<p>Nonparametric cost allocative efficiency models in the framework of data envelopment analysis are sensitive to the prices of inputs. Changes in input prices may change the efficiency classification of a decision-making unit. In this sense, it is of interest to determine the ranges for input prices in which the efficiency classification remains unchanged. This paper focuses on sensitivity analysis of cost efficiency of a specific allocative efficient firm. Cost stability region is defined as a region in which the efficiency classification does not change if the input-cost vector is changed in such a way that the new vector belongs to this region. Linearly independent supporting surfaces of the production possibility set are used to define this region. The proposed cost stability regions are used to discriminate the decision-making units. Two illustrative examples (one simple numerical example and one real example) are used to demonstrate the applicability of the proposed approach.</p>