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- W1569108694 abstract "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 $Z^d$ and its saturation. In this paperwe present an algorithm to compute an explicit description for theset of holes which is the difference of a semi-group $Q$ generatedby the vectors and its saturation. We apply our procedureto compute an infinite family of holes for thesemi-group of the $3times 4times 6$ transportation problem. Furthermore,we give an upper bound for the entries of the holes when the set ofholes is finite. Finally, we present an algorithm to find all $Q$-minimalsaturation points of $Q$." @default.
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- W1569108694 date "2009-06-08" @default.
- W1569108694 modified "2023-09-23" @default.
- W1569108694 title "Computing holes in semi-groups and its applications to transportation problems" @default.
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- W1569108694 doi "https://doi.org/10.11575/cdm.v4i1.62036.g46699" @default.
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