  Until this work, the packing radius of a poset code was only known in the
cases where the poset was a chain, a hierarchy, a union of disjoint chains of
the same size, and for some families of codes. Our objective is to approach the
general case of any poset. To do this, we will divide the problem into two
parts.
  The first part consists in finding the packing radius of a single vector. We
will show that this is equivalent to a generalization of a famous NP-hard
problem known as "the partition problem". Then, we will review the main results
known about this problem giving special attention to the algorithms to solve
it. The main ingredient to these algorithms is what is known as the
differentiating method, and therefore, we will extend it to the general case.
  The second part consists in finding the vector that determines the packing
radius of the code. For this, we will show how it is sometimes possible to
compare the packing radius of two vectors without calculating them explicitly.
