Dealing with the inverse DEA models and criterion models

Data envelopment analysis (DEA) is a mathematical programming based approach that uses the input-output data to measure the efficiency score of a group of homogenous decision making units (DMUs). In a different perspective, based on the fixed and perturbed output (input) level, the inverse DEA model tries to find the required input (producible output) that preserve efficiency score of DMU under evaluation. In fact, the efficiency score of DMUs are guaranteed using the inverse DEA models. To check this fact criterion model can be used to checking the efficiency score of DMUs after perturbation. This paper reviews the inverse DEA problem and relative criterion models and propose more realistic and more economical models in terms of computational complexity.