doi: 10.3934/jimo.2022088
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

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, and College of Business, Faculty of Sciences of Sfax, University of Sfax, Sfax, Tunisia and Al Ain University, Abu Dhabi, UAE, Tunisia and United Arab Emirates

*Corresponding author: Salma Mezghani

Received  September 2021 Revised  March 2022 Early access June 2022

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.

Citation: Salma Mezghani, Boukthir Haddar, Habib Chabchoub. The evolution of rectangular bin packing problem — A review of research topics, applications, and cited papers. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022088
References:
[1]

M. Abdel-BassetG. ManogaranL Abdel-Fatah and S. Mirjalili, An improved nature inspired meta-heuristic algorithm for 1-D bin packing problems, Personal and Ubiquitous Computing, 22 (2018), 1117-1132. 

[2]

A. C. Adamuthea and T. R. Nitave, Optimizing large scale bin packing problem with hybrid harmony search algorithm, International Journal of Industrial Engineering Computations, 12 (2021), 205-220. 

[3]

A. Aggoun, A. Rhiat, A. and F. Fages, Panorama of reallife applications in logistics embedding bin packing optimization algorithms, Robotics and Cloud Computing Technologies, The 3rd IEEE International Conference on Logistics Operations Management Gol'16, 2016, 1–4.

[4]

S. Agrawal, S. K. Bose and S. Sundarrajan, Grouping genetic algorithm for solving the server consolidation problem with conflicts, Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation, 2009, 1–8.

[5]

A. Almeida and M.B. Figueiredo, A particular approach for the three-dimensional packing problem with additional constraints, Computers and Operations Research, 37 (2010), 1968-1976.  doi: 10.1016/j.cor.2010.01.010.

[6]

R. Alvarez-ValdesF. Parreño and J.M. Tamarit, A GRASP/Path relinking algorithm for two- and three-dimensional multiple bin-size bin packing problems, Computers and Operations Research, 40 (2013), 3081-3090.  doi: 10.1016/j.cor.2012.03.016.

[7]

K. A. Amara and B. Djebbar, Bee colony optimization applied to the bin packing problem, International Journal of Computer and Information Engineering, 11 (2017), 275-279. 

[8]

C. Arbib and F. Marinelli, Maximum lateness minimization in one-dimensional bin packing, Omega, 68 (2016), 1-9. 

[9]

S. AstaE. özcan and A.J. Parkes, CHAMP: Creating heuristics via many parameters for online bin packing, Expert Systems with Applications, 63 (2016), 208-221. 

[10]

J. Augustine, S. Banerjee and S. Irani, Strip packing with precedence constraints and strip packing with release times, Theoretical Computer Science, 410 (2009), 3792–3803. doi: 10.1016/j.tcs.2009.05.024.

[11]

N. AydinI. Muter and Ş. İlker Birbil, Multi-objective temporal bin packing problem: An application in cloud computing, Computers & Operations Research, 121 (2020), 104-959.  doi: 10.1016/j.cor.2020.104959.

[12]

M. AyobM. Nazri and Y. Fei, Local search heuristics for the one dimensional bin packing problems, Journal of Applied Sciences, 6 (2013), 919-923. 

[13]

M. M. BaldiT. G. CrainicG. Perboli and R. Tadei, Branch-and-price and beam search algorithms for the variable cost and size bin packing problem with optional items, Annals of Operations Research, 222 (2014), 125-141.  doi: 10.1007/s10479-012-1283-2.

[14]

J. BaloghJ. BékésiG. DósaL. Epstein and A. Levin, Online bin packing with cardinality constraints resolved, Journal of Computer and System Sciences, 112 (2020), 34-49.  doi: 10.1016/j.jcss.2020.03.002.

[15]

J. BaloghJ. BékésiG. DósaJ. Sgall and R. van Stee, The optimal absolute ratio for online bin packing, Journal of Computer and System Sciences, 102 (2019), 1-17.  doi: 10.1016/j.jcss.2018.11.005.

[16]

J. Balogh, J. Békési and G. Galambos, On a multidimensional semi-on-line bin packing problem, In Proceedings of the eighth International Conference on Applied Informatics Eger, Hungary, January 27–30, 2010,191–197.

[17]

J. Balogh and J. Békési, An improved lower bound for the bin packing, Discrete Applied Mathematics, 66 (1996), 1-6. 

[18]

J. Bang-Jensen and R. Larsen, Efficient algorithms for real-life instances of the variable size bin packing problem, Computers and Operations Research, 39 (2012), 2848-2857. 

[19]

N. BansalZ. Liu and A. Sankar, Bin-packing with fragile objects and frequency allocation in cellular networks, Wireless Networks, 15 (2009), 821-830. 

[20]

N. Bansal and M. Sviridenko, Two-dimensional bin packing with one dimensional resource augmentation, Discrete Optimization, 4 (2007), 143-153.  doi: 10.1016/j.disopt.2006.09.001.

[21]

N. Bansal, A. Lodi and M. Sviridenko, A tale of two-dimensional bin packing, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, 2005,657–666.

[22]

C. Basnet and J. Wilson, Heuristics for determining the number of warehouses for storing non-compatible products, International Transactions in Operational Research, 12 (2005), 527-538.  doi: 10.1111/j.1475-3995.2005.00523.x.

[23]

B. Beisiegel, J. Kallrath, Y. Kochetov and A. Rudnev, Simulated annealing based algorithm for the 2D bin packing problem with impurities, Operations Research Proceedings 2005 Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), Bremen, (September 7–9, 2005), 1–6.

[24]

G. BelovG. Scheithauer and and E.A. Mukhacheva, One-dimensional heuristics adapted for two-dimensional rectangular strip packing, Journal of the Operational Research Society, 59 (2008), 823-832. 

[25]

M. Benazouz and J. M. Faure, Safety-level aware bin-packing approach for control functions assignment, In IFAC Proceedings Volumes (IFAC-PapersOnline), 48 (2015), 507-512. 

[26]

B. E. Bengtsson, Packing rectangular pieces–a heuristic approach, The Computer Journal, 25 (1982), 253-257.  doi: 10.1093/comjnl/25.3.353.

[27]

J.A. BennellL. Soon Lee and and C.N. Potts, A genetic algorithm for two-dimensional bin packing with due date, International Journal of Production Economics, 145 (2013), 547-560. 

[28]

B. Messaoud, C. Chu and M. L. Espinouse, An approach to solve cutting stock sheets, In Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics, (2004), 5109–5113.

[29]

J.O. Berkey and and P.Y. Wang, Two-dimensional finite bin-packing algorithms, Journal of the Operational Research Society, 38 (1987), 423-429. 

[30]

M. BeyazT. Dokeroglu and A. Cosar, Robust hyper-heuristic algorithms for the offline oriented/non-oriented 2D bin packing problems, Applied Soft Computing, 36 (2015), 236-245. 

[31]

C. Bllum and V. Schmid, Solving the 2D bin packing problem by means of a hybrid evolutionary algorithm, Procedia Computer Science, 18 (2013), 899-908. 

[32]

A. Bòdis, Bin packing with directed stackability conflicts, Acta Universitatis Sapientiae, Informatica, 7 (2015), 31-57. 

[33]

P. Boominathan and S. Rajkumar, Bin packing problems: Comparative analysis of heuristic, International Journal of Pharmacy and Technology, 8 (2016), 13350-13319. 

[34]

I. Borgulya, A hybrid evolutionary algorithm for the offline bin packing problem, Central European Journal of Operations Research, 29 (2021), 425-445.  doi: 10.1007/s10100-020-00695-5.

[35]

A. Bortfeldt and J. Homberger, Packing first, routing second-a heuristic for the vehicle routing and loading problem, Computers and Operations Research, 40 (2013), 873-885. 

[36]

A. Bortfeldt, A genetic algorithm for the two-dimensional strip packing problem with rectangular pieces, European Journal of Operational Research, 172 (2006), 814-837.  doi: 10.1016/j.ejor.2004.11.016.

[37]

M. A. Boschetti and A. Mingozzi, The two-dimensional finite bin packing problem. Part I: New lower bounds for the oriented case, Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 1 (2003), 27-42.  doi: 10.1007/s10288-002-0005-z.

