A cutting plane method and a parallel algorithm for packing rectangles in a circular container

•We propose the first linear model to pack rectangles in a circle.•A cutting plane method approximates a circular container from a square.•The feasibility of packings is effectively done with an adapted version of the model.•Optimal or new best known solutions for almost all instances from the liter...

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Published inEuropean journal of operational research Vol. 303; no. 1; pp. 114 - 128
Main Authors Silva, Allyson, Coelho, Leandro C., Darvish, Maryam, Renaud, Jacques
Format Journal Article
LanguageEnglish
Published Elsevier B.V 16.11.2022
Subjects
Circular container
Combinatorial optimization
Cutting plane method
Packing
Parallel computing
Parallel computing
Circular container
Packing
Combinatorial optimization
Cutting plane method
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Abstract •We propose the first linear model to pack rectangles in a circle.•A cutting plane method approximates a circular container from a square.•The feasibility of packings is effectively done with an adapted version of the model.•Optimal or new best known solutions for almost all instances from the literature.•Optimal solutions for instances with 30 items vs. 8 items from the literature. We study a two-dimensional packing problem where rectangular items are placed into a circular container to maximize either the number or the total area of items packed. We adapt a mixed-integer linear programming model from the case with a rectangular container and design a cutting plane method to solve this problem by adding linear cuts to forbid items from being placed outside the circle. We show that this linear model allows us to prove optimality for instances larger than those solved using the state-of-the-art non-linear model for the same problem. We also propose a simple parallel algorithm that efficiently enumerates all non-dominated subsets of items and verifies whether pertinent subsets fit into the container using an adapted version of our linear model. Computational experiments using large benchmark instances attest that this enumerative algorithm generally provides better solutions than the best heuristics from the literature when maximizing the number of items packed. Instances with up to 30 items are now solved to optimality, against the eight-item instance previously solved.
AbstractList •We propose the first linear model to pack rectangles in a circle.•A cutting plane method approximates a circular container from a square.•The feasibility of packings is effectively done with an adapted version of the model.•Optimal or new best known solutions for almost all instances from the literature.•Optimal solutions for instances with 30 items vs. 8 items from the literature. We study a two-dimensional packing problem where rectangular items are placed into a circular container to maximize either the number or the total area of items packed. We adapt a mixed-integer linear programming model from the case with a rectangular container and design a cutting plane method to solve this problem by adding linear cuts to forbid items from being placed outside the circle. We show that this linear model allows us to prove optimality for instances larger than those solved using the state-of-the-art non-linear model for the same problem. We also propose a simple parallel algorithm that efficiently enumerates all non-dominated subsets of items and verifies whether pertinent subsets fit into the container using an adapted version of our linear model. Computational experiments using large benchmark instances attest that this enumerative algorithm generally provides better solutions than the best heuristics from the literature when maximizing the number of items packed. Instances with up to 30 items are now solved to optimality, against the eight-item instance previously solved.
Author Coelho, Leandro C.
