A typology of cutting and packing problems

In this paper we consider the unconstrained, two-dimensional, guillotine cutting problem. This is the problem that occurs in the cutting of a number of rectangular pieces from a single large rectangle, so as to maximize the value of the pieces cut, where any cuts that are made are restricted to be guillotine cuts. We consider both the staged version of the problem (where the cutting is performed in a number of distinct stages) and the general (non-staged) version of the problem. A number of algorithms, both heuristic and optimal, based upon dynamic programming are presented. Computational results are given for large problems.

Algorithms for Unconstrained Two-Dimensional Guillotine Cutting

In this paper the problem of generating integer solutions to the standard one-dimensional cutting stock problem is treated. In particular, we study a specific class of heuristic approaches that have been proposed in the literature, and some straightforward variants. These methods are compared with respect to solution quality and computing time. Our evaluation is based on having solved 4,000 randomly generated test problems. Not only will it be shown that two methods are clearly superior to the others but also that they solve almost any instance of the standard one-dimensional cutting stock problem to an optimum.

Heuristics for the integer one-dimensional cutting stock problem: A computational study

Operational research '81: J.P. Brans (Ed.) Proceedings of the Ninth IFORS International Conference on Operational Research, Hamburg, Germany, July 20–24, 1981, North-Holland, Amsterdam, 1981, xx + 984 pages, Dfl.250.000

Classification and literature review of integrated lot-sizing and cutting stock problems

Because of the diversity of the structures of real-world trim loss (or cutting stock) problems there exist no general standard methods for solving these problems. Hence many solution methods for trim loss problems have been developed in practice, especially heuristics. Since these methods are strongly based on the particular problems to which they are applied, the study of papers on problems with a comparable structure may prove helpful. In this paper a detailed catalogue of criteria for characterization of real-world trim loss problems is developed in a differentiated and systematic manner. The main criteria are: dimension, planning situation, goal, restrictions and solution approach. The proposed system of classification is based on 34 case studies found in the relevant literature. The classification of these case studies is represented by means of a ‘classification schedule’. In view of existing formal similarities the classification system can also be of importance for (bin) packing and loading as well as some assortment problems.

Trim loss and related problems

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Trim loss and related problems