[38]

M. Buljubašić and M. Vasquez, Consistent neighborhood search for one-dimensional bin packing and two-dimensional vector packing, Computers and Operations Research, 76 (2016), 12-21.  doi: 10.1016/j.cor.2016.06.009.

[39]

A. R. Callaghan, A. R. Nair and K. E. Lewis, An extension of the orthogonal packing, In Proceedings of DETC'99: 1999 ASME Design Engineering Technical Conferences, Las Vegas, Nevada, (September 12-15 1999), 1–7.

[40]

A. Caprara, Packing 2-dimensional bins in harmony, In The $43^{rd}$ Annual IEEE Symposium on Foundations of Computer Science, Proceedings, (2002), 490–499. doi: 10.1287/moor.1070.0289.

[41]

M. CasazzaA. Ceselli and In formatica, Exactly solving packing problems with fragmentation, Computers and Operation Research, 75 (2015), 202-213.  doi: 10.1016/j.cor.2016.06.007.

[42]

S. CeschiaA. Schaerf and T. Stützle, Local search techniques for a routing-packing problem, Computers and Industrial Engineering, 66 (2013), 1138-1149. 

[43]

T. ChabotR. LahyaniL. Coelho and J. Renaud, Order picking problems under weight, fragility and category constraints, International Journal of Production Research, 55 (2017), 6361-6379. 

[44]

W.T. ChanF. Y.-L.Ch inD. ZhangG. Ye and Y. Zhang, Online bin packing of fragile objects with application in cellular networks, Journal of Combinatorial Optimization, 14 (2007), 427-435.  doi: 10.1007/s10878-007-9043-y.

[45]

M. Chanaleä and E. Ezugwu, Metaheuristic algorithms for one-dimensional bin-packing problems: A survey of recent advances and applications, Journal of Intelligent Systems, 30 (2021), 636-663. 

[46]

C. Charalambous and K. Fleszar, A constructive bin-oriented heuristic for the two-dimensional bin packing problem with guillotine cuts, Computers and Operations Research, 38 (2011), 1443-1451. 

[47]

A. V. Chekanin, Efficient algorithms for orthogonal packing problems, Computational Mathematics and Mathematical Physics, 53 (2013), 1457-1465.  doi: 10.1134/S0965542513100047.

[48]

M. Chen and W. Huang, A two-level search algorithm for 2D rectangular packing problem, Computers and Industrial Engineering, 53 (2007), 123-136. 

[49]

R. Christopher and P. Nelishia, Combining development and evolution case study: One dimensional bin-packing, In Proceedings of the seventh International Joint Conference on Computational Intelligence (IJCCI 2015), (2015), 188–195.

[50]

H.I. ChristensenA. KhanS. Pokutta and P. Tetali, Approximation and online algorithms for multidimensional bin packing: A survey, Computer Science Review, 24 (2017), 63-79.  doi: 10.1016/j.cosrev.2016.12.001.

[51]

H. I. ChristensenA. KhanS. Pokutta and P. Tetali, Approximation and online algorithms for multidimensional bin packing: A survey, Computer Science Review, 24 (2017), 63-79.  doi: 10.1016/j.cosrev.2016.12.001.

[52]

F. R. K. ChungM. R. Garey and D. S. Johnson, On packing two-dimensional bins, SIAM Journal on Algebraic Discrete Methods, 3 (1982), 66-76.  doi: 10.1137/0603007.

[53]

A. M. Chwatal and S. Pirkwieser, Solving the two-dimensional bin-packing problem with variable bin sizes by greedy randomized adaptive search procedures and variable neighborhood search, In International Conference on Computer Aided Systems Theory. Springer, Berlin, Heidelberg, (2011), 456–463.

[54]

W. Ciscal-TerryM. D. Amico and M. Iori, Bin Packing Problem With General Precedence Constraints, IFAC-PapersOnLine, 48 (2015), 2027-2029. 

[55]

F. ClautiauxA. JougletJ. Carlier and A. Moukrim, A new constraint programming approach for the orthogonal packing problem, Computers and Operations Research, 35 (2008), 944-959.  doi: 10.1016/j.cor.2006.05.012.

[56]

F. ClautiauxJ. Carlier and A. Moukrim, A new exact method for the two-dimensional bin-packing problem with fixed orientation, Operations Research Letters, 35 (2007), 357-364.  doi: 10.1016/j.orl.2006.06.007.

[57]

F. ClautiauxM. Dell'AmicoM. Iori and A. Khanafer, Lower and upper bounds for the bin packing problem with fragile objects, Discrete Applied Mathematics, 163(PART 1) (2014), 73-86.  doi: 10.1016/j.dam.2012.04.010.

[58]

E. G. Coffman, M. R. Garey and D. S. Johnson, Approximation algorithms for bin packing: A survey, in Approximation Algorithms, Ed. by D. Hochbaum (PWS Publishing Company), (1996), 46–93.

[59]

E. G. CoffmanM. R. GareyD. S. Johnson and R. E. Tarjan, Performance bounds for level-oriented two-dimensional packing algorithms, SIAM Journal on Computing, 9 (1980), 808-827.  doi: 10.1137/0209062.

[60]

E. G. CoffmanK. SoM. Hofri and A. C. Yao, A stochastic model of bin-packing, Information and Control, 44 (1980), 105-115.  doi: 10.1016/S0019-9958(80)90050-9.

[61]

I. CorreiaL. Gouveia and F. Saldanha-da-Gama, Solving the variable size bin packing problem with discretized formulations, Computers and Operations Research, 35 (2008), 2103-13.  doi: 10.1016/j.cor.2006.10.014.

[62]

G. CostaM. DelormeM. IoriE. Malaguti and S. Martello, Training software for orthogonal packing problems, Computers and Industrial Engineering, 111 (2017), 139-147. 

[63]

J.-F. CôtéM. Gendreau and J.-Y. Potvin, An exact algorithm for the two-dimensional orthogonal packing problem with unloading constraints, Operations Research, 62 (2014), 1126-1141.  doi: 10.1287/opre.2014.1307.

[64]

T. G. CrainicL. GobbatoG. Perboli and W. Rei, Logistics capacity planning: A stochastic bin packing formulation and a progressive hedging meta-heuristic, European Journal of Operational Research, 253 (2016), 404-417.  doi: 10.1016/j.ejor.2016.02.040.

[65]

T. G. CrainicL. GobbatoG. PerboliW. ReiJ. P. Watson and D. L. Woodruff, Bin packing problems with uncertainty on item characteristics: An application to capacity planning in logistics, Procedia Social and Behavioral Sciences, 111 (2014), 654-662.  doi: 10.1016/j.ejor.2016.02.040.

[66]

T. G. Crainic, G. Perboli, W. Rei and R. Tadei, Efficient heuristics for the variable size bin packing problem with fixed costs, Cirrelt Tech. Rep., 18 (2010).

[67]

T. G. CrainicG. Perboli and R. Tadei, Extreme point-based heuristics for three-dimensional bin packing, INFORMS Journal on Computing, 20 (2008), 368-384.  doi: 10.1287/ijoc.1070.0250.

[68]

Y. CuiY. Yao and Y. P. Cui, Hybrid approach for the two-dimensional bin packing problem with two-staged patterns, International Transactions in Operational Research, 23 (2016), 539-549.  doi: 10.1111/itor.12188.

[69]

Y. P. Cui and and T. Tang, Sequential heuristic for the two-dimensional bin-packing problem, European Journal of Operational Research, 240 (2015), 43-53.  doi: 10.1016/j.ejor.2014.06.032.

[70]

N. DahmaniS. Krichen and D. Ghazouani, A variable neighborhood descent approach for the two-dimensional bin packing problem, Electronic Notes in Discrete Mathematics, 47 (2015), 117-124.  doi: 10.1016/j.endm.2014.11.016.

[71]

K. Daoden and T. Thaiupathump, Applying shuffled frog leaping algorithm and bottom left fill algorithm in rectangular packing problem, In $7^{th}$ IEEE International Conference on Electronics Information and Emergency Communication (ICEIEC). IEEE, (2017), 136–139.

[72]

S. K. Das, M. Pervin, S. K. Roy and G. W. Weber, Multi-objective solid transportation-location problem with variable carbon emission in inventory management: A hybrid approach, Annals of Operations Research, (2021), 1–27.