Darvish, Maryam
Renaud, Jacques
Silva, Allyson
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Cites_doi 10.1093/imaman/13.2.95
10.1016/j.cor.2016.09.009
10.1016/j.cor.2019.104851
10.1016/j.ejor.2020.06.050
10.1016/j.cor.2018.02.012
10.1016/j.asoc.2018.11.021
10.1287/opre.13.1.94
10.1155/2009/150624
10.1016/j.ejor.2007.08.007
10.1287/opre.33.1.49
10.1016/j.cor.2010.10.022
10.1016/j.ejor.2018.04.014
10.1016/j.ejor.2018.04.046
10.1287/ijoc.1060.0181
10.1016/S0167-6377(03)00057-9
10.1016/j.ejor.2005.11.060
10.1287/ijoc.1090.0338
10.1016/j.cor.2010.12.001
10.1287/opre.2014.1307
10.1057/jors.2008.169
10.1007/s00542-014-2198-4
10.1016/j.ijpe.2013.04.047
10.1007/s10479-008-0463-6
10.1016/j.ejor.2011.06.001
10.1287/opre.1060.0369
10.1016/0377-2217(94)00002-T
10.1016/j.ejor.2020.02.048
10.1287/ijoc.2016.0710
10.1016/j.cor.2007.12.004
10.1111/itor.12107
10.1016/j.ejor.2005.12.048
10.1016/0377-2217(93)E0278-6
10.1287/ijoc.2018.0806
10.1016/j.ejor.2014.02.059
10.1016/j.ejor.2019.12.012
10.1007/s10107-002-0319-9
10.1016/j.cor.2011.12.010
10.1016/j.ejor.2005.12.047
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Keywords Parallel computing
Circular container
Packing
Combinatorial optimization
Cutting plane method
Language English
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References Egeblad, Pisinger (bib0015) 2009; 36
Beasley (bib0002) 1985; 33
Bouzid, Salhi (bib0005) 2020; 285
Clautiaux, Carlier, Moukrim (bib0011) 2007; 183
Zhong, Xu, Teng (bib0040) 2019; 75
Baldacci, Boschetti (bib0001) 2007; 183
Hadjiconstantinou, Christofides (bib0023) 1995; 83
Korf, Moffitt, Pollack (bib0028) 2010; 179
Martin, Morabito, Munari (bib0033) 2020; 115
Castro, Oliveira (bib0008) 2011; 215
Delorme, Iori, Martello (bib0014) 2017; 78
Iori, de Lima, Martello, Miyazawa, Monaci (bib0026) 2021; 289
Fan, Arevalo, Li, Foulds (bib0016) 2015; 21
Leung, Zhang, Zhou, Wu (bib0030) 2012; 39
López, Beasley (bib0032) 2018; 94
Caprara, Monaci (bib0006) 2004; 32
Kurpel, Scarpin, Pécora, Schenekemberg, Coelho (bib0029) 2020; 284
Silva, Oliveira, Wäscher (bib0037) 2014; 237
Bennell, Oliveira (bib0003) 2009; 60
Garey, Johnson (bib0021) 1979
Kartak, Ripatti (bib0027) 2018; 271
Fekete, Schepers (bib0018) 1997
Furini, Malaguti, Thomopulos (bib0020) 2016; 28
Wäscher, Haußner, Schumann (bib0038) 2007; 183
Cassioli, Locatelli (bib0007) 2011; 38
Gilmore, Gomory (bib0022) 1965; 13
Côté, Iori (bib0013) 2018; 30
Cintra, Miyazawa, Wakabayashi, Xavier (bib0010) 2008; 191
Hinostroza, Pradenas, Parada (bib0025) 2013; 145
Côté, Gendreau, Potvin (bib0012) 2014; 62
Chen, Lee, Shen (bib0009) 1995; 80
Fanslau, Bortfeldt (bib0017) 2010; 22
Lodi, Monaci (bib0031) 2003; 94
Pisinger, Sigurd (bib0036) 2007; 19
Fekete, Schepers, Van der Veen (bib0019) 2007; 55
Mesyagutov, Scheithauer, Belov (bib0034) 2012; 39
Hifi, M’hallah (bib0024) 2009; 2009
Boschetti, Mingozzi, Hadjiconstantinou (bib0004) 2002; 13
Pedroso, Cunha, Tavares (bib0035) 2016; 23
Wei, Hu, Lim, Liu (bib0039) 2018; 270
Pisinger (10.1016/j.ejor.2022.02.023_bib0036) 2007; 19
Hinostroza (10.1016/j.ejor.2022.02.023_bib0025) 2013; 145
Zhong (10.1016/j.ejor.2022.02.023_bib0040) 2019; 75
Bennell (10.1016/j.ejor.2022.02.023_bib0003) 2009; 60
Garey (10.1016/j.ejor.2022.02.023_bib0021) 1979
Bouzid (10.1016/j.ejor.2022.02.023_bib0005) 2020; 285
Cassioli (10.1016/j.ejor.2022.02.023_bib0007) 2011; 38
Caprara (10.1016/j.ejor.2022.02.023_bib0006) 2004; 32
Egeblad (10.1016/j.ejor.2022.02.023_bib0015) 2009; 36
Iori (10.1016/j.ejor.2022.02.023_bib0026) 2021; 289
Boschetti (10.1016/j.ejor.2022.02.023_bib0004) 2002; 13
Chen (10.1016/j.ejor.2022.02.023_bib0009) 1995; 80
Leung (10.1016/j.ejor.2022.02.023_bib0030) 2012; 39
Lodi (10.1016/j.ejor.2022.02.023_bib0031) 2003; 94
Gilmore (10.1016/j.ejor.2022.02.023_bib0022) 1965; 13
Côté (10.1016/j.ejor.2022.02.023_bib0012) 2014; 62
Hifi (10.1016/j.ejor.2022.02.023_bib0024) 2009; 2009
Fan (10.1016/j.ejor.2022.02.023_bib0016) 2015; 21
