On a transport problem and monoids of non-negative integers

Abstract

A problem about how to transport profitably a group of cars leads us to study the set $T$ formed by the integers $n$ such that the system of inequalities, with non-negative integer coefficients, $$a_1{x}_1+\cdots +a_p{x}_p+\alpha \le n\le b_1{x}_1+\cdots +b_p{x}_p-\beta$$ has at least one solution in ${\mathbb{N}}^p$. We will see that $T\cup \{0\}$ is a submonoid of $(\mathbb{N},+)$. Moreover, we show algorithmic processes to compute $T$.

9 pages

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