Robust mixed-integer linear programming models for the irregular strip packing problem

•Two new nesting MIP models are proposed, compared and assessed.•Direct geometry and no-fit-polygon convex decomposition are used.•General models as they easily support pieces with complex geometries.•Easier to implement than previous models in the literature.•Outperform the best exact approach know...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	European journal of operational research Jg. 253; H. 3; S. 570 - 583
Hauptverfasser:	Cherri, Luiz H., Mundim, Leandro R., Andretta, Marina, Toledo, Franklina M.B., Oliveira, José F., Carravilla, Maria Antónia
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Amsterdam Elsevier B.V 16.09.2016 Elsevier Sequoia S.A
Schlagworte:	Algorithms Cutting Cutting stock problem Geometry Handling Heuristic Integer programming Linear programming Mathematical models MIP models Nesting Operational research Optimization algorithms Packing Packing problem Polygons Strip Studies Nesting Cutting Packing MIP models
ISSN:	0377-2217, 1872-6860
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	•Two new nesting MIP models are proposed, compared and assessed.•Direct geometry and no-fit-polygon convex decomposition are used.•General models as they easily support pieces with complex geometries.•Easier to implement than previous models in the literature.•Outperform the best exact approach known in the literature. Two-dimensional irregular strip packing problems are cutting and packing problems where small pieces have to be cut from a larger object, involving a non-trivial handling of geometry. Increasingly sophisticated and complex heuristic approaches have been developed to address these problems but, despite the apparently good quality of the solutions, there is no guarantee of optimality. Therefore, mixed-integer linear programming (MIP) models started to be developed. However, these models are heavily limited by the complexity of the geometry handling algorithms needed for the piece non-overlapping constraints. This led to pieces simplifications to specialize the developed mathematical models. In this paper, to overcome these limitations, two robust MIP models are proposed. In the first model (DTM) the non-overlapping constraints are stated based on direct trigonometry, while in the second model (NFP−CM) pieces are first decomposed into convex parts and then the non-overlapping constraints are written based on nofit polygons of the convex parts. Both approaches are robust in terms of the type of geometries they can address, considering any kind of non-convex polygon with or without holes. They are also simpler to implement than previous models. This simplicity allowed to consider, for the first time, a variant of the models that deals with piece rotations. Computational experiments with benchmark instances show that NFP−CM outperforms both DTM and the best exact model published in the literature. New real-world based instances with more complex geometries are proposed and used to verify the robustness of the new models.
AbstractList	Two-dimensional irregular strip packing problems are cutting and packing problems where small pieces have to be cut from a larger object, involving a non-trivial handling of geometry. Increasingly sophisticated and complex heuristic approaches have been developed to address these problems but, despite the apparently good quality of the solutions, there is no guarantee of optimality. Therefore, mixed-integer linear programming (MIP) models started to be developed. However, these models are heavily limited by the complexity of the geometry handling algorithms needed for the piece non-overlapping constraints. This led to pieces simplifications to specialize the developed mathematical models. In this paper, to