Côté (10.1016/j.ejor.2022.02.023_bib0013) 2018; 30
Beasley (10.1016/j.ejor.2022.02.023_bib0002) 1985; 33
Wäscher (10.1016/j.ejor.2022.02.023_bib0038) 2007; 183
Cintra (10.1016/j.ejor.2022.02.023_bib0010) 2008; 191
Baldacci (10.1016/j.ejor.2022.02.023_bib0001) 2007; 183
Pedroso (10.1016/j.ejor.2022.02.023_bib0035) 2016; 23
Kartak (10.1016/j.ejor.2022.02.023_bib0027) 2018; 271
Martin (10.1016/j.ejor.2022.02.023_bib0033) 2020; 115
Clautiaux (10.1016/j.ejor.2022.02.023_bib0011) 2007; 183
Furini (10.1016/j.ejor.2022.02.023_bib0020) 2016; 28
Silva (10.1016/j.ejor.2022.02.023_bib0037) 2014; 237
Fekete (10.1016/j.ejor.2022.02.023_bib0019) 2007; 55
Fekete (10.1016/j.ejor.2022.02.023_bib0018) 1997
Kurpel (10.1016/j.ejor.2022.02.023_bib0029) 2020; 284
Castro (10.1016/j.ejor.2022.02.023_bib0008) 2011; 215
Fanslau (10.1016/j.ejor.2022.02.023_bib0017) 2010; 22
López (10.1016/j.ejor.2022.02.023_bib0032) 2018; 94
Korf (10.1016/j.ejor.2022.02.023_bib0028) 2010; 179
Mesyagutov (10.1016/j.ejor.2022.02.023_bib0034) 2012; 39
Delorme (10.1016/j.ejor.2022.02.023_bib0014) 2017; 78
Hadjiconstantinou (10.1016/j.ejor.2022.02.023_bib0023) 1995; 83
Wei (10.1016/j.ejor.2022.02.023_bib0039) 2018; 270
References_xml – volume: 179
  start-page: 261
  year: 2010
  end-page: 295
  ident: bib0028
  article-title: Optimal rectangle packing
  publication-title: Annals of Operations Research
  contributor:
    fullname: Pollack
– volume: 284
  start-page: 87
  year: 2020
  end-page: 107
  ident: bib0029
  article-title: The exact solutions of several types of container loading problems
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Coelho
– volume: 21
  start-page: 1411
  year: 2015
  end-page: 1414
  ident: bib0016
  article-title: Low-cost silicon wafer dicing using a craft cutter
  publication-title: Microsystem Technologies
  contributor:
    fullname: Foulds
– volume: 39
  start-page: 2425
  year: 2012
  end-page: 2438
  ident: bib0034
  article-title: LP bounds in various constraint programming approaches for orthogonal packing
  publication-title: Computers and Operations Research
  contributor:
    fullname: Belov
– volume: 183
  start-page: 1136
  year: 2007
  end-page: 1149
  ident: bib0001
  article-title: A cutting-plane approach for the two-dimensional orthogonal non-guillotine cutting problem
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Boschetti
– volume: 22
  start-page: 222
  year: 2010
  end-page: 235
  ident: bib0017
  article-title: A tree search algorithm for solving the container loading problem
  publication-title: INFORMS Journal on Computing
  contributor:
    fullname: Bortfeldt
– volume: 55
  start-page: 569
  year: 2007
  end-page: 587
  ident: bib0019
  article-title: An exact algorithm for higher-dimensional orthogonal packing
  publication-title: Operations Research
  contributor:
    fullname: Van der Veen
– volume: 271
  start-page: 33
  year: 2018
  end-page: 39
  ident: bib0027
  article-title: The minimum raster set problem and its application to the
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Ripatti
– volume: 78
  start-page: 290
  year: 2017
  end-page: 298
  ident: bib0014
  article-title: Logic based Benders’ decomposition for orthogonal stock cutting problems
  publication-title: Computers and Operations Research
  contributor:
    fullname: Martello
– volume: 183
  start-page: 1196
  year: 2007
  end-page: 1211
  ident: bib0011
  article-title: A new exact method for the two-dimensional orthogonal packing problem
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Moukrim
– volume: 115
  start-page: 104851
  year: 2020
  ident: bib0033
  article-title: A bottom-up packing approach for modeling the constrained two-dimensional guillotine placement problem
  publication-title: Computers & Operations Research
  contributor:
    fullname: Munari
– volume: 285
  start-page: 865
  year: 2020
