  The real Production Possibility Set (PPS) is completely generated by
observations in the real approach, but generating the integer PPS may not be
possible by only using observations in the integer approach. In other words,
this phenomenon says that all points in the real generated PPS are dominated by
a point of the linear combination of observations, whereas there might be some
points in the integer generated PPS which are not dominated with the points of
the linear combination of observations. This paper shows how the integer
production possibility set is made and the mixed-integer linear programming is
defined. The paper also addresses some shortcomings in the recent mixed-integer
linear programming while the integer axioms are considered.
