Cutting and packing

Abstract

Over a decade ago, the European Journal of Operational Research published its first special issue on Cutting and Packing [1] in conjunction with the founding of SICUP, the Special Interest Group on Cutting and Packing. The majority of the papers in the first special issue were focused on cutting problems in the aluminium, paper, and canvas industry, as well as container loading problems. In 1995, a second special issue appeared [2]. As before, the issue included a number of papers on traditional oneand two-dimensional cutting stock problems and container/pallet loading problems, but it also reported new research in nesting problems and introduced the use of metaheuristics such as simulated annealing and genetic algorithms for solving packing problems. Interest in solving these problems continues to grow: an increasing number of papers are being published in the literature each year on a range of cutting, packing, loading, and layout problems. Following the trend, this third special issue of EJOR reports current research that addresses a variety of cutting, packing and related problems where classical, as well heuristic approaches are applied. A first cluster of papers is dedicated to one-dimensional cutting and packing. De Carvalho reviews several models for problems of the cutting stock and bin packing type and analyses the relationship between them as grounds for the development of branch-and-price algorithms. In the two succeeding papers, new methods for the generation of integer solutions to the one-dimensional cutting stock problem with different standard lengths are presented. Belov and Scheithauer introduced an exact approach which uses Chvatal– Gomory cutting planes to tighten up the continuous relaxation of the classic model formulation. Despite the impressive computational results given, the suggested method may still not be applicable to all practical problems due to its computational requirements. In such cases, the heuristic solution method developed and evaluated by Holthaus may represent a feasible alternative. Important aspects of many real-world problems are considered in another two papers. Zak looks at cutting processes which extend over several stages. He proposes a solution method which is based on the classic column-generation procedure by Gilmore and Gomory and dynamically generates both rows (intermediate sizes) and columns (cutting patterns). However, the method does not guarantee that an optimal solution is found. In practice, the question of how to cut down orders from stock lengths is often interconnected with the problem of sequencing the cutting patterns in the most economical way. Armbruster describes such a problem at a steel service centre and suggests a European Journal of Operational Research 141 (2002) 239–240