Best-First Search Methods for Constrained Two-Dimensional Cutting Stock Problems

• Published in: Operations research Vol. 41; no. 4; pp. 768 - 776
• Main Authors: Viswanathan, K. V, Bagchi, A
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.07.1993; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Applied sciences; Artificial intelligence; artificial intelligence: search methods; computers/computer science; cutting stock/trim: rectangular stock sheets; Dynamic programming; Exact sciences and technology; Experimental results; Flows in networks. Combinatorial problems; Heuristics; Integers; Mathematical models; Maximum value; Operational research and scientific management; Operational research. Management science; Operations research; Optimal solutions; Problem solving; production/scheduling; Rectangles; Recursion; Cutting; Experimental result; Constraint; Combinatorial problem; Trim loss problem; Two dimensional model; Search algorithm
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.41.4.768

Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of dimensions ( L , W ) is supplied. There are n types of demanded rectangles r 1 , r 2 , ..., r n , with the i th type having length l i , width w i , value v i , and demand constraint b i . It is required to produce, from the stock rectangle S , a i copies of r i , 1 i n , to maximize a 1 v 1 + a 2 v 2 + · + a n v n subject to the constraints a i b i . Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.