Classification transitions under expansion of inputs and outputs in data envelopment analysis

An exchange between Thomas R. Nunamaker and T. Ahn, A. Charnes and W. W. Cooper which revolves around possible behavior of the DEA efficiency measure. In particular, Ahn, Charnes and Cooper provide a counterexample to Nunamaker's assertion that adding inputs to a DMU (Decision Making Unit) which had previously attained an efficiency of 0* = 1 with fewer inputs would never alter this value, no matter how inefficient the use of the additional inputs. Here we want to add additional insight by showing the condition under which Nunamaker's proposition is true. Using the notation and concepts from Charnes, Cooper and Thrall, we shall see that this proposition is true if and only if the previously attained 0* = 1 is uniquely optimal.