A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem

Many heuristic approaches have been proposed in the literature for the multiple length cutting stock problem, while only few results have been reported for exact solution algorithms. In this paper, we present a new branch-and-price-and-cut algorithm which outperforms other exact approaches proposed so far. Our conclusions are supported on many computational experiments conducted on instances from the literature. In the second part of the paper, we investigate the use of valid dual inequalities within the previous algorithm. We show how column generation can be accelerated in all the nodes of our branching tree using such inequalities. Until now, dual inequalities have been applied only for original linear programming relaxations. Their validity within a branch-and-bound procedure has never been investigated. Our computational experiments show that extending these inequalities to the whole branch-and-bound tree can significantly improve the convergence of our branch-and-price-and-cut algorithm.