  end-page: 883
  ident: bib0005
  article-title: Packing rectangles into a fixed size circular container: Constructive and metaheuristic search approaches
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Salhi
– start-page: 340
  year: 1979
  ident: bib0021
  article-title: Computers and intractability: A guide to the theory of NP-completeness
  publication-title: A series of books in the mathematical sciences
  contributor:
    fullname: Johnson
– volume: 270
  start-page: 448
  year: 2018
  end-page: 474
  ident: bib0039
  article-title: A best-fit branch-and-bound heuristic for the unconstrained two-dimensional non-guillotine cutting problem
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Liu
– volume: 62
  start-page: 1126
  year: 2014
  end-page: 1141
  ident: bib0012
  article-title: An exact algorithm for the two-dimensional orthogonal packing problem with unloading constraints
  publication-title: Operations Research
  contributor:
    fullname: Potvin
– volume: 30
  start-page: 646
  year: 2018
  end-page: 661
  ident: bib0013
  article-title: The meet-in-the-middle principle for cutting and packing problems
  publication-title: INFORMS Journal on Computing
  contributor:
    fullname: Iori
– volume: 60
  start-page: S93
  year: 2009
  end-page: S105
  ident: bib0003
  article-title: A tutorial in irregular shape packing problems
  publication-title: Journal of the Operational Research Society
  contributor:
    fullname: Oliveira
– volume: 39
  start-page: 64
  year: 2012
  end-page: 73
  ident: bib0030
  article-title: A hybrid simulated annealing metaheuristic algorithm for the two-dimensional knapsack packing problem
  publication-title: Computers and Operations Research
  contributor:
    fullname: Wu
– volume: 191
  start-page: 61
  year: 2008
  end-page: 85
  ident: bib0010
  article-title: Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Xavier
– volume: 80
  start-page: 68
  year: 1995
  end-page: 76
  ident: bib0009
  article-title: An analytical model for the container loading problem
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Shen
– volume: 23
  start-page: 355
  year: 2016
  end-page: 368
  ident: bib0035
  article-title: Recursive circle packing problems
  publication-title: International Transactions in Operational Research
  contributor:
    fullname: Tavares
– volume: 2009
  start-page: 150624
  year: 2009
  ident: bib0024
  article-title: A literature review on circle and sphere packing problems: Models and methodologies
  publication-title: Advances in Operations Research
  contributor:
    fullname: M’hallah
– volume: 32
  start-page: 5
  year: 2004
  end-page: 14
  ident: bib0006
  article-title: On the two-dimensional knapsack problem
  publication-title: Operations Research Letters
  contributor:
    fullname: Monaci
– volume: 33
  start-page: 49
  year: 1985
  end-page: 64
  ident: bib0002
  article-title: An exact two-dimensional non-guillotine cutting tree search procedure
  publication-title: Operations Research
  contributor:
    fullname: Beasley
– volume: 28
  start-page: 736
  year: 2016
  end-page: 751
  ident: bib0020
  article-title: Modeling two-dimensional guillotine cutting problems via integer programming
  publication-title: INFORMS Journal on Computing
  contributor:
    fullname: Thomopulos
– volume: 145
  start-page: 541
  year: 2013
  end-page: 546
  ident: bib0025
  article-title: Board cutting from logs: Optimal and heuristic approaches for the problem of packing rectangles in a circle
  publication-title: International Journal of Production Economics
  contributor:
    fullname: Parada
– volume: 19
  start-page: 36
  year: 2007
  end-page: 51
  ident: bib0036
  article-title: Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem
  publication-title: INFORMS Journal on Computing
  contributor:
    fullname: Sigurd
– volume: 215
  start-page: 45
  year: 2011
  end-page: 56
