  This paper addresses the problem of decomposing a numerical semigroup into
m-irreducible numerical semigroups. The problem originally stated in algebraic
terms is translated, introducing the so called Kunz-coordinates, to resolve a
series of several discrete optimization problems. First, we prove that finding
a minimal m-irreducible decomposition is equivalent to solve a multiobjective
linear integer problem. Then, we restate that problem as the problem of finding
all the optimal solutions of a finite number of single objective integer linear
problems plus a set covering problem. Finally, we prove that there is a
suitable transformation that reduces the original problem to find an optimal
solution of a compact integer linear problem. This result ensures a polynomial
time algorithm for each given multiplicity m. We have implemented the different
algorithms and have performed some computational experiments to show the
efficiency of our methodology.