overcome these limitations, two robust MIP models are proposed. In the first model (DTM ) the non-overlapping constraints are stated based on direct trigonometry, while in the second model (NFP-CMNFP-CM) pieces are first decomposed into convex parts and then the non-overlapping constraints are written based on nofit polygons of the convex parts. Both approaches are robust in terms of the type of geometries they can address, considering any kind of non-convex polygon with or without holes. They are also simpler to implement than previous models. This simplicity allowed to consider, for the first time, a variant of the models that deals with piece rotations. Computational experiments with benchmark instances show that NFP-CMNFP-CM outperforms both DTM and the best exact model published in the literature. New real-world based instances with more complex geometries are proposed and used to verify the robustness of the new models. •Two new nesting MIP models are proposed, compared and assessed.•Direct geometry and no-fit-polygon convex decomposition are used.•General models as they easily support pieces with complex geometries.•Easier to implement than previous models in the literature.•Outperform the best exact approach known in the literature. Two-dimensional irregular strip packing problems are cutting and packing problems where small pieces have to be cut from a larger object, involving a non-trivial handling of geometry. Increasingly sophisticated and complex heuristic approaches have been developed to address these problems but, despite the apparently good quality of the solutions, there is no guarantee of optimality. Therefore, mixed-integer linear programming (MIP) models started to be developed. However, these models are heavily limited by the complexity of the geometry handling algorithms needed for the piece non-overlapping constraints. This led to pieces simplifications to specialize the developed mathematical models. In this paper, to overcome these limitations, two robust MIP models are proposed. In the first model (DTM) the non-overlapping constraints are stated based on direct trigonometry, while in the second model (NFP−CM) pieces are first decomposed into convex parts and then the non-overlapping constraints are written based on nofit polygons of the convex parts. Both approaches are robust in terms of the type of geometries they can address, considering any kind of non-convex polygon with or without holes. They are also simpler to implement than previous models. This simplicity allowed to consider, for the first time, a variant of the models that deals with piece rotations. Computational experiments with benchmark instances show that NFP−CM outperforms both DTM and the best exact model published in the literature. New real-world based instances with more complex geometries are proposed and used to verify the robustness of the new models. Two-dimensional irregular strip packing problems are cutting and packing problems where small pieces have to be cut from a larger object, involving a non-trivial handling of geometry. Increasingly sophisticated and complex heuristic approaches have been developed to address these problems but, despite the apparently good quality of the solutions, there is no guarantee of optimality. Therefore, mixed-integer linear programming (MIP) models started to be developed. However, these models are heavily limited by the complexity of the geometry handling algorithms needed for the piece non-overlapping constraints. This led to pieces simplifications to specialize the developed mathematical models. In this paper, to overcome these limitations, two robust MIP models are proposed. In the first model (DTM ) the non-overlapping constraints are stated based on direct trigonometry, while in the second model (NFP-CM) pieces are first decomposed into convex parts and then the non-overlapping constraints are written based on nofit polygons of the convex parts. Both approaches are robust in terms of the type of geometries they can address, considering any kind of non-convex polygon with or without holes. They are also simpler to implement than previous models. This simplicity allowed to consider, for the first time, a variant of the models that deals with piece rotations. Computational experiments with benchmark instances show that NFP-CM outperforms both DTM and the best exact model published in the literature. New real-world based instances with more complex geometries are proposed and used to verify the robustness of the new models.
Author	Toledo, Franklina M.B. Carravilla, Maria Antónia Oliveira, José F. Cherri, Luiz H. Andretta, Marina Mundim, Leandro R.
Author_xml	– sequence: 1 givenname: Luiz H. orcidid: 0000-0003-3958-2629 surname: Cherri fullname: Cherri, Luiz H. email: lhcherri@icmc.usp.br, luizcherri@gmail.com organization: University of São Paulo, Avenida Trabalhador São-carlense, 400, 13566-590 São Carlos - SP, Brazil – sequence: 2 givenname: Leandro R. surname: Mundim fullname: Mundim, Leandro R. organization: University of São Paulo, Avenida Trabalhador São-carlense, 400, 13566-590 São Carlos - SP, Brazil – sequence: 3 givenname: Marina orcidid: 0000-0002-7068-6947 surname: Andretta fullname: Andretta, Marina organization: University of São Paulo, Avenida Trabalhador São-carlense, 400, 13566-590 São Carlos - SP, Brazil – sequence: 4 givenname: Franklina M.B. surname: Toledo fullname: Toledo, Franklina M.B. organization: University of São Paulo, Avenida Trabalhador São-carlense, 400, 13566-590 São Carlos - SP, Brazil – sequence: 5 givenname: José F. surname: Oliveira fullname: Oliveira, José F. organization: INESC TEC, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal – sequence: 6 givenname: Maria Antónia orcidid: 0000-0002-9245-2674 surname: Carravilla fullname: Carravilla, Maria Antónia organization: INESC TEC, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
BookMark	eNp9kD2P1DAQQC10SOx9_AGqSDQ0CTM2ibMSDTrxJZ2EhOBay3Emi0NiL2PnBP8er5bqiqs8xXsz1rsUFyEGEuIlQoOA3Zu5oTlyI8vcgGoA9s_EDnst667v4ELsQGldS4n6hbhMaQYAbLHdiftvcdhSrlb_h8bah0wH4mrxgSxXR44Htuvqw6Fa40hLqqbIVf5JlWemw7YUKGX2x-po3a8TVpRhofVaPJ_skujm_3slfnz88P32c3339dOX2_d3tWs7zLXVne7lMCjCSaNy2OPYyn6UAyBMzilwPVI7YDcomAhbJZVtSe21nqwDq67E6_Pecvf3Rimb1SdHy2IDxS2ZsrCD9q1CXdBXj9A5bhzK7wzqvVT9HjpZKHmmHMeUmCZzZL9a_msQzCm1mc0ptTmlNqBMSV2k_pHkfLbZx5DZ-uVp9d1ZLXHpwROb5DwFR6NnctmM0T-l_wOxTpxm
CODEN	EJORDT
CitedBy_id	crossref_primary_10_1007_s10479_025_06506_x crossref_primary_10_1007_s10898_018_0637_y crossref_primary_10_1016_j_cie_2021_107467 crossref_primary_10_1007_s10898_021_01002_5 crossref_primary_10_1016_j_ejor_2019_06_008 crossref_primary_10_3389_fmech_2022_966691 crossref_primary_10_1016_j_cie_2020_106607 crossref_primary_10_1016_j_eswa_2023_120548 crossref_primary_10_1016_j_cie_2023_109318 crossref_primary_10_1016_j_ejor_2019_03_040 crossref_primary_10_1016_j_ejor_2019_04_045 crossref_primary_10_1111_itor_12642 crossref_primary_10_1016_j_apm_2018_11_008 crossref_primary_10_1016_j_cie_2020_106757 crossref_primary_10_1080_00207543_2016_1229070 crossref_primary_10_1016_j_cor_2017_10_001 crossref_primary_10_1016_j_ejor_2024_03_004 crossref_primary_10_1007_s11804_025_00644_1 crossref_primary_10_1016_j_ejor_2025_05_019 crossref_primary_10_1016_j_renene_2018_02_059 crossref_primary_10_1109_ACCESS_2020_2994635 crossref_primary_10_1016_j_ejor_2018_03_029 crossref_primary_10_1109_ACCESS_2019_2957283 crossref_primary_10_1007_s10898_018_0638_x crossref_primary_10_1111_itor_13122 crossref_primary_10_3390_math12172670 crossref_primary_10_1109_ACCESS_2018_2876546 crossref_primary_10_15807_jorsj_61_132 