  ident: bib0008
  article-title: Scheduling inspired models for two-dimensional packing problems
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Oliveira
– volume: 75
  start-page: 148
  year: 2019
  end-page: 161
  ident: bib0040
  article-title: Multi-module satellite component assignment and layout optimization
  publication-title: Applied Soft Computing
  contributor:
    fullname: Teng
– volume: 94
  start-page: 257
  year: 2003
  end-page: 278
  ident: bib0031
  article-title: Integer linear programming models for 2-staged two-dimensional knapsack problems
  publication-title: Mathematical Programming
  contributor:
    fullname: Monaci
– volume: 13
  start-page: 95
  year: 2002
  end-page: 119
  ident: bib0004
  article-title: New upper bounds for the two-dimensional orthogonal non-guillotine cutting stock problem
  publication-title: IMA Journal of Management Mathematics
  contributor:
    fullname: Hadjiconstantinou
– volume: 289
  start-page: 399
  year: 2021
  end-page: 415
  ident: bib0026
  article-title: Exact solution techniques for two-dimensional cutting and packing
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Monaci
– volume: 237
  start-page: 846
  year: 2014
  end-page: 856
  ident: bib0037
  article-title: 2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problems
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Wäscher
– volume: 183
  start-page: 1109
  year: 2007
  end-page: 1130
  ident: bib0038
  article-title: An improved typology of cutting and packing problems
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Schumann
– volume: 94
  start-page: 106
  year: 2018
  end-page: 117
  ident: bib0032
  article-title: Packing unequal rectangles and squares in a fixed size circular container using formulation space search
  publication-title: Computers and Operations Research
  contributor:
    fullname: Beasley
– volume: 36
  start-page: 1026
  year: 2009
  end-page: 1049
  ident: bib0015
  article-title: Heuristic approaches for the two-and three-dimensional knapsack packing problem
  publication-title: Computers & Operations Research
  contributor:
    fullname: Pisinger
– volume: 13
  start-page: 94
  year: 1965
  end-page: 120
  ident: bib0022
  article-title: Multistage cutting stock problems of two and more dimensions
  publication-title: Operations Research
  contributor:
    fullname: Gomory
– volume: 83
  start-page: 39
  year: 1995
  end-page: 56
  ident: bib0023
  article-title: An exact algorithm for general, orthogonal, two-dimensional knapsack problems
  publication-title: European Journal of Operational Research
  contributor:
    fullname: Christofides
– start-page: 144
  year: 1997
  end-page: 156
  ident: bib0018
  article-title: A new exact algorithm for general orthogonal
  publication-title: European symposium on algorithms
  contributor:
    fullname: Schepers
– volume: 38
  start-page: 1342
  year: 2011
  end-page: 1350
  ident: bib0007
  article-title: A heuristic approach for packing identical rectangles in convex regions
  publication-title: Computers and Operations Research
  contributor:
    fullname: Locatelli
– volume: 13
  start-page: 95
  issue: 2
  year: 2002
  ident: 10.1016/j.ejor.2022.02.023_bib0004
  article-title: New upper bounds for the two-dimensional orthogonal non-guillotine cutting stock problem
  publication-title: IMA Journal of Management Mathematics
  doi: 10.1093/imaman/13.2.95
  contributor:
    fullname: Boschetti
– volume: 78
  start-page: 290
  year: 2017
  ident: 10.1016/j.ejor.2022.02.023_bib0014
  article-title: Logic based Benders’ decomposition for orthogonal stock cutting problems
  publication-title: Computers and Operations Research
  doi: 10.1016/j.cor.2016.09.009
  contributor:
    fullname: Delorme
– volume: 115
  start-page: 104851
  year: 2020
  ident: 10.1016/j.ejor.2022.02.023_bib0033
