In mathematical terms, the afore-mentioned objective in conjunction with certain assumptions about the producible production points (i.e. efficient input-output combinations permitted by the technology) leads to the formulation of a fractional programming problem. The solution of an equivalent linear program identifies a set of units that are deemed as efficient and all other units are deemed as inefficient. Determination of fully efficient units (also known as best practice units) enables the construction of a piece-wise linear frontier, the so-called “best practice frontier” which isolates potentially efficient units (all points on the frontier) from inefficient ones (all productively attainable points surrounded –enveloped- by the frontier). All units residing on the frontier can be thought of as either the ones that produce a certain level of output using the lowest allowed amount of inputs or the ones than produce the highest attainable level of output using a certain amount of inputs. Thus, all these technically efficient units on the frontier are assigned an efficiency score of 1 (100%) whereas technically inefficient ones are assigned a positive score less than 1 (less than 100%). The percentage score of an inefficient unit can be derived in one of two alternative ways referred to as input-orientated and output-orientated efficiency scores. In input-orientation the score represents the maximum allowed equiproportionate (i.e. radial) reduction of its inputs that is still capable of producing the same level of output. Accordingly, in output-orientation the score reflects the maximum equiproportionate (radial) expansion of its outputs that can be produced using the same level of inputs. In geometric terms this can be thought of as the maximum allowed contraction or required expansion of the unit’s input/output position ray until the unit has reached the efficient frontier.