[73]

S. K. DasS. K. Roy and G. W. Weber, Heuristic approaches for solid transportation-p-facility location problem, Central European Journal of Operations Research, 28 (2019), 939-961.  doi: 10.1007/s10100-019-00610-7.

[74]

S. K. Das and S. K. Roy, Effect of variable carbon emission in a multi-objective transportation-p-facility location problem under neutrosophic environment, Computers and Industrial Engineering, 132 (2019), 311-324. 

[75]

S. K. DasS. K. Roy and G. W. Weber, An exact and a heuristic approach for the transportation-p-facility location problem, Computational Management Science, 17 (2020), 389-407.  doi: 10.1007/s10287-020-00363-8.

[76]

M. DawandeJ. Kalagnanam and J. Sethuraman, Variable sized bin packing With color constraints, Electronic Notes in Discrete Mathematics, 7 (2001), 154-157. 

[77]

J. L. De Castro SilvaN. Y. Soma and N. Maculan, A greedy search for the three-dimensional bin packing problem: The packing static stability case, International Transactions in Operational Research, 10 (2003), 141-153.  doi: 10.1111/1475-3995.00400.

[78]

M. Dell'Amico, J. C. D. Díaz and M. Iori, The bin packing problem with precedence constraints, $15^{th}$ IFAC Symposium on Information Control in Manufacturing, 60 (2015), 1491–1504. doi: 10.1287/opre.1120.1109.

[79]

M. Dell'AmicoJ. C. D. Díaz and M. Iori, The bin packing problem with precedence constraints, Operations Research, 60 (2012), 1491-1504.  doi: 10.1287/opre.1120.1109.

[80]

M. Delorme, M. Iori and S. Martello, Bin packing and cutting stock problems: Mathematical models and exact algorithms, AIRO 2014 Conference, (2015). doi: 10.1016/j.ejor.2016.04.030.

[81]

T. A. De Queiroz and F. K. Miyazawa, Two-dimensional strip packing problem with load balancing, load bearing and multi-drop constraints, International Journal of Production Economics, 145 (2013), 511-530.  doi: 10.1016/j.dam.2013.08.019.

[82]

W. B. Dowsland, Two and three dimensional packing problems and solution methods, Operational Research Society of New Zeland, 13 (1985), 1-18. 

[83]

H. Dyckhoff, A typology of cutting and packing problems, European Journal of Operational Research, 4 (1990), 145-159.  doi: 10.1016/0377-2217(90)90350-K.

[84]

A. Ekici, Variable-sized bin packing problem with conflicts and item fragmentation, Computers and Industrial Engineering, 163 (2022), 107-844.  doi: 10.1016/j.cor.2020.105113.

[85]

J. El HayekA. Moukrim and S. Negre, New resolution algorithm and pretreatments for the two-dimensional bin-packing problem, Computers and Operations Research, 35 (2008), 3184-3201. 

[86]

S. ElhedhliF. Gzara and Y. F. Yan, A MIP-based slicing heuristic for three-dimensional bin packing, Optimization Letters, 11 (2017), 1547-1563.  doi: 10.1007/s11590-017-1154-5.

[87]

S. ElhedhliL. LiM Gzara and and J. Naoum-Sawaya, A branch-and-price algorithm for the bin packing problem with conflicts, INFORMS Journal on Computing, 23 (2011), 404-415.  doi: 10.1287/ijoc.1100.0406.

[88]

A. Elloumi, H. Kamoun, B. Jarboui and A. Dammak, The classroom assignment problem: Complexity, size reduction and heuristics, Applied Soft Computing Journal, 14(PART C) (2014), 677–686.

[89]

L. Epstein and T. Erlebach, Approximation and online algorithms, Lecture Notes in Computer Science, (2018), 327–347. doi: 10.1007/978-3-030-04693-4.

[90]

L. Epstein and A. Levin, An AFPTAS for variable sized bin packing with general activation costs, Journal of Computer and System Sciences, 84 (2017), 79-96.  doi: 10.1016/j.jcss.2016.07.007.

[91]

L. EpsteinL. M. Favrholdt and J. S. Kohrt, Comparing online algorithms for bin packing problems, Journal of Scheduling, 15 (2012), 13-21.  doi: 10.1007/s10951-009-0129-5.

[92]

L. EpsteinL. M. Favrholdt and A. Levin, Online variable-sized bin packing with conflicts, Discrete Optimization, 8 (2011), 333-343.  doi: 10.1016/j.disopt.2010.11.001.

[93]

L. Epstein and and M. Levy, Dynamic multi-dimensional bin packing, Journal of Discrete Algorithms, 8 (2010), 356-372.  doi: 10.1016/j.jda.2010.07.002.

[94]

L. Epstein and A. Levin, On bin packing with conflicts, SIAM Journal on Optimization, 19 (2008), 1270-1298.  doi: 10.1137/060666329.

[95]

S. ErbayrakV. Özkır and U. Mahir Yıldırım, Multi-objective 3D bin packing problem with load balance and product family concerns, Computers and Industrial Engineering, 159 (2021), 107-518. 

[96]

A. FernàndezC. GilR. Banos and M. G. Montoya, A parallel multi-objective algorithm for two-dimensional bin packing with rotations and load balancing, Expert Systems with Applications, 40 (2013), 5169-5180. 

[97]

H. Firat and N. Alpaslan, An effective approach to the two-dimensional rectangular packing problem in the manufacturing industry, Computers and Industrial Engineering, 148 (2020), 106-687. 

[98]

K. Fleszar, Three insertion heuristics and a justification improvement heuristic for two-dimensional bin packing with guillotine cuts, Computers and Operations Research, 40 (2013), 463-474. 

[99]

D. K. Friesen and M. A. Langston, Variable sized bin packing, SIAM Journal on Computing, 15 (1986), 222-230.  doi: 10.1007/BF01934179.

[100]

G. FuellererR. F. Doerner and M. Iori, Metaheuristics for vehicle routing problems with three-dimensional loading constraints, European Journal of Operational Research, 201 (2010), 751-759. 

[101]

M. Gabay and S. Zaourar, Vector bin packing with heterogeneous bins: Application to the machine reassignment problem, Annals of Operations Research, 242 (2016), 161-194.  doi: 10.1007/s10479-015-1973-7.

[102]

M. GajdaA. TrivellaR. Mansini and D. Pisinger, An optimization approach for a complex real-life container loading problem, Omega, 107 (2022), 102-559. 

[103]

J. Gardeyn and T. Wauters, A goal-driven ruin and recreate heuristic for the 2D variable-sized bin packing problem with guillotine constraints, European Journal of Operational Research, 301 (2022), 432-444.  doi: 10.1016/j.ejor.2021.11.031.

[104]

M. R. GareyR. L. Graham and D. S. Johnson, Resource constrained scheduling as generalized bin packing, Journal of Combinatorial, series A, 21 (1976), 257-298.  doi: 10.1016/0097-3165(76)90001-7.

[105]

M. J. Geiger, Bin packing under multiple objectives - a heuristic approximation approach, In The Fourth International Conference on Evolutionary Multi Criterion Optimization, (2008), 53–56.

[106]

M. GendreauG. Laporte and F. Semet, Heuristics and lower bounds for the bin packing problem with conflicts, Computers and Operations Research, 31 (2004), 347-358.  doi: 10.1016/S0305-0548(02)00195-8.

[107]

J. A. George and D. F. Robinson, A heuristic for packing boxes into a container, Computers and Operations Research, 7 (1980), 147-156. 

[108]

N. Goldberg and S. Karhi, Online packing of arbitrary sized items into designated and multipurpose bins, European Journal of Operational Research, 279 (2019), 54-67.  doi: 10.1016/j.ejor.2019.05.029.

[109]

I. Golan, Performance bounds for orthogonal oriented two-dimensional packing algorithms, SIAM Journal on Computing, 10 (1981), 571-583.  doi: 10.1137/0210042.

[110]

P. Gomez-Meneses and M. Randall, A hybrid extremal optimisation approach for the bin packing problem, In Artificial Life: Borrowing from Biology, Proceedings, (2009), 242–251.

[111]

A. Grange, I. Kacem and S. Martin, Algorithms for the pagination problem, a bin packing with overlapping items, preprint, arXiv: 1605.00558, (2016).

