decision-making in some cases where slacks play important roles. In this paper, we proposed an integrated framework of inverse DEA called inverse non-radial DEA since it is based on non-radial DEA by multi-objective programming, which covers existing inverse DEA models. To further illustrate the inverse non-radial DEA, we construct the concrete mathematical formula of inverse SBM and some properties. In contrast to the radial approach, inverse non-radial DEA can overcome the error caused by ignoring slacks and provides more valuable information about inputs and outputs for decision-making by considering slacks. Although inverse non-radial DEA models are usually non-linear, we can convert it into a one-dimensional search problem about efficiency score, which can be solved by many existing efficient algorithms. A practical example is provided to demonstrate the advantages of inverse non-radial DEA models over inverse radial DEA models.