An integer programming model for two- and three-stage two-dimensional cutting stock problems

• Published in: European journal of operational research 2010-09, Vol.205 (3), p.699-708
• Main Authors: Silva, Elsa, Alvelos, Filipe, Valério de Carvalho, J.M.
• Format: Article
• Language: English
• Subjects: 2D rectangular SSSCSP with guillotine constraints; Applied sciences; Computation; Cutting; Cutting 2D rectangular SSSCSP with guillotine constraints Integer programming Length of the cutting operations; Cutting stock problem; Decision making models; Decision theory. Utility theory; Exact sciences and technology; Flows in networks. Combinatorial problems; Integer programming; Length of the cutting operations; Mathematical programming; Operational research; Operational research and scientific management; Operational research. Management science; Plates; Raw materials; Rectangular plates; Studies; Two dimensional
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2010.01.039

In this paper, an integer programming model for two-dimensional cutting stock problems is proposed. In the problems addressed, it is intended to cut a set of small rectangular items of given sizes from a set of larger rectangular plates in such a way that the total number of used plates is minimized. The two-stage and three-stage, exact and non-exact, problems are considered. Other issues are also addressed, as the rotation of items, the length of the cuts and the value of the remaining plates. The new integer programming model can be seen as an extension of the “one-cut model” proposed by Dyckhoff for the one-dimensional cutting stock problem. In the proposed model, each decision variable is associated with cutting one item from a plate or from a part of a plate resulting from previous cuts (residual plates). Comparative computational results of the proposed model and of models from the literature are presented and discussed.