[112]

R. Gupta, S. K. Bose, S. Sundarrajan, M. Chebiyam and A. Chakrabarti, A two stage heuristic algorithm for solving the server consolidation problem with item-item and bin-item incompatibility constraints, Proceedings - 2008 IEEE International Conference on Services Computing, SCC 2008, 2, 2008, 39–46.

[113]

J. N. D. Gupta and J. C. Ho, New heuristic algorithm for the one-dimensional bin-packing problem, Production Planning and Control, 10 (1999), 598-603. 

[114]

F. GzaraS. Elhedhli and B. C. Yildiz, The pallet loading problem: Three-dimensional bin packing with practical constraints, European Journal of Operational Research, 287 (2020), 1062-1074.  doi: 10.1016/j.ejor.2020.04.053.

[115]

E. Hadjiconstantinou and and M. Iori, A hybrid genetic algorithm for the two-dimensional single large object placement problem, European Journal of Operational Research, 183 (2007), 1150-1166.  doi: 10.1016/j.ejor.2005.11.061.

[116]

B. T. HanG. Diehr and and J. S. Cook, Multiple-type, two-dimensional bin packing problems: Applications and algorithms, Annals of Operations Research, 50 (1994), 239-261.  doi: 10.1007/BF02085642.

[117]

K. Hamdi-DhaouiN. Labadie and A. Yalaoui, The bi-objective two-dimensional loading vehicle routing problem with partial conflicts, International Journal of Production Research, 52 (2014), 5565-5582. 

[118]

K. Hamdi-DhaouiN. Labadie and A. Yalaoui, Algorithms for the two dimensional bin packing problem with partial conflicts, RAIRO - Operations Research, 46 (2012), 41-62.  doi: 10.1051/ro/2012007.

[119]

M. Haouari and M. Serairi, Relaxations and exact solution of the variable sized bin packing problem, Computational Optimization and Applications, 48 (2011), 345-368.  doi: 10.1007/s10589-009-9276-z.

[120]

M. Haouari and M. Serairi, Heuristics for the variable sized bin-packing problem, Computers and Operations Research, 36 (2009), 2877-2884.  doi: 10.1016/j.cor.2008.12.016.

[121]

Y. Harrath, A Three-Stage Layer-Based Heuristic to Solve the 3D Bin-Packing Problem under Balancing Constraint, Journal of King Saud University - Computer and Information Sciences, 2021.

[122]

N. Hashim, F. Zulkipli, S. Januri and S. S. R. Shariff, An alternative heuristics for bin packing problem, Proceedings of the 2014 International Conference on Industrial Engineering and Operations Management Bali, Indonesia, (January 7–9 2014), 1560–1568.

[123]

K. Heßler, S. Irnich, T. Kreiter and U. Pferschy, Bin packing with lexicographic objectives for loading weight- and volume-constrained trucks in a direct-shipping system, OR Spectrum, (2021), 1–43. doi: 10.1007/s00291-021-00628-x.

[124]

V. HemmelmayrV. Schmid and C. Blum, Variable neighbourhood search for the variable sized bin packing problem, Computers and Operations Research, 39 (2012), 1097-1108.  doi: 10.1016/j.cor.2011.07.003.

[125]

J. Herrera-FranklinA. Rosete and M. García-Borroto, A fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing, Inteligencia Artificial, 24 (2021), 71-89. 

[126]

M. HifiI. KacemS. Nègre and L. Wu, A linear programming approach for the three-dimensional bin-packing problem, Electronic Notes in Discrete Mathematics, 36(C) (2010), 993-1000. 

[127]

S. HongD. ZhangH. C. LauX. Zeng and Y.W. Si, A hybrid heuristic algorithm for the 2D variable-sized bin packing problem, European Journal of Operational Research, 238 (2014), 95-103.  doi: 10.1016/j.ejor.2014.03.049.

[128]

E. Hopper and B. C. H. Turton, Empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem, European Journal of Operational Research, 128 (2001), 34-57. 

[129]

E. Hopper and B. Turton, A genetic algorithm for a 2D industrial packing problem, Computers and Industrial Engineering, 37 (1999), 375-378. 

[130]

E. Hopper and B. Turton, Application of genetic algorithms to packing problems–A review, In Proceedings of the 2nd On-line World Conference on Soft Computing in Engineering Design and Manufacturing, Springer Verlag, London, (1997), 279–288.

[131]

E. Hopper and B. Turton, Empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem, European Journal of Operational Research, 128 (2001), 34-57. 

[132]

Q. HuA. Lim and W. Zhu, The two-dimensional vector packing problem with piecewise linear cost function, Omega (United Kingdom), 50 (2015), 43-53. 

[133]

S.-M. Hwang, C.-Y. Kao and J. T. Horng, On solving rectangle bin packing problems using genetic algorithms, In Systems, Man, and Cybernetics, Humans, Information and Technology, 1994 IEEE International Conference on IEEE, (1994), 1583–1590. doi: 10.1109/21.310541.

[134]

S. Illich and L. While, Multi-objective strip packing, Journal of Advanced Research in Evolutionary Algorithms, 1(April) (2009), 1-26. 

[135]

S. Illich, L. While and L. Barone, Multi-objective strip packing using an evolutionary algorithm, IEEE Congress on Evolutionary Computation, CEC 2007, (2007), 4207–4214.

[136]

S. ImahoriM. Yagiura and T. Ibaraki, Improved local search algorithms for the rectangle packing problem with general spatial costs, European Journal of Operational Research, 167 (2005), 48-67.  doi: 10.1016/j.ejor.2004.02.020.

[137]

S. ImahoriM. Yagiura and T. Ibaraki, Local search algorithms for the rectangle packing problem, Mathematical Programming, 3 (2003), 543-569.  doi: 10.1007/s10107-003-0427-1.

[138]

H. IwasawaY. HuH. Hashimoto and S. Imahori, A heuristic algorithm for the container loading problem with complex loading constraints, Journal of Advanced Mechanical Design, Systems, and Manufacturing, 10 (2016), 1-12. 

[139]

K. Jansen and K-M. Klein, About the structure of the integer cone and its application to bin packing, Mathematics of Operations Research, 45.4 (2020), 1498-1511.  doi: 10.1287/moor.2019.1040.

[140]

K. JansenS. KratschD. Marx and I. Schlotter, Bin packing with fixed number of bins revisited, Journal of Computer and System Sciences, 79 (2013), 39-49.  doi: 10.1016/j.jcss.2012.04.004.

[141]

J JerstichelP. De CausmaeckerF. C. R. Spieksma and G. Vanden Berghe, Exact and heuristic methods for placing ships in locks, European Journal of Operational Research, 235 (2014), 387-398.  doi: 10.1016/j.ejor.2013.06.045.

[142]

L. JunqueiraR. Morabito and D. S. Yamashita, Three-dimensional container loading models with cargo stability and load bearing constraints, Computers and Operations Research, 39 (2012), 74-85.  doi: 10.1016/j.cor.2010.07.017.

[143]

J. Jylänki, A thousand ways to pack the bin-a practical approach to two-dimensional rectangle bin packing, retrived from http://clb.demon.fi/files/RectangleBinPack.pdf, 2010.

[144]

M. A. Kaaouache and S. Bouamama, Solving bin packing problem with a hybrid genetic algorithm for VM placement in cloud, Procedia Computer Science, 60 (2015), 1061-1069. 

[145]

I. Kacem and A. Bekrar, An exact method for the 2d guillotine strip packing problem, Advances in Operations Research, 2009 (2009), 1-20. 

[146]

L. KacprzakJ. Rudy and D. Żelazny, Multi-criteria 3-dimension bin packing problem, Research in Logistics and Production, 5 (2015), 85-94. 

[147]

K. KangI. Moon and H. Wang, A hybrid genetic algorithm with a new packing strategy for the three-dimensional bin packing problem, Applied Mathematics and Computation, 219 (2012), 1287-1299.  doi: 10.1016/j.amc.2012.07.036.

[148]

J. Kang and S. Park, Algorithms for the variable sized bin packing problem, European Journal of Operational Research, 147 (2003), 365-372.  doi: 10.1016/S0377-2217(02)00247-3.

[149]

L. V. Kantorovich, Mathematical methods of organizing and planning production, Management Science, 6 (1960) 363–422. doi: 10.1287/mnsc.6.4.366.

