In this paper we develop a new version of the algortihm proposed in [17] for solving exactly some variants of (un)weighted constrained two-dimensional cutting stock problems. We introduce one-dimensional bounded knapsacks in order to obtain an improved initial lower bound for limitating...

In this paper we propose two exact algorithms for solving both two-staged and three-staged unconstrained (un) weighted cutting problems. The two-staged problem is solved by applying a dynamic programming procedure originally developed by Gilmore and Gomory [10]. The three-staged problem is...

In this paper, we propose two efficient algorithms in order to approximately solve the Knapsack Sharing Problem (KSP). In KSP, we have a knapsack of capicity c and a set of n objects, where each object j, j=1,...,n, is associated with a profit pj and a weight wj. The set of objects is divided...

In this paper we propose two algorithms for solving both unweighted and weighted constrained two-dimensional two-staged cutting stock problems. The problem is called two-staged cutting problem because each produced (sub) optimal cutting pattern is realized by using two cut-phases.