Models for the two‐dimensional rectangular single large placement problem with guillotine cuts and constrained pattern. (25th July 2019)

• Record Type: Journal Article
• Authors: Martin, Mateus; Birgin, Ernesto G.; Lobato, Rafael D.; Morabito, Reinaldo; Munari, Pedro
• Is Part Of: International transactions in operational research. Volume 27:Number 2(2020)
• Page Start: 767
• Page End: 793
• Publication Date: 2019-07-25
• Subjects: cutting and packing problems -- constrained two‐dimensional guillotine cuts -- integer programming models -- branch‐and‐Benders‐cut algorithm; Operations research -- Periodicals; 003
• DOI: 10.1111/itor.12703
• Languages: English
• ISSNs: 0969-6016

Abstract

Abstract: In this paper, we address the constrained two‐dimensional rectangular guillotine single large placement problem (2D_R_CG_SLOPP). This problem involves cutting a rectangular object to produce smaller rectangular items from orthogonal guillotine cuts. In addition, there is an upper limit on the number of copies that can be produced of each item type. To model this problem, we propose a new pseudopolynomial integer nonlinear programming (INLP) formulation and obtain an equivalent integer linear programming (ILP) formulation from it. Additionally, we developed a procedure to reduce the numbers of variables and constraints of the integer linear programming (ILP) formulation, without loss of optimality. From the ILP formulation, we derive two new pseudopolynomial models for particular cases of the 2D_R_CG_SLOPP, which consider only two‐staged or one‐group patterns. Finally, as a specific solution method for the 2D_R_CG_SLOPP, we apply Benders decomposition to the proposed ILP formulation and develop a branch‐and‐Benders‐cut algorithm. All proposed approaches are evaluated through computational experiments using benchmark instances and compared with other formulations available in the literature. The results show that the new formulations are appropriate in scenarios characterized by few item types that are large with respect to the object's dimensions.