Two-dimensional cutting stock problem research: A review and a new rectangular layout algorithm

Abstract

The two-dimensional cutting stock problem addresses the allocation of a required bill of materials onto stock sheets in a manner that minimizes the trim losses. This paper surveys the progress made on the study of the problem from the original contributions by Gilmore and Gomory in the mid-1960s to the present. Conclusions are for these algorithms to find greater application in industry, one must consider the allocation of both regular and irregular shapes. Moreover, the objective of minimizing the trim losses is not an adequate performance measure when the cutting department is placed in the perspective of the entire manufacturing system. The costs of inventory and production have to be included in the objective to be minimized in order to ensure maximum production efficiency. In addition, an algorithm based on the first fit decreasing heuristic 1 is presented to achieve layouts of rectangular bills of material on rectangular stock sheets, and its performance is examined. A number of nesting algorithms are currently in use in industry, but virtually all of these systems are considered to be highly proprietary and specific. The cutting stock problem has been variously adapted to applications in numerous industries. From its original form described later, it has been modified for use in paper, lumber, cloth, metal, leather stamping and other industries. In each case, the problem has been reformulated to suit the needs of the specific industry.