inverse directional slacks-based measures with negative outputs

In conventional inverse data envelopment analysis (dea) models, the performance measures are assessed while positive factors are presented. however, in some examinations, there are negative data. therefore, in this research, inverse directional slacks-based approaches have been extended to estimate inputs (outputs) for the perturbations of outputs (inputs) while the performance is preserved and negative measures are presented. the presented inverse directional slacks-based models are multi-objective and solved by using the weighted sum method. a numerical example is provided to illustrate the introduced technique.