The cutting stock problem (CS) min \(1\cdot y\), s.t. yM\(\geq w\), \(y\geq 0\), y integral, is strongly related to the knapsack problem (KP) max \(c\cdot x\), s.t. \(a\cdot x\leq b\), \(x\geq 0\), integral, by taking M as the matrix (of rows) of the maximal element of \(\{x\in {\mathbb{Z}}^ n_+|\) ax\(\leq b\}\). It was observed that the solutions of (CS) often meets the ''integer round-up property'' (IRU): the optimal solution to (CS) equals the least integer greater than or equal to the optimal value of the linear relaxation of (CS). The author shows how this property is related to the ''integral decomposition property'' of arbitrary polyhedra (in the nonnegative orthant). Especially the problem (CS) has the IRU-property if the coefficients build a chain of successive divisors: \(a_ i/a_{i+1}/b\).