crossref_primary_10_1016_j_ejor_2019_02_004 crossref_primary_10_1016_j_aei_2021_101403 crossref_primary_10_1016_j_asoc_2021_108060 crossref_primary_10_1016_j_cor_2025_107209 crossref_primary_10_3390_math11020327 crossref_primary_10_3390_math12223470 crossref_primary_10_1007_s00366_018_0668_5 crossref_primary_10_1016_j_ejor_2022_07_050 crossref_primary_10_1016_j_cor_2023_106398 crossref_primary_10_1016_j_ejor_2023_08_009 crossref_primary_10_1016_j_cor_2023_106476 crossref_primary_10_1016_j_eswa_2022_118207 crossref_primary_10_3390_math12152414 crossref_primary_10_1016_j_asoc_2020_106485 crossref_primary_10_1080_0951192X_2022_2050302 crossref_primary_10_1051_itmconf_20171400005 crossref_primary_10_1002_pts_2679 crossref_primary_10_1080_00207543_2017_1394598 crossref_primary_10_1109_ACCESS_2019_2914248 crossref_primary_10_3390_app11115217 crossref_primary_10_1155_2018_3525384 crossref_primary_10_1016_j_gmod_2023_101205 crossref_primary_10_1016_j_eswa_2017_03_059 crossref_primary_10_1016_j_eswa_2025_129621 crossref_primary_10_3390_math10162941 crossref_primary_10_1016_j_ejor_2020_07_003
Cites_doi	10.1007/s10732-008-9088-9 10.1007/s101070100263 10.1016/j.dam.2012.03.026 10.1016/j.ejor.2004.09.008 10.1016/j.ejor.2005.12.047 10.1016/j.cor.2011.05.025 10.1016/j.ijpe.2013.04.009 10.1016/j.ejor.2013.06.020 10.1016/j.cad.2012.03.004 10.1287/ijoc.15.3.310.16082 10.1016/j.ejor.2006.11.038 10.1016/j.ijpe.2013.04.007 10.1016/j.ejor.2005.11.063 10.1016/j.disopt.2009.04.002 10.1111/j.1475-3995.2009.00707.x
ContentType	Journal Article
Copyright	2016 Elsevier B.V. Copyright Elsevier Sequoia S.A. Sep 16, 2016
Copyright_xml	– notice: 2016 Elsevier B.V. – notice: Copyright Elsevier Sequoia S.A. Sep 16, 2016
DBID	AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 L7M L~C L~D 7TA JG9
DOI	10.1016/j.ejor.2016.03.009
DatabaseName	CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Materials Business File Materials Research Database
DatabaseTitle	CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional Materials Research Database Materials Business File
DatabaseTitleList	Materials Research Database Technology Research Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Computer Science Business
EISSN	1872-6860
EndPage	583
ExternalDocumentID	4072043921 10_1016_j_ejor_2016_03_009 S0377221716301370
Genre	Feature
GroupedDBID	--K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 6OB 7-5 71M 8P~ 9JN 9JO AAAKF AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AARIN AAXUO AAYFN ABAOU ABBOA ABFNM ABFRF ABJNI ABMAC ABUCO ABYKQ ACAZW ACDAQ ACGFO ACGFS ACIWK ACNCT ACRLP ACZNC ADBBV ADEZE ADGUI AEBSH AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD APLSM ARUGR AXJTR BKOJK BKOMP BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HAMUX IHE J1W KOM LY1 M41 MHUIS MO0 MS~ N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 RIG ROL RPZ RXW SCC SDF SDG SDP SDS SES SPC SPCBC SSB SSD SSV SSW SSZ T5K TAE TN5 U5U XPP ZMT ~02 ~G- 1OL 29G 41~ 9DU AAAKG AAQXK AATTM AAXKI AAYWO AAYXX ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADIYS ADJOM ADMUD ADNMO ADXHL AEIPS AEUPX AFFNX AFJKZ AFPUW AGQPQ AI. AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CITATION EFKBS FEDTE FGOYB HVGLF HZ~ R2- SEW VH1 WUQ ~HD 7SC 7TB 8FD FR3 JQ2 L7M L~C L~D 7TA JG9
ID	FETCH-LOGICAL-c561t-a76782bb3e1f713c181d528d2b010fcc30c81e5b16b30fe15323a5e3977fac0a3
ISICitedReferencesCount	67
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000376544700003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0377-2217
IngestDate	Thu Oct 02 06:20:03 EDT 2025 Sun Nov 09 06:05:21 EST 2025 Tue Nov 18 20:47:29 EST 2025 Sat Nov 29 01:41:16 EST 2025 Fri Feb 23 02:27:40 EST 2024
IsDoiOpenAccess	false
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	3
Keywords	Nesting Cutting Packing MIP models
Language	English
