Relations between capacity utilization, minimal bin size and bin number

Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Buchwald, Torsten [verfasserIn] Hoffmann, Kirsten [verfasserIn] Scheithauer, Guntram [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	Cutting and packing Bin packing problem Strip packing problem

Übergeordnetes Werk:	Enthalten in: Annals of operations research - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984, 217(2014), 1 vom: 15. März, Seite 55-76
Übergeordnetes Werk:	volume:217 ; year:2014 ; number:1 ; day:15 ; month:03 ; pages:55-76

Links:	Volltext

DOI / URN:	10.1007/s10479-014-1572-z

Katalog-ID:	SPR010635394

Internformat


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520			\|a Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width.
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700	1		\|a Hoffmann, Kirsten \|e verfasserin \|4 aut
700	1		\|a Scheithauer, Guntram \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Annals of operations research \|d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 \|g 217(2014), 1 vom: 15. März, Seite 55-76 \|w (DE-627)320615421 \|w (DE-600)2021913-1 \|x 1572-9338 \|7 nnns
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912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_101
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
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912			\|a GBV_ILN_4249
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912			\|a GBV_ILN_4306
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912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
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matchkey_str	article:15729338:2014----::eainbtenaaiytlztomnmli
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allfields	10.1007/s10479-014-1572-z doi (DE-627)SPR010635394 (SPR)s10479-014-1572-z-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE 85.03 bkl Buchwald, Torsten verfasserin aut Relations between capacity utilization, minimal bin size and bin number 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width. Cutting and packing (dpeaa)DE-He213 Bin packing problem (dpeaa)DE-He213 Strip packing problem (dpeaa)DE-He213 Hoffmann, Kirsten verfasserin aut Scheithauer, Guntram verfasserin aut Enthalten in Annals of operations research Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 217(2014), 1 vom: 15. März, Seite 55-76 (DE-627)320615421 (DE-600)2021913-1 1572-9338 nnns volume:217 year:2014 number:1 day:15 month:03 pages:55-76 https://dx.doi.org/10.1007/s10479-014-1572-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 85.03 ASE AR 217 2014 1 15 03 55-76
spelling	10.1007/s10479-014-1572-z doi (DE-627)SPR010635394 (SPR)s10479-014-1572-z-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE 85.03 bkl Buchwald, Torsten verfasserin aut Relations between capacity utilization, minimal bin size and bin number 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width. Cutting and packing (dpeaa)DE-He213 Bin packing problem (dpeaa)DE-He213 Strip packing problem (dpeaa)DE-He213 Hoffmann, Kirsten verfasserin aut Scheithauer, Guntram verfasserin aut Enthalten in Annals of operations research Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 217(2014), 1 vom: 15. März, Seite 55-76 (DE-627)320615421 (DE-600)2021913-1 1572-9338 nnns volume:217 year:2014 number:1 day:15 month:03 pages:55-76 https://dx.doi.org/10.1007/s10479-014-1572-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 85.03 ASE AR 217 2014 1 15 03 55-76
allfields_unstemmed	10.1007/s10479-014-1572-z doi (DE-627)SPR010635394 (SPR)s10479-014-1572-z-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE 85.03 bkl Buchwald, Torsten verfasserin aut Relations between capacity utilization, minimal bin size and bin number 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width. Cutting and packing (dpeaa)DE-He213 Bin packing problem (dpeaa)DE-He213 Strip packing problem (dpeaa)DE-He213 Hoffmann, Kirsten verfasserin aut Scheithauer, Guntram verfasserin aut Enthalten in Annals of operations research Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 217(2014), 1 vom: 15. März, Seite 55-76 (DE-627)320615421 (DE-600)2021913-1 1572-9338 nnns volume:217 year:2014 number:1 day:15 month:03 pages:55-76 https://dx.doi.org/10.1007/s10479-014-1572-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 85.03 ASE AR 217 2014 1 15 03 55-76
allfieldsGer	10.1007/s10479-014-1572-z doi (DE-627)SPR010635394 (SPR)s10479-014-1572-z-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE 85.03 bkl Buchwald, Torsten verfasserin aut Relations between capacity utilization, minimal bin size and bin number 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width. Cutting and packing (dpeaa)DE-He213 Bin packing problem (dpeaa)DE-He213 Strip packing problem (dpeaa)DE-He213 Hoffmann, Kirsten verfasserin aut Scheithauer, Guntram verfasserin aut Enthalten in Annals of operations research Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 217(2014), 1 vom: 15. März, Seite 55-76 (DE-627)320615421 (DE-600)2021913-1 1572-9338 nnns volume:217 year:2014 number:1 day:15 month:03 pages:55-76 https://dx.doi.org/10.1007/s10479-014-1572-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 85.03 ASE AR 217 2014 1 15 03 55-76
