An integer feasibility problem is a fundamental problem in many areas, such
as operations research, number theory, and statistics. To study a family of
systems with no nonnegative integer solution, we focus on a commutative
semigroup generated by a finite set of vectors in Zd and its saturation. In
this paper we present an algorithm to compute an explicit description for the
set of holes which is the difference of a semi-group Q generated by the
vectors and its saturation. We apply our procedure to compute an infinite
family of holes for the semi-group of the 3×4×6 transportation
problem. Furthermore, we give an upper bound for the entries of the holes when
the set of holes is finite. Finally, we present an algorithm to find all
Q-minimal saturation points of Q.Comment: Presentation has been improved according to comments by referees.
This manuscript has been accepted to "Contributions to Discrete Mathematics