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c561t-a76782bb3e1f713c181d528d2b010fcc30c81e5b16b30fe15323a5e3977fac0a3
Notes	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ORCID	0000-0003-3958-2629 0000-0002-7068-6947 0000-0002-9245-2674
OpenAccessLink	http://dx.doi.org/10.1016/j.ejor.2016.03.009
PQID	1792389062
PQPubID	45678
PageCount	14
ParticipantIDs	proquest_miscellaneous_1816054317 proquest_journals_1792389062 crossref_primary_10_1016_j_ejor_2016_03_009 crossref_citationtrail_10_1016_j_ejor_2016_03_009 elsevier_sciencedirect_doi_10_1016_j_ejor_2016_03_009
PublicationCentury	2000
PublicationDate	2016-09-16
PublicationDateYYYYMMDD	2016-09-16
PublicationDate_xml	– month: 09 year: 2016 text: 2016-09-16 day: 16
PublicationDecade	2010
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	European journal of operational research
PublicationYear	2016
Publisher	Elsevier B.V Elsevier Sequoia S.A
Publisher_xml	– name: Elsevier B.V – name: Elsevier Sequoia S.A
References	Gomes, Oliveira (bib0011) 2006; 171 Greene (bib0012) 1983; 1 Imamichi, Yagiura, Nagamochi (bib0013) 2009; 6 Leung, Lin, Zhang (bib0014) 2012; 39 Alvarez-Valdes, Martinez, Tamarit (bib0001) 2013; 145 (2015). Martello, Monaci, Vigo (bib0015) 2003; 15 Sato, Martins, Tsuzuki (bib0016) 2012; 44 Dolan, Moré (bib0007) 2002; 91 . Wäscher, Haußner, Schumann (bib0019) 2007; 183 Bennell, Oliveira (bib0003) 2008; 184 Toledo, Carravilla, Ribeiro, Oliveira, Gomes (bib0017) 2013; 145 Egeblad, Nielsen, Odgaard (bib0008) 2007; 183 Umetani, Yagiura, Imahori, Imamichi, Nonobe, Ibaraki (bib0018) 2009; 16 Carravilla, Ribeiro (bib0004) 2005 Elkeran (bib0009) 2013; 231 Computational Geometry Algorithms Library. Cuninghame-Green (bib0006) 1989; 12 Fischetti, Luzzi (bib0010) 2009; 15 Baldacci, Boschetti, Ganovelli, Maniezzo (bib0002) 2014; 163 10.1016/j.ejor.2016.03.009_bib0005 Baldacci (10.1016/j.ejor.2016.03.009_bib0002) 2014; 163 Alvarez-Valdes (10.1016/j.ejor.2016.03.009_bib0001) 2013; 145 Toledo (10.1016/j.ejor.2016.03.009_bib0017) 2013; 145 Wäscher (10.1016/j.ejor.2016.03.009_bib0019) 2007; 183 Umetani (10.1016/j.ejor.2016.03.009_bib0018) 2009; 16 Sato (10.1016/j.ejor.2016.03.009_bib0016) 2012; 44 Carravilla (10.1016/j.ejor.2016.03.009_bib0004) 2005 Greene (10.1016/j.ejor.2016.03.009_bib0012) 1983; 1 Bennell (10.1016/j.ejor.2016.03.009_bib0003) 2008; 184 Egeblad (10.1016/j.ejor.2016.03.009_bib0008) 2007; 183 Dolan (10.1016/j.ejor.2016.03.009_bib0007) 2002; 91 Cuninghame-Green (10.1016/j.ejor.2016.03.009_bib0006) 1989; 12 Fischetti (10.1016/j.ejor.2016.03.009_bib0010) 2009; 15 Gomes (10.1016/j.ejor.2016.03.009_bib0011) 2006; 171 Imamichi (10.1016/j.ejor.2016.03.009_bib0013) 2009; 6 Elkeran (10.1016/j.ejor.2016.03.009_bib0009) 2013; 231 Leung (10.1016/j.ejor.2016.03.009_bib0014) 2012; 39 Martello (10.1016/j.ejor.2016.03.009_bib0015) 2003; 15
References_xml	– start-page: 113 year: 2005 end-page: 127 ident: bib0004 article-title: CP and MIP in the resolution of hard combinatorial problems: a case study with nesting problems publication-title: CSCLP 2005 joint ERCIM/CoLogNET international workshop on constraint solving and constraint logic programming – reference: (2015). – volume: 1 start-page: 235 year: 1983 end-page: 259 ident: bib0012 article-title: The decomposition of polygons into convex parts publication-title: Computational Geometry – volume: 231 start-page: 757 year: 2013 end-page: 769 ident: bib0009 article-title: A new approach for sheet nesting problem using guided cuckoo search and pairwise clustering publication-title: European Journal of Operational Research – volume: 163 start-page: 17 year: 2014 end-page: 33 ident: bib0002 article-title: Algorithms for nesting with defects publication-title: Discrete Applied Mathematics – volume: 15 start-page: 310 year: 2003 end-page: 319 ident: bib0015 article-title: An exact approach to the strip–packing problem publication-title: INFORMS Journalon Computing – volume: 145 start-page: 478 year: 2013 end-page: 487 ident: bib0017 article-title: The dotted-board model: A new MIP model for nesting irregular shapes publication-title: International Journal of Production Economics – volume: 16 start-page: 661 year: 2009 end-page: 683 ident: bib0018 article-title: Solving the irregular strip packing problem via guided local search for overlap minimization publication-title: International Transactions in Operational Research – reference: , Computational Geometry Algorithms Library. – reference: . – volume: 15 start-page: 201 year: 2009 end-page: 226 ident: bib0010 article-title: Mixed–integer programming models for nesting problems publication-title: Journal of Heuristics – volume: 171 start-page: 811 year: 2006 end-page: 829 ident: bib0011 article-title: Solving irregular strip packing problems by hybridising simulated annealing and linear programming publication-title: European Journal of Operational Research – volume: 6 start-page: 345 year: 2009 end-page: 361 ident: bib0013 article-title: An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem publication-title: Discrete Optimization – volume: 91 start-page: 201 year: 2002 end-page: 213 ident: bib0007 article-title: Benchmarking optimization software with performance profiles publication-title: Mathematical Programming – volume: 12 start-page: 50 year: 1989 end-page: 53 ident: bib0006 article-title: Geometry, shoemaking and the milk tray problem publication-title: NewScientist – volume: 44 start-page: 766 year: 2012 end-page: 777 ident: bib0016 article-title: An algorithm for the strip packing problem using collision free region and exact fitting placement publication-title: Computer-Aided Design – volume: 184 start-page: 397 year: 2008 end-page: 415 ident: bib0003 article-title: The geometry of nesting problems: A tutorial publication-title: European Journal of Operational Research – volume: 183 start-page: 1249 year: 2007 end-page: 1266 ident: bib0008 article-title: Fast neighborhood search for two- and three-dimensional nesting problems publication-title: European Journal of Operational Research – volume: 183 start-page: 1109 year: 2007 end-page: 1130 ident: bib0019 article-title: An improved typology of cutting and packing problems publication-title: European Journal of Operational Research – volume: 145 start-page: 463 year: 2013 end-page: 477 ident: bib0001 article-title: A branch & bound algorithm for cutting and packing irregularly shaped pieces publication-title: International Journal of Production Economics – volume: 39 start-page: 678 year: 2012 end-page: 686 ident: bib0014 article-title: Extended local search algorithm based on nonlinear programming for two-dimensional irregular strip packing problem publication-title: Computers & Operations Research – volume: 15 start-page: 201 issue: 3 year: 2009 ident: 10.1016/j.ejor.2016.03.009_bib0010 article-title: Mixed–integer programming models for nesting problems publication-title: Journal of Heuristics doi: 10.1007/s10732-008-9088-9 – volume: 91 start-page: 201 issue: 2 year: 2002 ident: 10.1016/j.ejor.2016.03.009_bib0007 article-title: Benchmarking optimization software with performance profiles publication-title: Mathematical Programming doi: 10.1007/s101070100263 – volume: 163 start-page: 17 issue: 0 year: 2014 ident: 10.1016/j.ejor.2016.03.009_bib0002 article-title: Algorithms for nesting with defects publication-title: Discrete Applied Mathematics doi: 10.1016/j.dam.2012.03.026 – start-page: 113 year: 2005 ident: 10.1016/j.ejor.2016.03.009_bib0004 article-title: CP and MIP in the resolution of hard combinatorial problems: a case study with nesting problems – ident: 