[150]

G. CaKa rloff and H. Y. Rabani, An improved approximation algorithm for two-dimensional bin packing, Journal of Computer and System Sciences, 574 (2000), 564-574. 

[151]

A. KhanaferF. Clautiaux and E. G. Talbi, Tree-decomposition based heuristics for the two-dimensional bin packing problem with conflicts, Computers and Operations Research, 39 (2012), 54-63.  doi: 10.1016/j.cor.2010.07.009.

[152]

A. KhanaferF. Clautiaux and E. G. Talbi, The min-conflict packing problem, Computers and Operations Research, 39 (2012), 2122-2132.  doi: 10.1016/j.cor.2011.10.021.

[153]

A. KhanaferF. Clautiaux and E. G. Talbi, New lower bounds for bin packing problems with conflicts, European Journal of Operational Research, 206 (2010), 281-288.  doi: 10.1016/j.ejor.2010.01.037.

[154]

N.G. Kinnersley and M. Langston, Online variable-sized bin packing, Discrete Applied Mathematics, 22 (1989), 143-148.  doi: 10.1016/0166-218X(88)90089-3.

[155]

R. Korf, A new algorithm for optimal bin packing, Aaai/Iaai, (2002), 731–736.

[156]

R. KorfM. D. Moffitt and M. E. Pollack, Optimal rectangle packing, Annals of Operations Research, 179 (2008), 261-295.  doi: 10.1007/s10479-008-0463-6.

[157]

T. Kucukyilmaza and H. E. Kiziloz, Cooperative parallel grouping genetic algorithm for the one-dimensional bin packing problem, Computers and Industrial Engineering, 125 (2018), 157-170. 

[158]

S. Kumar, V. Rao and D. Tirupati, A heuristic procedure for one dimensional bin packing problem with additional constraints, IIMA Working Papers from Indian Institute of Management Ahmedabad, Research and Publication Department, No WP2003-11-02, (2003).

[159]

A. Laurent and N. Klement, Bin packing problem with priorities and incompatibilities using PSO: Application in a health care community, IFAC PapersOnLine, 52 (2019), 2596-2601. 

[160]

A. Layeb and S. R. Boussalia, A novel quantum inspired cuckoo search algorithm for bin packing problem, International Journal of Information Technology and Computer Science, 4 (2012), 58-67. 

[161]

J. LeeB. Kim and A. L. Johnson, 3 A two-dimensional bin packing problem with size changeable items for the production of wind turbine flanges in the open die forging industry, IIE Transactions, 45 (2012), 1332-1344. 

[162]

S.C.H. LeungX. ZhouD. Zhang and J. Zheng, Extended guided tabu search and a new packing algorithm for the two-dimensional loading vehicle routing problem, Computers and Operations Research, 38 (2011), 205-215.  doi: 10.1016/j.cor.2010.04.013.

[163]

T. W. LeungC. K. Chan and M. D. Troutt, Application of a mixed simulated annealing-genetic algorithm heuristic for the two-dimensional orthogonal packing problem, European Journal of Operational Research, 145 (2003), 530-542.  doi: 10.1016/S0377-2217(02)00218-7.

[164]

R. LewisX. SongK. Dowsland and J. Thompson, An investigation into two bin packing problems with ordering and orientation implications, European Journal of Operational Research, 213 (2011), 52-65.  doi: 10.1016/j.ejor.2011.03.016.

[165]

K. LiH. LiuY. Wu and X. Xu, A two-dimensional bin-packing problem with conflict penalties, International Journal of Production Research, 52 (2014), 7223-7238. 

[166]

C. LinJ. R. KangW. Y. Liu and C. C. Li, On two-door three-dimensional container packing problem under home delivery service, Journal of Industrial and Production Engineering, 33 (2016), 205-2014. 

[167]

Q. LiuH. ChengT. TianY. WangJ. LengR. Zhao and L. Wei, Algorithms for the variable-sized bin packing problem with time windows, Computers and Industrial Engineering, 155 (2021), 107-175.  doi: 10.1137/S009753979834669X.

[168]

W. LiuT. Deng and J. Li, Product packing and stacking under uncertainty: A robust approach, European Journal of Operational Research, 277 (2019), 903-917.  doi: 10.1016/j.ejor.2019.03.040.

[169]

Y. LiuC. Chu and K. Wang, A new heuristic algorithm for a class of two-dimensional bin-packing problems, International Journal of Advanced Manufacturing Technology, 57 (2011), 1235-1244. 

[170]

D. S. LiuK. C. TanS. Y. HuangC. K. Goh and W. K. Ho, On solving multiobjective bin packing problems using evolutionary particle swarm optimization, European Journal of operational Research, 190 (2008), 357-382.  doi: 10.1016/j.ejor.2007.06.032.

[171]

F. O. LuizS. I. RenanB. C. LuísaM. LeandroE. M. FabioM. Gabriel and B. C. Claudio, A variable neighborhood search algorithm for the bin packing problem with compatible categories, Expert Systems with Applications, 124 (2019), 209-225. 

[172]

A. LodiM. Monaci and E. Pietrobuoni, Partial enumeration algorithms for two-dimensional bin packing problem with guillotine constraints, Discrete Applied Mathematics, 217 (2017), 40-47.  doi: 10.1016/j.dam.2015.09.012.

[173]

A. LodiS. Martello and D. Vigo, Models and bounds for two-dimensional level packing problems, Journal of Combinatorial Optimization, 8 (2004), 363-379.  doi: 10.1023/B:JOCO.0000038915.62826.79.

[174]

A. LodiS. Martello and M. Monaci, Two-dimensional packing problems: A survey, European Journal of Operational Research, 141 (2002), 241-252.  doi: 10.1016/S0377-2217(02)00123-6.

[175]

A. LodiS. Martello and D. Vigo, Recent advances on two-dimensional bin packing problems, Discrete Applied Mathematics, 123 (2002), 379-396.  doi: 10.1016/S0166-218X(01)00347-X.

[176]

A. LodiS. Martello and D. Vigo, Heuristic algorithms for the three-dimensional bin packing problem, European Journal of Operational Research, 141 (2002), 410-420.  doi: 10.1016/S0377-2217(02)00134-0.

[177]

A. LodiS. Martello and D. Vigo, Approximation algorithms for the oriented two-dimensional bin packing problem, European Journal of Operational Research, 112 (1999), 158-166.  doi: 10.1287/opre.48.2.256.12386.

[178]

A. LodiS. Martello and D. Vigo, Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems, INFORMS Journal on Computing, 11 (1999), 345-357.  doi: 10.1287/ijoc.11.4.345.

[179]

K. Loh, Weight annealing heuristics for solving the two-dimensional bin packing problem outline of presentation two-dimensional bin packing problems, (2009).

[180]

E. López-CamachoH. Terashima-MarinP. Ross and G. Ochoa, A unified hyper-heuristic framework for solving bin packing problems, Expert Systems with Applications, 41 (2014), 6876-6889. 

[181]

D. Mack and A. Bortfeldt, A heuristic for solving large bin packing problems in two and three dimensions, Central European Journal of Operations Research, 20 (2012), 337-354. 

[182]

B. MahvashA. Awasthi and S. Chauhan, A column generation-based heuristic for the three-dimensional bin packing problem with rotation, Journal of the Operational Research Society, 69 (2017), 78-90. 

[183]

M. MaizaA. Labed and M. S. Radjef, Efficient algorithms for the offline variable sized bin-packing problem, Journal of Global Optimization, 57 (2013), 1025-1038.  doi: 10.1007/s10898-012-9989-x.

[184]

M. Maiza and M. S. Radjef, Heuristics for solving the bin-packing, Applied Mathematical Science, 5 (2011), 1739-1752. 

[185]

M. Maiza and C. Guéret, A new lower bound for bin-packing problem with general conflicts graph, $23^{rd}$ European Conference on Operational Research (EURO'XXIII), Bonn, Germany, (2009), 1–5.

[186]

M. Maiza, M. S. Radjef and L. Sais, Efficient lower bounds for packing problems in heterogeneous bins with conflicts constraint, Applied Mathematics and Approximation Theory, Advances in Intelligent Systems and Computing 441, (2016), 263–270.

