The evolution of rectangular bin packing problem — A review of research topics, applications, and cited papers

Salma Mezghani; Boukthir Haddar; Habib Chabchoub

doi:10.3934/jimo.2022088

Article Contents

2023, Volume 19, Issue 5: 3329-3361. Doi: 10.3934/jimo.2022088

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The evolution of rectangular bin packing problem — A review of research topics, applications, and cited papers

1.
Laboratoire OLID, LR19ES21, University of Sfax, Higher Institute Of Industrial Management Of Sfax, 3021, Sfax, Tunisie, Tunisia
2.
Data Engineering and Semantics Research Unit, Faculty of Sciences of Sfax, University of Sfax, Sfax, Tunisia
3.
College of Business, Al Ain University, Abu Dhabi, UAE

^*Corresponding author: Salma Mezghani
^*Corresponding author: Salma Mezghani

Received: September 2021

Revised: March 2022

Early access: June 2022

Published: May 2023

Abstract / Introduction Full Text(HTML) Figure(3) / Table(7) Related Papers Cited by

Abstract

Bin packing problem (BPP) is one of the fastest-growing research issues within the field of combinatorial optimization. Over the last years, several studies carried out various BPP variants, mathematical models, and proposed methods to the BPPs. The classical BPP consists of packing a set of rectangular items in a minimum number of rectangular bins while respecting some constraints.

Throughout the years, an improved typology was introduced by Wäscher et al. (2007), providing an excellent instrument for the organization and categorization criteria that defined the problem categories different from those of Dyckhoff (1990). Several early literature reviews have been conducted on various aspects of related packing problem variants.

The contribution of this paper is to provide a comprehensive and refined taxonomy intended for BPPs. In addition to that, it is an up-to-date review based on a chronological taxonomy of the literature and depicts further research horizons.

This systematic review allowed us to identify other characteristics and constraints, based on Wäscher's original ideas, mainly distinguished according to real cases studies. The detailed analysis provides a valuable framework for understanding the research gaps for future studies that should be acknowledged while proposing and solving new extensions.

Note: The addresses of second and third authors have been corrected online.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

Full Text(HTML)

Figure 1. Example of bin packing

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Figure 2. The distribution of problem types according to addressed characteristics (Dimensionality, constraints, No constraints)

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Figure 3. % of BPP constraints through the years

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Table 1. Problem types – input minimization ([253])

Assortment of small items		Characteristics of large objects
		Weakly heterogeneous	Strongly heterogeneous
All dimensions fixed	Identical	Single Stock Size Cutting Stock Problem (SSSCSP)	Single Bin Size Bin Packing Problem (SBSBPP)
	Weakly heterogeneous	Multiple Stock Size Cutting Stock Problem (MSSCSP)	Multiple Bin Size Bin Packing Problem (MBSBPP)
	Strongly heterogeneous	Residual Cutting Stock Problem (RCSP)	Residual Bin Packing Problem (RBPP)
One large object variable dimension(s)}		Open Dimensions Problem (ODP)}

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Table 2. The number of papers on BPP until 2022

Year	Number of papers
1980-1989	10
1990-1999	14
2000-2004	23
2005-2009	40
2010-2014	83
2015-2022	80

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Table 3. A BPP classification

1. Physical characteristics based on the structure
1.1.Items	Strongly heterogeneous items
1.2.Bins	1.2.1. On large objects
	1.2.2. Several large objects
	Identical bins
	Weakly heterogeneous bins
1.3.Dimensionality	1.3.1.One-Dimensional (1D)
	1.3.2.Two-Dimensional (2D)
	1.3.3.Three-Dimensional (3D) or more
2. Scenario characteristics based on reality
2.1.Objective	2.1.1.Single objective
2.1.Objective	2.1.2.Multiple objectives
2.2.Problem data	2.2.1.On-line
	2.2.2.Off-line
	2.2.3.Stochastic
	2.2.4. Dynamic
2.3.Constraints	2.3.1.Basic Geometric constraints : Containment, Overlap 2.3.2.Reaslistic Additional constraints a. Rotation b. Guillotine c. Stability d. Precedence e. Fragility f. Conflicts

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Table 4. Number of papers where the constraint types have been discussed

Constraints type	Number of papers ($ N=250 $)
No constraints	122
Orientation	64
Guillotine	33
Precedence	28
Fragility	11
Stability	14
Conflicts	29

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Table 5. Number of papers where the constraint types have been discussed

Number of Constraints	0	1	2	3	4	5	6
Number of papers ($ N=232 $)	122	84	32	7	2	0	0

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Table 6. Number of constraints considered in the reviewed papers

