Inverse data envelopment analysis without convexity: double frontiers

In this research, inverse data envelopment analysis (IDEA) approaches are proposed to measure inputs changes for output perturbations made while the convexity assumption is relaxed. Actually, inverse free disposal hull (IFDH) techniques under constant returns to scale (CRS) assumption are introduced from two perspectives, optimistic and pessimistic. In models proposed in this study, the efficiency of decision-making units (DMUs) is maintained after adding perturbed DMU with new input and output values. These inverse problems are multiobjective nonlinear that are converted to equivalent linear models and finding all Pareto efficient solutions is discussed. The models have also been tested using a real-world case study from the banking sector. The findings reveal valuable facts concerning the changes of inputs for changes of outputs from optimistic and pessimistic aspects while the convexity axiom is dropped.