pessimistic meta-frontier approach to assess the performance of heterogeneous entities with undesirable

In real world applications, there are situations that the performance of heterogeneous entities should be evaluated while undesirable outputs are presented. the existing data envelopment analysis (dea) models analyze the efficiency of non-homogenous firms relative to the best practice frontier. in the current paper, the group and meta pessimistic efficiency of firms and technological gaps are investigated while there are undesirable outputs. approaches are based upon convex and non-convex meta-technologies. to more illustrate, directional distance function dea models are introduced for this purpose. a numerical example is used to illustrate the proposed approach.