No.	Papers	Real world Applications
1	[102]	logistics company that loads and ships hundreds of trucks
9	[123]	A direct-shipping system in the food and beverage industry
15	[258]	The task allocation problem of aircraft maintenance
50	[138]	The Challenge Renault/ESICUP 2015
52	[197]	The fruit company in Rio Negro
53	[198]	A Portuguese trading company
58	[246]	The Renault for the 2014/2015 ESICUP challenge
70	[101]	The Machine Reassignment Problem
75	[211]	Assembly design problem
76	[231]	The Renault / ESICUP challenge
82	[262]	The pharmaceutical industry
86	[88]	The Faculty of Economics and Management Sciences of Sfax
91	[200]	An Engine Assembly Line
94	[249]	The Steel Industry
97	[242]	Cellular automata (CA)
98	[141]	The ship placement problem
104	[42]	The industrial beanTech
109	[204]	A Thai Seasoning Company
112	[192]	The industrial Tunisian Foam Company
126	[161]	The production of wind turbine flanges in the open die forging industry
128	[252]	The industry company
131	[194]	The industrial Tunisian Foam Company
136	[18]	Two real life problems from two industrial companies.
143	[195]	The industrial Tunisian Foam Company SOTIM
146	[164]	The air cargo industry.
147	[225]	The roofing industry and the construction of packing boxes
173	[232]	The automobile industry
184	[234]	The Assembly Line Balancing Problem
193	[23]	The Steel industry
224	[39]	A municipal building, a land allocation problem

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Table 7. Classification of the selected papers addressing the BPP problem and its variants