10.1016/j.ejor.2016.03.009_bib0005 – volume: 171 start-page: 811 issue: 3 year: 2006 ident: 10.1016/j.ejor.2016.03.009_bib0011 article-title: Solving irregular strip packing problems by hybridising simulated annealing and linear programming publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2004.09.008 – volume: 183 start-page: 1109 issue: 3 year: 2007 ident: 10.1016/j.ejor.2016.03.009_bib0019 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 – volume: 39 start-page: 678 issue: 3 year: 2012 ident: 10.1016/j.ejor.2016.03.009_bib0014 article-title: Extended local search algorithm based on nonlinear programming for two-dimensional irregular strip packing problem publication-title: Computers & Operations Research doi: 10.1016/j.cor.2011.05.025 – volume: 145 start-page: 478 issue: 2 year: 2013 ident: 10.1016/j.ejor.2016.03.009_bib0017 article-title: The dotted-board model: A new MIP model for nesting irregular shapes publication-title: International Journal of Production Economics doi: 10.1016/j.ijpe.2013.04.009 – volume: 231 start-page: 757 issue: 3 year: 2013 ident: 10.1016/j.ejor.2016.03.009_bib0009 article-title: A new approach for sheet nesting problem using guided cuckoo search and pairwise clustering publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2013.06.020 – volume: 44 start-page: 766 issue: 8 year: 2012 ident: 10.1016/j.ejor.2016.03.009_bib0016 article-title: An algorithm for the strip packing problem using collision free region and exact fitting placement publication-title: Computer-Aided Design doi: 10.1016/j.cad.2012.03.004 – volume: 15 start-page: 310 issue: 3 year: 2003 ident: 10.1016/j.ejor.2016.03.009_bib0015 article-title: An exact approach to the strip–packing problem publication-title: INFORMS Journalon Computing doi: 10.1287/ijoc.15.3.310.16082 – volume: 184 start-page: 397 issue: 2 year: 2008 ident: 10.1016/j.ejor.2016.03.009_bib0003 article-title: The geometry of nesting problems: A tutorial publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2006.11.038 – volume: 145 start-page: 463 issue: 2 year: 2013 ident: 10.1016/j.ejor.2016.03.009_bib0001 article-title: A branch & bound algorithm for cutting and packing irregularly shaped pieces publication-title: International Journal of Production Economics doi: 10.1016/j.ijpe.2013.04.007 – volume: 183 start-page: 1249 issue: 3 year: 2007 ident: 10.1016/j.ejor.2016.03.009_bib0008 article-title: Fast neighborhood search for two- and three-dimensional nesting problems publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2005.11.063 – volume: 1 start-page: 235 year: 1983 ident: 10.1016/j.ejor.2016.03.009_bib0012 article-title: The decomposition of polygons into convex parts publication-title: Computational Geometry – volume: 6 start-page: 345 issue: 4 year: 2009 ident: 10.1016/j.ejor.2016.03.009_bib0013 article-title: An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem publication-title: Discrete Optimization doi: 10.1016/j.disopt.2009.04.002 – volume: 12 start-page: 50 issue: 1677 year: 1989 ident: 10.1016/j.ejor.2016.03.009_bib0006 article-title: Geometry, shoemaking and the milk tray problem publication-title: NewScientist – volume: 16 start-page: 661 issue: 6 year: 2009 ident: 10.1016/j.ejor.2016.03.009_bib0018 article-title: Solving the irregular strip packing problem via guided local search for overlap minimization publication-title: International Transactions in Operational Research doi: 10.1111/j.1475-3995.2009.00707.x
SSID	ssj0001515
Score	2.483909
Snippet	•Two new nesting MIP models are proposed, compared and assessed.•Direct geometry and no-fit-polygon convex decomposition are used.•General models as they... Two-dimensional irregular strip packing problems are cutting and packing problems where small pieces have to be cut from a larger object, involving a...