  article-title: A bottom-up packing approach for modeling the constrained two-dimensional guillotine placement problem
  publication-title: Computers & Operations Research
  doi: 10.1016/j.cor.2019.104851
  contributor:
    fullname: Martin
– volume: 289
  start-page: 399
  issue: 2
  year: 2021
  ident: 10.1016/j.ejor.2022.02.023_bib0026
  article-title: Exact solution techniques for two-dimensional cutting and packing
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2020.06.050
  contributor:
    fullname: Iori
– volume: 94
  start-page: 106
  year: 2018
  ident: 10.1016/j.ejor.2022.02.023_bib0032
  article-title: Packing unequal rectangles and squares in a fixed size circular container using formulation space search
  publication-title: Computers and Operations Research
  doi: 10.1016/j.cor.2018.02.012
  contributor:
    fullname: López
– volume: 75
  start-page: 148
  year: 2019
  ident: 10.1016/j.ejor.2022.02.023_bib0040
  article-title: Multi-module satellite component assignment and layout optimization
  publication-title: Applied Soft Computing
  doi: 10.1016/j.asoc.2018.11.021
  contributor:
    fullname: Zhong
– volume: 13
  start-page: 94
  issue: 1
  year: 1965
  ident: 10.1016/j.ejor.2022.02.023_bib0022
  article-title: Multistage cutting stock problems of two and more dimensions
  publication-title: Operations Research
  doi: 10.1287/opre.13.1.94
  contributor:
    fullname: Gilmore
– volume: 2009
  start-page: 150624
  year: 2009
  ident: 10.1016/j.ejor.2022.02.023_bib0024
  article-title: A literature review on circle and sphere packing problems: Models and methodologies
  publication-title: Advances in Operations Research
  doi: 10.1155/2009/150624
  contributor:
    fullname: Hifi
– volume: 191
  start-page: 61
  issue: 1
  year: 2008
  ident: 10.1016/j.ejor.2022.02.023_bib0010
  article-title: Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2007.08.007
  contributor:
    fullname: Cintra
– volume: 33
  start-page: 49
  issue: 1
  year: 1985
  ident: 10.1016/j.ejor.2022.02.023_bib0002
  article-title: An exact two-dimensional non-guillotine cutting tree search procedure
  publication-title: Operations Research
  doi: 10.1287/opre.33.1.49
  contributor:
    fullname: Beasley
– volume: 39
  start-page: 64
  issue: 1
  year: 2012
  ident: 10.1016/j.ejor.2022.02.023_bib0030
  article-title: A hybrid simulated annealing metaheuristic algorithm for the two-dimensional knapsack packing problem
  publication-title: Computers and Operations Research
  doi: 10.1016/j.cor.2010.10.022
  contributor:
    fullname: Leung
– volume: 270
  start-page: 448
  issue: 2
  year: 2018
  ident: 10.1016/j.ejor.2022.02.023_bib0039
  article-title: A best-fit branch-and-bound heuristic for the unconstrained two-dimensional non-guillotine cutting problem
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2018.04.014
  contributor:
    fullname: Wei
– volume: 271
  start-page: 33
  issue: 1
  year: 2018
  ident: 10.1016/j.ejor.2022.02.023_bib0027
  article-title: The minimum raster set problem and its application to the d-dimensional orthogonal packing problem
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2018.04.046
  contributor:
    fullname: Kartak
– volume: 19
  start-page: 36
  issue: 1
  year: 2007
  ident: 10.1016/j.ejor.2022.02.023_bib0036
  article-title: Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem
  publication-title: INFORMS Journal on Computing
  doi: 10.1287/ijoc.1060.0181
  contributor:
    fullname: Pisinger
– volume: 32
  start-page: 5
  issue: 1
  year: 2004
  ident: 10.1016/j.ejor.2022.02.023_bib0006
  article-title: On the two-dimensional knapsack problem
  publication-title: Operations Research Letters
  doi: 10.1016/S0167-6377(03)00057-9
  contributor:
    fullname: Caprara
– volume: 183
  start-page: 1136
  issue: 3
  year: 2007
  ident: 10.1016/j.ejor.2022.02.023_bib0001
  article-title: A cutting-plane approach for the two-dimensional orthogonal non-guillotine cutting problem