allfieldsSound	10.1007/s10479-014-1572-z doi (DE-627)SPR010635394 (SPR)s10479-014-1572-z-e DE-627 ger DE-627 rakwb eng 004 ASE 004 ASE 85.03 bkl Buchwald, Torsten verfasserin aut Relations between capacity utilization, minimal bin size and bin number 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width. Cutting and packing (dpeaa)DE-He213 Bin packing problem (dpeaa)DE-He213 Strip packing problem (dpeaa)DE-He213 Hoffmann, Kirsten verfasserin aut Scheithauer, Guntram verfasserin aut Enthalten in Annals of operations research Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 217(2014), 1 vom: 15. März, Seite 55-76 (DE-627)320615421 (DE-600)2021913-1 1572-9338 nnns volume:217 year:2014 number:1 day:15 month:03 pages:55-76 https://dx.doi.org/10.1007/s10479-014-1572-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 85.03 ASE AR 217 2014 1 15 03 55-76
language	English
source	Enthalten in Annals of operations research 217(2014), 1 vom: 15. März, Seite 55-76 volume:217 year:2014 number:1 day:15 month:03 pages:55-76
sourceStr	Enthalten in Annals of operations research 217(2014), 1 vom: 15. März, Seite 55-76 volume:217 year:2014 number:1 day:15 month:03 pages:55-76
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Cutting and packing Bin packing problem Strip packing problem
dewey-raw	004
isfreeaccess_bool	false
container_title	Annals of operations research
authorswithroles_txt_mv	Buchwald, Torsten @@aut@@ Hoffmann, Kirsten @@aut@@ Scheithauer, Guntram @@aut@@
publishDateDaySort_date	2014-03-15T00:00:00Z
hierarchy_top_id	320615421
dewey-sort	14
id	SPR010635394
language_de	englisch
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author	Buchwald, Torsten
spellingShingle	Buchwald, Torsten ddc 004 bkl 85.03 misc Cutting and packing misc Bin packing problem misc Strip packing problem Relations between capacity utilization, minimal bin size and bin number
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topic_title	004 ASE 85.03 bkl Relations between capacity utilization, minimal bin size and bin number Cutting and packing (dpeaa)DE-He213 Bin packing problem (dpeaa)DE-He213 Strip packing problem (dpeaa)DE-He213
topic	ddc 004 bkl 85.03 misc Cutting and packing misc Bin packing problem misc Strip packing problem
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title	Relations between capacity utilization, minimal bin size and bin number
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title_full	Relations between capacity utilization, minimal bin size and bin number
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author_browse	Buchwald, Torsten Hoffmann, Kirsten Scheithauer, Guntram
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title_sort	relations between capacity utilization, minimal bin size and bin number
title_auth	Relations between capacity utilization, minimal bin size and bin number
abstract	Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width.
abstractGer	Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width.
abstract_unstemmed	Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width.
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title_short	Relations between capacity utilization, minimal bin size and bin number
url	https://dx.doi.org/10.1007/s10479-014-1572-z
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author2	Hoffmann, Kirsten Scheithauer, Guntram
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doi_str	10.1007/s10479-014-1572-z
up_date	2024-07-03T17:21:48.302Z
_version_	1803579354830077952
fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR010635394</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220110221228.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2014 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10479-014-1572-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR010635394</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10479-014-1572-z-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">85.03</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Buchwald, Torsten</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Relations between capacity utilization, minimal bin size and bin number</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2014</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer %${k} \ge 3%$ that at most %${k}-1%$ bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed %${k}/4%$-times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cutting and packing</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bin packing problem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Strip packing problem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hoffmann, Kirsten</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Scheithauer, Guntram</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Annals of operations research</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984</subfield><subfield code="g">217(2014), 1 vom: 15. 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