SourceID	proquest crossref elsevier
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	570
SubjectTerms	Algorithms Cutting Cutting stock problem Geometry Handling Heuristic Integer programming Linear programming Mathematical models MIP models Nesting Operational research Optimization algorithms Packing Packing problem Polygons Strip Studies
Title	Robust mixed-integer linear programming models for the irregular strip packing problem
URI	https://dx.doi.org/10.1016/j.ejor.2016.03.009 https://www.proquest.com/docview/1792389062 https://www.proquest.com/docview/1816054317
Volume	253
WOSCitedRecordID	wos000376544700003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-6860 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001515 issn: 0377-2217 databaseCode: AIEXJ dateStart: 19950105 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1db9MwFLWqDSF44KOAKAxkJN6iVLFT18njmIYG2iY0FdS3KHYcqV2XVGk7VfwmfiTXX2kp6sQeeIkqJ7XS3hPf45t7z0Xoo5SMx0ADwryMynAgiiIUMBYOSyITyVgsrEjSOb-8TMbj9Fun88vXwtzOeFUl63U6_6-mhjEwti6dvYe520lhAD6D0eEIZofjPxn-qharxTK4maxVERo1CNUEmkxqUWubjXWj4wOmB86iTTOcNI1pS9_o8pHJPIC99LWtVDcdZ_ZG8B2bhYHGxxWdgFAbaD4x8o8mArCa_AzO-hsrV4Xt5nwO0xVNHVy150ym5dJy2wvY0Fet_xjVM1XUnnXrjvN5cNH_1N8OYJChzraw9ZW-cIvzkFJbwukXZWolhB364q0lltlGI85bM9sG5y9HYGMS076a1lr1lQytlG26cXv-Vf-ON2xzFH362zTTc2R6jiyKM1Mtekg5S2ENPTz-cjr-2np-TQ7NWyv3g1yRls0n3L2TfURohxIYnjN6hp64DQo-tsB6jjqq6qKHvj6ii576PiDYuYUuerwlavkC_bAAxH8AEFsA4i0AYgtADADEAEDcAhAbAGIHQOwA-BJ9_3w6OjkLXfeOUAInX4Y5Bx5EhYgVKTmJJVDJgtGkoCIiUSllHMmEKCbIUMRRqcDz0jhnSm9IylxGefwKHVR1pV4jPIgGAyZhXKRKN5bOeUEL2AlLGglOy7KHiP8rM-mk7XWHlVm234g9FLTfmVthlzuvZt5CmaOmlnJmALg7v3fkzZm5Z3KREa3ZmWiB8B760J6GZV2_q8srVa_gmoQMI61Twd_c60bfokebZ-wIHSyblXqHHsjb5WTRvHeA_Q0Htcl-
linkProvider	Elsevier
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Robust+mixed-integer+linear+programming+models+for+the+irregular+strip+packing+problem&rft.jtitle=European+journal+of+operational+research&rft.au=Cherri%2C+Luiz+H.&rft.au=Mundim%2C+Leandro+R.&rft.au=Andretta%2C+Marina&rft.au=Toledo%2C+Franklina+M.B.&rft.date=2016-09-16&rft.issn=0377-2217&rft.volume=253&rft.issue=3&rft.spage=570&rft.epage=583&rft_id=info:doi/10.1016%2Fj.ejor.2016.03.009&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_ejor_2016_03_009
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-2217&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-2217&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-2217&client=summon