[187]

A. Malapert, C. Guéret and N. Jussien, Two-dimensional pickup and delivery routing problem with loading constraints, In CPAIOR'08 $1^{st}$ Workshop on Bin Packing and Placement Constraints (BPPC'08), (2008), 1–6.

[188]

S. MartelloM. Monaci and D. Vigo, An exact approach to the strip-packing problem, INFORMS Journal on Computing, 15 (2003), 310-319.  doi: 10.1287/ijoc.15.3.310.16082.

[189]

S. Martello and P. Toth, Lower bounds and reduction procedures for the bin packing problem, Discrete Applied Mathematics, 28 (1990), 59-70.  doi: 10.1016/0166-218X(90)90094-S.

[190]

A. Martinez-SykoraR. Alvarez-ValdesJ. Bennell and J. M. Tamarit, Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts, Omega (United Kingdom), 52 (2015), 15-32. 

[191]

F. Mao, E. Blanco, M. Fu, R. Jain, A. Gupta, S. Mancel and Y. Tian, Small boxes big data: A deep learning approach to optimize variable sized bin packing, 2017 IEEE Third International Conference on Big Data Computing Service and Applications, (2017).

[192]

S. Mezghani, H. Chabchoub and B. Aouni, Manager's preferences in the bi-objectives bin packing problem, In 2013 $5^{th}$ International Conference on Modeling, Simulation and Applied Optimization (ICMSAO). IEEE, (2013), 1–4.

[193]

S. Mezghani and A. Frikha, Heuristics approaches for the industrial storage problem, In 2013 fifth International Conference on Modeling, Simulation and Applied Optimization, ICMSAO, (2013).

[194]

S. Mezghani and A. Frikha, A heuristic approach to the warehouse management problem: A real case study, International Journal of Logistics Systems and Management, 13 (2012), 342-357. 

[195]

S. Mezghani and A. Frikha, Three-dimensional bin packing problem with variable bin length application in industrial storage problem, $4^{th}$ International Conference on Logistics, LOGISTIQUA'2011, (2011), 508–513. doi: 10.1016/j.ejor.2009.05.040.

[196]

G. Miranda, J. De Armas, C. Segura and C. León, Hyperheuristic codification for the multi-objective 2D guillotine strip packing problem, WCCI 2010 - 2010 IEEE World Congress on Computation Intelligence, July, 18-23, Barcelona, Spain, (2010).

[197]

F. MiguelM. FrutosF. Tohmé and M. Méndez, Integrating packing and distribution problems and optimization through mathematical programming, Decision Science Letters, 5 (2016), 317-326. 

[198]

A. Moura and A. Bortfeldt, A two-stage packing problem procedure, International Transactions in Operational Research, 0 (2016), 1-16.  doi: 10.1111/itor.12251.

[199]

A.E.F. MuritibaM. IoriE. Malaguti and P. Toth, Algorithms for the bin packing problem with conflicts, INFORMS Journal on Computing, 22 (2010), 401-415.  doi: 10.1287/ijoc.1090.0355.

[200]

B. Naderi and M. Yazdani, A real multi-objective bin packing problem: A case study of an engine assembly line, Arabian Journal for Science and Engineering, 39 (2014), 5271-5277. 

[201]

N. Ntene and J. H. van Vuuren, A survey and comparison of guillotine heuristics for the 2D oriented offline strip packing problem, Discrete Optimization, 6 (2009), 174-188.  doi: 10.1016/j.disopt.2008.11.002.

[202]

J. F. OliveiraA. Neuenfeldt JúniorE. Silva and M. A. Carravilla, A survey on heuristics for the two-dimensional rectangular strip packing problem, Pesquisa Operacional, 36 (2016), 197-226. 

[203]

F. G. OrtmannN. Ntene and J. H. van Vuuren, New and improved level heuristics for the rectangular strip packing and variable-sized bin packing problems, European Journal of Operational Research, 203 (2010), 306-315.  doi: 10.1016/j.ejor.2011.06.022.

[204]

T. Osogami and H. Okano, Local search algorithms for the bin packing problem and their relationships to various, Heuristics, 9 (2003), 29-49. 

[205]

C. PaquayS. Limbourg and M. Schyns, A tailored two-phase constructive heuristic for the three-dimensional multiple bin size bin packing problem with transportation constraints, European Journal of Operational Research, 267 (2018), 52-64.  doi: 10.1016/j.ejor.2017.11.010.

[206]

C. Paquay, M. Schyns and S. Limbourg, Three dimensional bin packing problem applied to air cargo, In Proceedings of the $4^{th}$ International Conference on Information Systems, Logistics and Supply Chain Creative Logistics For an Uncertain World, (2012), 1–6.

[207]

K. ParkS. Park and W. Kim, A heuristic for an assembly line balancing problem with incompatibility, range, and partial precedence constraints, Computers and Industrial Engineering, 32 (1997), 321-332. 

[208]

F. Parre{ñ}oR. Alvarez-ValdesJ. F. Oliveira and J. M. Tamarit, A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing, Annals of Operations Research, 179 (2010), 203-220.  doi: 10.1007/s10479-008-0449-4.

[209]

S. PatelK. Patel and V. Agrawal, Effectiveness of FireFly algorithm in solving bin packing problem, International Journal of Advanced Research in Computer Science and Software Engineering, 3 (2013), 402-405. 

[210]

J. Pereira, Procedures for the bin packing problem with precedence constraints, European Journal of Operational Research, 17 (2015), 48-1.  doi: 10.1016/j.ejor.2015.10.048.

[211]

J. Pereira and M. Vilà, Variable neighborhood search heuristics for a test assembly design problem, Expert Systems with Applications, 42 (2015), 4805-4817. 

[212]

N. Pillay, A study of evolutionary algorithm selection hyper-heuristics for the one-dimensional bin-packing problem, South African Computer Journal, 48 (2012), 31-40. 

[213]

C.-M. PinteaC. Pascan and M. Hajdu-Macelaru, Comparing several heuristics for a packing problem, International Journal of Advanced Intelligence Paradigms, 4 (2012), 268-277. 

[214]

D. Pisinger and M. Sigurd, Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem, INFORMS Journal on Computing, 19 (2007), 36-51.  doi: 10.1287/ijoc.1060.0181.

[215]

D. Pisinger and M. Sigurd, The two-dimensional bin packing problem with variable bin sizes and costs, Discrete Optimization, 2 (2005), 154-167.  doi: 10.1016/j.disopt.2005.01.002.

[216]

S. Polyakovskiy and R. M'Hallah, Just-in-time two-dimensional bin packing, Omega, 102 (2021), 102-311. 

[217]

S. Polyakovskiy and R. M'Hallah, A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates, European Journal of Operational Research, 266 (2018), 819-839.  doi: 10.1016/j.ejor.2017.10.046.

[218]

S. Polyakovsky and R. M'Hallah, An agent-based approach to the two-dimensional guillotine bin packing problem, European Journal of Operational Research, 192 (2009), 767-781. 

[219]

J. Puchinger and G. R. Raidl, Models and algorithms for three-stage two-dimensional bin packing, European Journal of Operational Research, 183 (2007), 1304-1327.  doi: 10.1016/j.ejor.2005.11.064.

[220]

M. Quiroz-CastellanosL. Cruz-ReyesJ. Torres-JimenezS. C. GomezJ. F. HuacujaA. Héctor and C. F. Alvim, A grouping genetic algorithm with controlled gene transmission for the bin packing problem, Computers and Operations Research, 55 (2014), 52-64.  doi: 10.1016/j.cor.2014.10.010.

[221]

R. G. van Vuuren and J. H. van Rakotonirainy, Improved metaheuristics for the two-dimensional strip packing problem, Applied Soft Computing, 92 (2020), 106-268. 

[222]

A. G. RamosJ. F. Oliveira and M. P. Lopes, A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions, International Transactions in Operational Research, 23 (2016), 215-238.  doi: 10.1111/itor.12124.

[223]

K. RaphaelD. Mauro and I. Manuel, Bin packing problem with general precedence constraints, Journal of Chemical Information and Modeling, 53 (2013), 1689-1699. 

[224]

M. RemicG. Žerovnik and J. Žerovnik, An experimental comparison of some heuristics for cardinality constrained bin packing problem, Business Systems Research, 3 (2012), 57-63. 