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2005.11.060
  contributor:
    fullname: Baldacci
– volume: 22
  start-page: 222
  issue: 2
  year: 2010
  ident: 10.1016/j.ejor.2022.02.023_bib0017
  article-title: A tree search algorithm for solving the container loading problem
  publication-title: INFORMS Journal on Computing
  doi: 10.1287/ijoc.1090.0338
  contributor:
    fullname: Fanslau
– volume: 38
  start-page: 1342
  issue: 9
  year: 2011
  ident: 10.1016/j.ejor.2022.02.023_bib0007
  article-title: A heuristic approach for packing identical rectangles in convex regions
  publication-title: Computers and Operations Research
  doi: 10.1016/j.cor.2010.12.001
  contributor:
    fullname: Cassioli
– volume: 62
  start-page: 1126
  issue: 5
  year: 2014
  ident: 10.1016/j.ejor.2022.02.023_bib0012
  article-title: An exact algorithm for the two-dimensional orthogonal packing problem with unloading constraints
  publication-title: Operations Research
  doi: 10.1287/opre.2014.1307
  contributor:
    fullname: Côté
– volume: 60
  start-page: S93
  issue: 1
  year: 2009
  ident: 10.1016/j.ejor.2022.02.023_bib0003
  article-title: A tutorial in irregular shape packing problems
  publication-title: Journal of the Operational Research Society
  doi: 10.1057/jors.2008.169
  contributor:
    fullname: Bennell
– volume: 21
  start-page: 1411
  issue: 7
  year: 2015
  ident: 10.1016/j.ejor.2022.02.023_bib0016
  article-title: Low-cost silicon wafer dicing using a craft cutter
  publication-title: Microsystem Technologies
  doi: 10.1007/s00542-014-2198-4
  contributor:
    fullname: Fan
– start-page: 340
  year: 1979
  ident: 10.1016/j.ejor.2022.02.023_bib0021
  article-title: Computers and intractability: A guide to the theory of NP-completeness
  contributor:
    fullname: Garey
– volume: 145
  start-page: 541
  issue: 2
  year: 2013
  ident: 10.1016/j.ejor.2022.02.023_bib0025
  article-title: Board cutting from logs: Optimal and heuristic approaches for the problem of packing rectangles in a circle
  publication-title: International Journal of Production Economics
  doi: 10.1016/j.ijpe.2013.04.047
  contributor:
    fullname: Hinostroza
– volume: 179
  start-page: 261
  issue: 1
  year: 2010
  ident: 10.1016/j.ejor.2022.02.023_bib0028
  article-title: Optimal rectangle packing
  publication-title: Annals of Operations Research
  doi: 10.1007/s10479-008-0463-6
  contributor:
    fullname: Korf
– volume: 215
  start-page: 45
  issue: 1
  year: 2011
  ident: 10.1016/j.ejor.2022.02.023_bib0008
  article-title: Scheduling inspired models for two-dimensional packing problems
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2011.06.001
  contributor:
    fullname: Castro
– volume: 55
  start-page: 569
  issue: 3
  year: 2007
  ident: 10.1016/j.ejor.2022.02.023_bib0019
  article-title: An exact algorithm for higher-dimensional orthogonal packing
  publication-title: Operations Research
  doi: 10.1287/opre.1060.0369
  contributor:
    fullname: Fekete
– volume: 80
  start-page: 68
  issue: 1
  year: 1995
  ident: 10.1016/j.ejor.2022.02.023_bib0009
  article-title: An analytical model for the container loading problem
  publication-title: European Journal of Operational Research
  doi: 10.1016/0377-2217(94)00002-T
  contributor:
    fullname: Chen
– volume: 285
  start-page: 865
  issue: 3
  year: 2020
  ident: 10.1016/j.ejor.2022.02.023_bib0005
  article-title: Packing rectangles into a fixed size circular container: Constructive and metaheuristic search approaches
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2020.02.048
  contributor:
    fullname: Bouzid
– volume: 28
  start-page: 736
  issue: 4
  year: 2016
  ident: 10.1016/j.ejor.2022.02.023_bib0020
  article-title: Modeling two-dimensional guillotine cutting problems via integer programming
  publication-title: INFORMS Journal on Computing