No.	paper	Problem type	Data		Dimensionality			Objective		Constraints

1	[102]	SBSBPP		x			x	x		x			x	x	x
2	[84]	MBSBPP		x	x			x							x
3	[260]	SBSBPP		x		x		x
4	[121]	SBSBPP		x			x	x		x
5	[14]	SBSBPP	x			x		x
6	[103]	MBSBPP		x		x		x		x	x
7	[2]	SBSBPP		x	x			x
8	[45]*	SBSBPP		x	x			x
9	[123]	SBSBPP		x		x			x
10	[95]	SBSBPP		x			x		x	x				x
11	[34]	SBSBPP		x	x			x
12	[250]	SBSBPP		x		x		x
13	[167]	MBSBPP		x	x			x
14	[235]	SBSBPP		x				x
15	[258]	MBSBPP		x	x			x
16	[11]	MBSBPP		x	x			x
17	[216]	SBSBPP		x	x				x
18	[125]	SBSBPP		x		x		x			x
19	[97]	SBSBPP		x		x		x
20	[221]	ODP		x		x		x
21	[143]	SBSBPP	x			x		x
22	[114]	SBSBPP		x			x	x					x	x
23	[171]	SBSBPP		x	x			x							x
24	[15]	SBSBPP	x		x			x
25	[159]	SBSBPP		x	x			x						x	x
26	[108]	MBSBPP	x		x			x							x
27	[217]	SBSBPP		x		x		x		x
28	[157]	SBSBPP		x	x			x
29	[1]	SBSBPP		x	x			x
30	[273]	SBSBPP		x			x	x
31	[205]	MBSBPP		x			x	x		x		x		x
32	[62]	SBSBPP		x		x		x		x
33	[90]	MBSBPP		x	x			x
34	[51]*	SBSBPP and ODP	x	x	x	x		x		x	x
35	[172]	SBSBPP		x		x		x			x
36	[263]	SBSBPP		x		x		x		x	x		x
37	[86]	SBSBPP		x			x	x						x
38	[191]	MBSBPP		x	x			x
39	[71]	SBSBPP		x		x		x
40	[7]	SBSBPP		x		x		x
41	[182]	SBSBPP		x			x	x		x
42	[206]	SBSBPP		x			x	x		x		x		x
43	[8]	SBSBPP		x	x			x
44	[9]	SBSBPP	x		x			x
45	[38]	SBSBPP		x	x	x		x
46	[33]*	SBSBPP and MSBPP		x		x	x	x	x		x
47	[64]	MBSBPP	x		x			x
48	[68]	SBSBPP		x		x		x			x
49	[111]	SBSBPP		x	x			x
50	[138]	MBSBPP		x			x	x		x
51	[139]	SBSBPP		x	x			x
52	[197]	SBSBPP		x		x		x
53	[198]	SBSBPP		x			x	x				x	x	x
54	[202]*	ODP		x		x		x		x	x
55	[166]	SBSBPP		x			x	x		x			x
56	[269]	ODP		x		x		x		x	x
57	[245]	MBSBPP		x			x	x		x			x
58	[246]	MBSBPP		x			x	x		x
59	[270]	SBSBPP	x			x		x		x
60	[271]	SBSBPP		x	x			x
61	[25]	SBSBPP		x		x		x							x
62	[30]	SBSBPP		x		x		x		x
63	[32]	SBSBPP		x	x			x							x
64	[41]	SBSBPP		x	x			x
65	[54]	SBSBPP		x	x			x					x
66	[69]	SBSBPP		x		x		x		x	x
67	[70]	SBSBPP		x		x		x
68	[78]	SBSBPP		x	x			x					x
69	[80]*	SBSBPP		x	x			x
70	[101]	MBSBPP		x	x			x
70	[101]	MBSBPP		x	x			x							x
71	[247]	MBSBPP		x	x			x
72	[132]	SBSBPP		x		x		x
73	[144]	SBSBPP		x	x			x
74	[210]	SBSBPP		x	x			x					x
75	[211]	SBSBPP		x	x			x
76	[231]	MBSBPP		x			x	x		x
77	[50]	SBSBPP		x	x			x
78	[251]	SBSBPP		x		x		x		x
78	[251]	ODP		x		x		x		x
79	[255]	SBSBPP		x		x		x
80	[13]	MBSBPP		x		x		x
81	[49]	SBSBPP		x		x		x
82	[262]	MBSBPP		x			x	x		x
83	[117]	SBSBPP		x		x			x							x
84	[57]	SBSBPP		x	x			x				x
85	[63]	SBSBPP		x		x		x		x			x
86	[88]	MBSBPP		x	x			x					x
87	[122]	SBSBPP		x	x			x
88	[165]	SBSBPP		x		x		x		x					x
89	[127]	MBSBPP		x		x		x			x
90	[180]	MBSBPP		x	x	x		x
91	[200]	SBSBPP		x	x				x				x
92	[220]	SBSBPP		x	x			x
93	[238]	SBSBPP		x		x		x
94	[249]	SBSBPP		x			x	x		x	x
95	[266]	SBSBPP		x	x			x							x
96	[264]	SBSBPP	x		x			x
97	[242]	SBSBPP		x	x			x
98	[141]	SBSBPP		x		x		x					x			x
99	[6]	MBSBPP		x		x	x	x
100	[256]	SBSBPP and MBSBPP		x	x	x		x
101	[27]	SBSBPP		x		x			x	x			x
102	[31]	SBSBPP		x		x		x
103	[35]	SBSBPP		x			x			x		x	x
104	[42]	SBSBPP		x			x			x		x	x
105	[47]	SBSBPP		x		x	x	x
106	[81]	ODP		x		x		x		x			x
107	[96]	SBSBPP		x		x		x	x	x
108	[98]	SBSBPP		x		x		x		x	x
109	[204]	SBSBPP		x			x	x							x
110	[140]	SBSBPP		x	x			x
111	[183]	MBSBPP		x	x			x
112	[192]	SBSBPP		x		x			x						x
113	[193]	MBSBPP		x			x	x
114	[209]	SBSBPP		x	x			x
115	[223]	SBSBPP		x	x			x					x
116	[230]	SBSBPP		x	x			x							x
117	[156]	SBSBPP		x	x			x
118	[12]	SBSBPP		x	x			x
119	[53]	MBSBPP		x		x		x		x	x
120	[79]	SBSBPP		x	x			x					x
121	[181]	SBSBPP		x		x	x	x		x	x
122	[151]	SBSBPP		x	x			x	x						x
123	[152]	SBSBPP		x		x		x							x
