An improvement of viswanathan and bagchi's exact algorithm for constrained two-dimensional cutting stock

Abstract

Viswanathan and Bagchi [ Operations Research, 1993, 41(4), 768–776] [1] have proposed a bottom-up algorithm which combines in the nice tree-search procedure Gilmore and Gomory's algorithm, called at each node of the tree, for solving exactly the constrained two-dimensional cutting problem. This algorithm is one of the best exact algorithms known today. In this paper, we propose an improved version of this algorithm by introducing one-dimensional bounded knapsacks in the original algorithm. Then, by exploiting dynamic programming properties, we obtain good lower and upper bounds which lead to significant branching cuts. Finally, the improved version is compared to the standard version of Viswanathan and Bagchi on some small and medium instances.