We propose two combinatoric methods that generate constrained cutting patterns by successive horizontal and vertical builds of ordered rectangles. Each of the algorithms uses a parameter to bound the maximum acceptable percentages of waste they create. Error bounds measure how close the pattern wastes are to the waste of the optimal solution. We also discuss computational results and applications of the methods to a general cutting stock problem.

Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems

More than 400 books, articles, dissertations, and working papers are included in this bibliography on cutting and packing problems. The list of published articles and dissertations is a nearly exhaustive compilation of the English-language references on the subject. The list of working papers, although extensive, presents only a sample of the recent work in this field. All of the books and journal articles listed in the bibliography have been categorized according to the dimensionality of the problems studied and the solution methodologies employed.

https://www.jstor.org/stable/info/2583579

Cutting and Packing Problems: A Categorized, Application-Orientated Research Bibliography

The trim-loss and assortment problems: A survey

The cutting stock problem — a survey

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 r1, r2, …, rn, with the ith type having length li, width wi, value vi, and demand constraint bi. It is required to produce, from the stock rectangle S, ai copies of ri, 1 ≤ i ≤ n, to maximize a1v1 + a2v2 + · + anvn subject to the constraints ai ≤ bi. 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.

Best-first search methods for constrained two-dimensional cutting stock problems

The cutting stock problem occurs where large rectangles of some material require cutting into smaller rectangles, in the most appropriate way, to satisfy an order book. A linear programming approach to the problem has been suggested by P. C. Gilmore and R. E. Gomory. An application of this approach in the glass industry is described which is shown to be inadequate since it only satisfies a wastage criterion. In practice, multiple criteria must be satisfied and two alternative approaches using linear programming and heuristic scheduling are proposed.

https://link.springer.com/content/pdf/10.1057%2Fjors.1974.5.pdf

A. S. Gregory

Papers

The Cutting Stock Problem in the Flat Glass Industry