Finding strong defining hyperplanes of production possibility set with stochastic data

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In data envelopment analysis (DEA), identification of the strong defining hyperplanes of the empirical production possibility set (PPS) is important, because they can be used for determining rates of change of outputs with change in inputs. Also, efficient hyperplanes determine the nature of returns to scale, and also is important for defining a suitable pattern for inefficient DMUs. As we know, stochastic data are one of the different kinds of data that show some uncertainty in inputs and outputs. Therefore we apply an algorithm for transforming stochastic models in to linear models using Production Possibility Set (PPS). In this paper, we deal with the problem of finding the strong defining hyperplanes of the PPS with stochastic data. A numerical example shows the reasonability of our method.