Sensitivity and stability of the classifications of returns to scale in data envelopment analysis

Sensitivity of the returns to scale (RTS) classifications in data envelopme nt analysis is studied by means of linear programming problems. The stabili ty region for an observation preserving its current RTS classification (con stant, increasing or decreasing returns to scale) can be easily investigate d by the optimal values to a set of particular DEA-type formulations. Neces sary and sufficient conditions are determined for preserving the RTS classi fications when input or output data perturbations are non-proportional. It is shown that the sensitivity analysis method under proportional data pertu rbations can also be used to estimate the RTS classifications and discover the identical RTS regions yielded by the input-based and the output-based D EA methods. Thus, our approach provides information on both the RTS classif ications and the stability of the classifications. This sensitivity analysi s method can easily be applied via existing DEA codes.