  doi: 10.1287/ijoc.2016.0710
  contributor:
    fullname: Furini
– volume: 36
  start-page: 1026
  issue: 4
  year: 2009
  ident: 10.1016/j.ejor.2022.02.023_bib0015
  article-title: Heuristic approaches for the two-and three-dimensional knapsack packing problem
  publication-title: Computers & Operations Research
  doi: 10.1016/j.cor.2007.12.004
  contributor:
    fullname: Egeblad
– volume: 23
  start-page: 355
  issue: 1–2
  year: 2016
  ident: 10.1016/j.ejor.2022.02.023_bib0035
  article-title: Recursive circle packing problems
  publication-title: International Transactions in Operational Research
  doi: 10.1111/itor.12107
  contributor:
    fullname: Pedroso
– volume: 183
  start-page: 1196
  issue: 3
  year: 2007
  ident: 10.1016/j.ejor.2022.02.023_bib0011
  article-title: A new exact method for the two-dimensional orthogonal packing problem
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2005.12.048
  contributor:
    fullname: Clautiaux
– start-page: 144
  year: 1997
  ident: 10.1016/j.ejor.2022.02.023_bib0018
  article-title: A new exact algorithm for general orthogonal d-dimensional knapsack problems
  contributor:
    fullname: Fekete
– volume: 83
  start-page: 39
  issue: 1
  year: 1995
  ident: 10.1016/j.ejor.2022.02.023_bib0023
  article-title: An exact algorithm for general, orthogonal, two-dimensional knapsack problems
  publication-title: European Journal of Operational Research
  doi: 10.1016/0377-2217(93)E0278-6
  contributor:
    fullname: Hadjiconstantinou
– volume: 30
  start-page: 646
  issue: 4
  year: 2018
  ident: 10.1016/j.ejor.2022.02.023_bib0013
  article-title: The meet-in-the-middle principle for cutting and packing problems
  publication-title: INFORMS Journal on Computing
  doi: 10.1287/ijoc.2018.0806
  contributor:
    fullname: Côté
– volume: 237
  start-page: 846
  issue: 3
  year: 2014
  ident: 10.1016/j.ejor.2022.02.023_bib0037
  article-title: 2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problems
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2014.02.059
  contributor:
    fullname: Silva
– volume: 284
  start-page: 87
  issue: 1
  year: 2020
  ident: 10.1016/j.ejor.2022.02.023_bib0029
  article-title: The exact solutions of several types of container loading problems
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2019.12.012
  contributor:
    fullname: Kurpel
– volume: 94
  start-page: 257
  issue: 2
  year: 2003
  ident: 10.1016/j.ejor.2022.02.023_bib0031
  article-title: Integer linear programming models for 2-staged two-dimensional knapsack problems
  publication-title: Mathematical Programming
  doi: 10.1007/s10107-002-0319-9
  contributor:
    fullname: Lodi
– volume: 39
  start-page: 2425
  issue: 10
  year: 2012
  ident: 10.1016/j.ejor.2022.02.023_bib0034
  article-title: LP bounds in various constraint programming approaches for orthogonal packing
  publication-title: Computers and Operations Research
  doi: 10.1016/j.cor.2011.12.010
  contributor:
    fullname: Mesyagutov
– volume: 183
  start-page: 1109
  issue: 3
  year: 2007
  ident: 10.1016/j.ejor.2022.02.023_bib0038
  article-title: An improved typology of cutting and packing problems
  publication-title: European Journal of Operational Research
  doi: 10.1016/j.ejor.2005.12.047
  contributor:
    fullname: Wäscher
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Snippet •We propose the first linear model to pack rectangles in a circle.•A cutting plane method approximates a circular container from a square.•The feasibility of...
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StartPage 114
SubjectTerms Circular container
Combinatorial optimization
Cutting plane method
Packing
Parallel computing
Title A cutting plane method and a parallel algorithm for packing rectangles in a circular container
URI https://dx.doi.org/10.1016/j.ejor.2022.02.023
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