Models for the two‐dimensional rectangular single large placement problem with guillotine cuts and constrained pattern

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...

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Vydané v:International transactions in operational research Ročník 27; číslo 2; s. 767 - 793
Hlavní autori: Martin, Mateus, Birgin, Ernesto G., Lobato, Rafael D., Morabito, Reinaldo, Munari, Pedro
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Blackwell Publishing Ltd 01.03.2020
Predmet:
Algorithms
Benders decomposition
branch‐and‐Benders‐cut algorithm
constrained two‐dimensional guillotine cuts
Constraints
cutting and packing problems
Formulations
Integer programming
integer programming models
Integers
Linear programming
Nonlinear programming
Operations research
Placement
Two dimensional models
ISSN:0969-6016, 1475-3995
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Shrnutí: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.
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ISSN:0969-6016
1475-3995
DOI:10.1111/itor.12703