[225]

J. RenY. Tian and T. Sawaragi, A tree search method for the container loading problem with shipment priority, European Journal of Operational Research, 214 (2011), 526-535. 

[226]

M. G. C. Resende and J. F. Gonçalve, A hybrid heuristic for the constrained two-dimensional non-guillotine orthogonal cutting problem, AT & T Labs Research Technical Report, (2006).

[227]

M. C. RiffX. Bonnaire and B. Neveu, A revision of recent approaches for two-dimensional strip-packing problems, Engineering Applications of Artificial Intelligence, 22 (2009), 833-837. 

[228]

P. Ross, J. G. Marin-Blazquez, S. Schulenburg and E. Hart, Learning a procedure that can solve hard bin-packing problems: A new GA-based approach to hyper-heuristics, In Genetic and Evolutionary Computation Conference (GECCO), (2003), 1295–1306.

[229]

P. Ross, S. Schulenburg, J. G. Marin-Blazquez and E. Hart, Hyper-heuristics: learning to combine simple heuristics in bin-packing problems, In Proceedings of the 12th annual conference on Genetic and evolutionary computation, (2002), 942–948.

[230]

R. Sadykov and F. Vanderbeck, Bin packing with conflicts: A generic branch-and-price algorithm, INFORMS Journal on Computing, 25 (2013), 244-255.  doi: 10.1287/ijoc.1120.0499.

[231]

R.D. Saraiva, N. Nepomuceno and P. R. Pinheiro, A layer-building algorithm for the three-dimensional multiple bin packing problem: A case study in an automotive company, In IFAC Proceedings Volumes (IFAC-PapersOnline), (2015). 490–495.

[232]

M. Sathe, O Schenk and H. Burkhart, Solving bi-objective many-constraint bin packing problems in automobile sheet metal forming processes, In International Conference on Evolutionary Multi-Criterion Optimization. Springer Berlin Heidelberg, (2009), 246–260.

[233]

A. SavićT. Šukilović and V. Filipović, Solving the two-dimensional packing problem with m- M calculus, Journal of Operations Research, 21 (2011), 93-102.  doi: 10.2298/YJOR1101093S.

[234]

P. Schaus and Y. Deville, A global constraint for bin-packing with precedences: Application to the assembly line balancing problem, In Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, (July 13-17), 369–374.

[235]

X ScheplerA. RossiE. Gurevsky and A. Dolgui, Solving robust bin-packing problems with a branch-and-price approach, European Journal of Operational Research, 297 (2021), 795-1192.  doi: 10.1016/j.ejor.2021.05.041.

[236]

A. SchollR. Klein and C. Jürgens, Bison: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem, Computers and Operations Research, 24(7) (1997), 627-645. 

[237]

M. Serairi and M. Haouari, A computational study of lower bounds for the two dimensional bin packing problem, Electronic Notes in Discrete Mathematics, 36(C) (2010), 891-897. 

[238]

E. SilvaJ.F. Oliveira and G. Wäscher, 2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problems, European Journal of Operational Research, 237 (2014), 846-856.  doi: 10.1016/j.ejor.2014.02.059.

[239]

K. Sim, E. Hart and B. Paechter, A hyper-heuristic classifier for one dimensional bin packing problems: Improving classification accuracy by attribute evolution, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7492 LNCS(PART 2), (2012), 48–357.

[240]

A. Soke and Z. Bingul, Hybrid genetic algorithm and simulated annealing for two-dimensional non-guillotine rectangular packing problems, Engineering Applications of Artificial Intelligence, 19 (2006), 557-567. 

[241]

U. Sommerweiß, Heuristics for the rectangle packing problem, Partially supported by BMBF, registration number 03-TE7DRE-8, 3 (1996), 1-21. 

[242]

D. Stathis, I. Vourkas and G. C. Sirakoulis, Solving AI problems with memristors: A case study for optimal bin packing, In PCI'14, October 02 - 04 2014, Athens, Greece, (2014), 1–6.

[243]

Y. Tao and F. Wang, An effective tabu search approach with improved loading algorithms for the 3L-CVRP, Computers and Operations Research, 55 (2015), 127-140.  doi: 10.1016/j.cor.2013.10.017.

[244]

J. TernoG. ScheithauerU. Sommerweiß and J. Riehme, An efficient approach for the multi-pallet loading problem, European Journal of Operational Research, 123 (2000), 372-381.  doi: 10.1016/S0377-2217(99)00263-5.

[245]

T. TianW. ZhuA. Lim and L. Wei, The multiple container loading problem with preference, European Journal of Operational Research, 248 (2016), 84-94.  doi: 10.1016/j.ejor.2015.07.002.

[246]

T. A. M. Toffolo, E. Esprit, T. Wauters and G. Vanden Berghe, A two-dimensional heuristic decomposition approach to a three-dimensional multiple container loading problem, European Journal of Operational Research, (2016), 1–26. doi: 10.1016/j.ejor.2016.07.033.

[247]

N. VakhaniaaJ. A. Hernandezb and C. Zavala, A single-machine scheduling problem to minimize the maximum lateness is tightly related with a variation of bin packing problem with different bin, Ciência e Técnica Vitivinícola, 30 (2015), 0-15. 

[248]

J. M. V. De Carvalho, LP models for bin packing and cutting stock problems, European Journal of Operational Research, 141 (2002), 253-273.  doi: 10.1016/S0377-2217(02)00124-8.

[249]

J. P. L. Viegas, S. M. Vieira, J. M. C. Sousa and E. M. P. Henriques, Metaheuristics for the 3D bin packing problem in the steel industry, Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014, (2014), 338–343.

[250]

N. WangJ. S. WangY. X. Zhang and T. Z. Li, Two-dimensional bin-packing problem with rectangular and circular regions solved by genetic algorithm, IAENG International Journal of Applied Mathematics, 51 (2021), 1-11. 

[251]

Y. Wang and L. Chen, Two-dimensional residual-space-maximized packing, Expert Systems with Applications, 42 (2015), 3297-3305. 

[252]

B. Wang, J. Liu and Y. Y. M. Keech, A constructive heuristic for two-dimensional bin packing, Proceedings of the 2012 2nd International Conference on Computer and Information Applications (ICCIA 2012), (2012), 210–213.

[253]

G. WäscherH. Haußner and H. Schumann, An improved typology of cutting and packing problems, European Journal of Operational Research, 183 (2007), 1109-1130. 

[254]

S. Watanabe, T. Hiroyasu and M. Miki, Multi-objective rectangular packing problem and its applications, In Evolutionary Multi-Criterion Optimization, Proceedings, (2003), 565–577.

[255]

L. WeiZ. ZhangD. Zhang and A. Lim, A variable neighborhood search for the capacitated vehicle routing problem with two-dimensional loading constraints, European Journal of Operational Research, 243 (2015), 798-814. 

[256]

L. WeiW. C. OonW. Zhu and A. Lim, A goal-driven approach to the 2D bin packing and variable-sized bin packing problems, European Journal of Operational Research, 224 (2013), 110-121.  doi: 10.1016/j.ejor.2012.08.005.

[257]

L. WeiW. C. OonW. Zhu and A. Lim, A skyline heuristic for the 2D rectangular packing and strip packing problems, European Journal of Operational Research, 215 (2011), 337-346.  doi: 10.1016/j.ejor.2011.06.022.

[258]

M. WittemanQ. Deng and B. F. Santos, A bin packing approach to solve the aircraft maintenance task allocation problem, European Journal of Operational Research, 294 (2021), 365-376.  doi: 10.1016/j.ejor.2021.01.027.

[259]

L. WongL. S. Lee and U. P. M. Serdang, Heuristic placement routines for two-dimensional bin packing problem, Journal of Mathematics and Statistics, 5 (2009), 334-341. 

[260]

L. WuX. LiC. Liu and W. Xiao, NHACR: A novel heuristic approach for 2D rectangle packing area minimization problem with central rectangle, Engineering Applications of Artificial Intelligence, 103 (2021), 104-291. 

[261]

Y. WuW. LiM. Goh and R. Souza, Three dimensional bin packing problem with variable bin height, European Journal of Operational Research, 202 (2010), 347-355.  doi: 10.1016/j.ejor.2009.05.040.