124	[20]	SBSBPP		x		x		x
125	[213]	SBSBPP		x		x		x
126	[161]	SBSBPP		x		x		x			x
127	[124]	MBSBPP		x	x			x
128	[252]	SBSBPP		x		x		x
129	[272]	SBSBPP		x		x	x	x
130	[147]	SBSBPP		x			x	x		x
131	[194]	MBSBPP		x			x	x
132	[265]	SBSBPP		x	x			x
133	[160]	SBSBPP		x	x			x
134	[118]	SBSBPP		x		x		x								x
135	[212]	SBSBPP		x	x			x
136	[18]	SBSBPP and MBSBPP		x	x			x
137	[224]	SBSBPP		x	x			x
138	[142]	SBSBPP		x			x	x				x		x
139	[233]	ODP and SBSBPP		x		x		x		x
140	[162]	SBSBPP		x		x		x					x
141	[46]	SBSBPP		x		x		x		x	x
142	[169]	SBSBPP		x		x		x		x	x
143	[195]	MBSBPP		x			x	x
144	[184]	SBSBPP		x	x			x							x
145	[119]	MBSBPP		x	x			x
146	[164]	SBSBPP		x			x	x		x		x		x
147	[225]	SBSBPP		x	x			x		x			x
148	[268]	SBSBPP		x		x	x	x
149	[257]	ODP and SBSBPP		x		x		x		x
150	[93]	MBSBPP	x		x			x							x
151	[100]	SBSBPP		x			x	x		x		x	x	x
152	[16]	SBSBPP	x			x		x
153	[5]	SBSBPP		x			x	x					x
154	[203]	ODP and MBSBPP		x		x		x		x
155	[66]	MBSBPP		x	x			x
156	[126]	SBSBPP		x			x	x
157	[208]			x		x	x	x
158	[237]	SBSBPP		x		x		x
159	[145]	ODP and SBSBPP		x		x		x			x
160	[196]	ODP		x		x			x		x
161	[153]	SBSBPP		x	x			x	x						x
162	[199]	SBSBPP		x	x			x							x
163	[259]	SBSBPP		x		x		x		x
164	[218]	SBSBPP		x		x		x		x	x
165	[227]*	ODP		x		x		x		x	x
166	[110]	SBSBPP		x	x			x
167	[4]			x	x				x						x
168	[10]	ODP		x		x		x					x
169	[120]	MBSBPP		x	x			x
170	[134]	ODP		x		x			x	x
171	[185]	SBSBPP		x	x			x							x
172	[201]	ODP		x		x		x			x
173	[232]	SBSBPP		x	x				x
174	[261]	SBSBPP and MBSBPP		x			x	x		x
175	[19]	SBSBPP		x	x			x				x
176	[24]	ODP		x		x		x
177	[55]	SBSBPP		x		x		x
178	[67]	SBSBPP		x		x	x	x
179	[85]	SBSBPP		x		x		x		x
180	[105]	SBSBPP		x	x				x
181	[112]	SBSBPP		x			x	x							x
182	[170]	SBSBPP		x		x			x
183	[187]	SBSBPP		x		x		x					x	x
184	[234]	SBSBPP		x	x			x					x
185	[48]	ODP		x		x		x		x
186	[56]	SBSBPP		x		x		x
187	[94]	SBSBPP	x	x	x			x							x
188	[135]	ODP		x		x			x
189	[214]	SBSBPP		x		x		x			x			x
190	[115]	ODP		x		x		x
191	[219]	SBSBPP		x		x		x
192	[44]	SBSBPP	x		x			x				x
193	[23]	MBSBPP		x		x		x
194	[36]	ODP		x		x		x		x	x
195	[226]	SBSBPP		x		x		x
196	[240]	SBSBPP		x		x		x
197	[21]	SBSBPP		x		x		x			x
198	[22]	SBSBPP		x	x			x							x
199	[136]	SBSBPP		x		x		x
200	[215]	MBSBPP		x		x		x
201	[106]	SBSBPP		x	x			x							x
202	[244]	SBSBPP		x	x			x
203	[173]	ODP and SBSBPP		x		x		x		x
204	[77]	SBSBPP		x			x	x						x
205	[137]	SBSBPP		x		x		x		x
206	[148]	MBSBPP		x	x			x
207	[254]	SBSBPP		x		x			x
208	[163]	SBSBPP		x		x		x
209	[188]	ODP		x		x		x
210	[158]	SBSBPP		x	x			x
211	[228]	SBSBPP		x	x			x
212	[37]	SBSBPP		x		x		x
213	[40]	SBSBPP		x		x		x
214	[174]	SBSBPP		x		x		x
215	[176]	SBSBPP		x			x	x
216	[175]*	SBSBPP		x		x		x		x	x
217	[155]	SBSBPP		x	x			x
218	[248]*	SBSBPP		x	x			x
219	[229]	SBSBPP		x	x			x
220	[76]	MBSBPP		x	x			x
221	[128]	SBSBPP		x		x		x		x
222	[150]	SBSBPP		x		x		x		x
223	[244]	SBSBPP		x			x	x		x		x		x
224	[39]	ODP		x		x		x
225	[113]	SBSBPP		x	x			x
226	[129]	SBSBPP		x		x		x		x
227	[178]	SBSBPP		x		x		x		x	x
228	[177]	SBSBPP		x		x		x
229	[236]	SBSBPP		x	x			x
230	[130]*	SBSBPP		x		x	x	x			x
231	[267]	MBSBPP	x		x			x
232	[17]	SBSBPP	x		x			x
233	[241]	SBSBPP		x		x		x		x
234	[116]	MBSBPP		x		x		x
235	[133]	ODP and SBSBPP		x		x		x		x
236	[189]	SBSBPP		x	x			x
237	[154]	MBSBPP	x		x			x
238	[29]	ODP		x		x		x
239	[99]	MBSBPP		x	x			x
240	[82]*	SBSBPP		x		x	x	x		x	x
241	[52]	SBSBPP		x		x		x
242	[26]	ODP and SBSBPP		x		x		x		x
243	[109]	ODP		x		x		x
244	[59]	ODP		x		x		x
245	[107]	SBSBPP		x			x	x					x
246	[60]	SBSBPP	x		x			x

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