  We introduce the concept of homogeneous numerical semigroups and show that
all homogeneous numerical semigroups with Cohen-Macaulay tangent cones are of
homogeneous type. In embedding dimension three, we classify all numerical
semigroups of homogeneous type in to numerical semigroups with complete
intersection tangent cones and the homogeneous ones with Cohen-Macaulay tangent
cones. We also study the behavior of the homogeneous property by gluing and
shiftings to construct a large family of homogeneous numerical semigroups with
Cohen-Macaulay tangent cones. In particular we show that these properties
fulfill assymptotically in the shifting classes. Several explicit examples are
provided along the paper to illustrate the property.
