Constrained two-dimensional cutting: an improvement of Christofides and Whitlock's exact algorithm

Abstract

Christofides and Whitlock have developed a top-down algorithm which combines in a nice tree search procedure Gilmore and Gomory's algorithm and a transportation routine called at each node of the tree for solving exactly the constrained two-dimensional cutting problem. Recently, another bottom-up algorithm has been developed and reported as being more efficient. In this paper, we propose a modification to the branching strategy and we introduce the one-dimensional bounded knapsack in the original Christofides and Whitlock algorithm. Then, by exploiting dynamic programming properties we obtain good lower and upper bounds which lead to significant branching cuts, resulting in a drastic reduction of calls of the transportation routine. Finally, we propose an incremental solution of the numerous generated transportation problems. The resulting algorithm reveals superior performance to other known algorithms.

Keywords:

• cutting problem
• knapsack
• dynamic programming
• heuristic