[262]

L. Xueping, Z. Zhaoxia and K. Zhang, A genetic algorithm for the three-dimensional bin packing problem with heterogeneous bins, In Proceedings of the 2014 Industrial and Systems Engineering Research Conference, (2014).

[263]

Y. YaoC. Lai and Y. Cui, A constructive heuristic for the two-dimensional bin packing based on value correction, International Journal of Computer Applications in Technology, 55 (2017), 12-21. 

[264]

A. Yarimcam, S. Asta, E. Ozcan and A. J. Parkes, Heuristic generation via parameter tuning for online bin packing, In IEEE SSCI 2014 - 2014 IEEE Symposium Series on Computational Intelligence - EALS 2014: 2014 IEEE Symposium on Evolving and Autonomous Learning Systems, Proceedings, (2014), 102–108.

[265]

R. Yesodha and T. Amudha, Bio-inspired metaheuristics for bin packing problems, International Journal of Emerging Technologies in Computational and Applied Sciences (IJETCAS), 1961 (2013), 329-333. 

[266]

Y. Yuan, Y.J. Li and Y. Q. Wang, An improved ACO algorithm for the bin packing problem with conflicts based on graph coloring model, In International Conference on Management Science and Engineering - Annual Conference Proceedings, (2014), 3–9.

[267]

G Zhang and R. E. Burkard, A new version of on-line variable-sized bin packing, Discrete Applied Mathematics, 72 (1997), 193-197.  doi: 10.1016/S0166-218X(96)00018-2.

[268]

Z. ZhangS. GuoW. ZhuW. C. Oon and A. Lim, Space defragmentation heuristic for 2D and 3D bin packing problems, IJCAI International Joint Conference on Artificial Intelligence, 3 (2011), 699-704.  doi: 10.1016/j.ejor.2012.05.031.

[269]

D. ZhangL. S. C. H. Shi and T. Wu, A priority heuristic for the guillotine rectangular packing problem, Information Processing Letters, 116 (2016), 15-21. 

[270]

X. Zhao and H. Shen, Online algorithms for 2D bin packing with advice, Neurocomputing, 189 (2016), 25-32. 

[271]

D. Zhu, Max-min bin packing algorithm and its application in nano-particles filling, Chaos, Solitons & Fractals, 89 (2016), 83-90. 

[272]

W. ZhuZ. ZhangW. C. Oon and A. Lim, Space defragmentation for packing problems, European Journal of Operational Research, 222 (2012), 452-462.  doi: 10.1016/j.ejor.2012.05.031.

[273]

A. ZudioD. H. da Silva CostaB. P. MasquioI. M. Coelho and P. E. D. Pinto, BRKGA/VND hybrid algorithm for the classic three-dimensional bin packing problem, Electronic Notes in Discrete Mathematics, 66 (2018), 175-182.  doi: 10.1016/j.endm.2018.03.023.

show all references

References:
[1]

M. Abdel-BassetG. ManogaranL Abdel-Fatah and S. Mirjalili, An improved nature inspired meta-heuristic algorithm for 1-D bin packing problems, Personal and Ubiquitous Computing, 22 (2018), 1117-1132. 

[2]

A. C. Adamuthea and T. R. Nitave, Optimizing large scale bin packing problem with hybrid harmony search algorithm, International Journal of Industrial Engineering Computations, 12 (2021), 205-220. 

[3]

A. Aggoun, A. Rhiat, A. and F. Fages, Panorama of reallife applications in logistics embedding bin packing optimization algorithms, Robotics and Cloud Computing Technologies, The 3rd IEEE International Conference on Logistics Operations Management Gol'16, 2016, 1–4.

[4]

S. Agrawal, S. K. Bose and S. Sundarrajan, Grouping genetic algorithm for solving the server consolidation problem with conflicts, Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation, 2009, 1–8.

[5]

A. Almeida and M.B. Figueiredo, A particular approach for the three-dimensional packing problem with additional constraints, Computers and Operations Research, 37 (2010), 1968-1976.  doi: 10.1016/j.cor.2010.01.010.

[6]

R. Alvarez-ValdesF. Parreño and J.M. Tamarit, A GRASP/Path relinking algorithm for two- and three-dimensional multiple bin-size bin packing problems, Computers and Operations Research, 40 (2013), 3081-3090.  doi: 10.1016/j.cor.2012.03.016.

[7]

K. A. Amara and B. Djebbar, Bee colony optimization applied to the bin packing problem, International Journal of Computer and Information Engineering, 11 (2017), 275-279. 

[8]

C. Arbib and F. Marinelli, Maximum lateness minimization in one-dimensional bin packing, Omega, 68 (2016), 1-9. 

[9]

S. AstaE. özcan and A.J. Parkes, CHAMP: Creating heuristics via many parameters for online bin packing, Expert Systems with Applications, 63 (2016), 208-221. 

[10]

J. Augustine, S. Banerjee and S. Irani, Strip packing with precedence constraints and strip packing with release times, Theoretical Computer Science, 410 (2009), 3792–3803. doi: 10.1016/j.tcs.2009.05.024.

[11]

N. AydinI. Muter and Ş. İlker Birbil, Multi-objective temporal bin packing problem: An application in cloud computing, Computers & Operations Research, 121 (2020), 104-959.  doi: 10.1016/j.cor.2020.104959.

[12]

M. AyobM. Nazri and Y. Fei, Local search heuristics for the one dimensional bin packing problems, Journal of Applied Sciences, 6 (2013), 919-923. 

[13]

M. M. BaldiT. G. CrainicG. Perboli and R. Tadei, Branch-and-price and beam search algorithms for the variable cost and size bin packing problem with optional items, Annals of Operations Research, 222 (2014), 125-141.  doi: 10.1007/s10479-012-1283-2.

[14]

J. BaloghJ. BékésiG. DósaL. Epstein and A. Levin, Online bin packing with cardinality constraints resolved, Journal of Computer and System Sciences, 112 (2020), 34-49.  doi: 10.1016/j.jcss.2020.03.002.

[15]

J. BaloghJ. BékésiG. DósaJ. Sgall and R. van Stee, The optimal absolute ratio for online bin packing, Journal of Computer and System Sciences, 102 (2019), 1-17.  doi: 10.1016/j.jcss.2018.11.005.

[16]

J. Balogh, J. Békési and G. Galambos, On a multidimensional semi-on-line bin packing problem, In Proceedings of the eighth International Conference on Applied Informatics Eger, Hungary, January 27–30, 2010,191–197.

[17]

J. Balogh and J. Békési, An improved lower bound for the bin packing, Discrete Applied Mathematics, 66 (1996), 1-6. 

[18]

J. Bang-Jensen and R. Larsen, Efficient algorithms for real-life instances of the variable size bin packing problem, Computers and Operations Research, 39 (2012), 2848-2857. 

[19]

N. BansalZ. Liu and A. Sankar, Bin-packing with fragile objects and frequency allocation in cellular networks, Wireless Networks, 15 (2009), 821-830. 

[20]

N. Bansal and M. Sviridenko, Two-dimensional bin packing with one dimensional resource augmentation, Discrete Optimization, 4 (2007), 143-153.  doi: 10.1016/j.disopt.2006.09.001.

[21]

N. Bansal, A. Lodi and M. Sviridenko, A tale of two-dimensional bin packing, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, 2005,657–666.

[22]

C. Basnet and J. Wilson, Heuristics for determining the number of warehouses for storing non-compatible products, International Transactions in Operational Research, 12 (2005), 527-538.  doi: 10.1111/j.1475-3995.2005.00523.x.

[23]

B. Beisiegel, J. Kallrath, Y. Kochetov and A. Rudnev, Simulated annealing based algorithm for the 2D bin packing problem with impurities, Operations Research Proceedings 2005 Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), Bremen, (September 7–9, 2005), 1–6.

[24]

G. BelovG. Scheithauer and and E.A. Mukhacheva, One-dimensional heuristics adapted for two-dimensional rectangular strip packing, Journal of the Operational Research Society, 59 (2008), 823-832. 

[25]

M. Benazouz and J. M. Faure, Safety-level aware bin-packing approach for control functions assignment, In IFAC Proceedings Volumes (IFAC-PapersOnline), 48 (2015), 507-512. 

[26]

B. E. Bengtsson, Packing rectangular pieces–a heuristic approach, The Computer Journal, 25 (1982), 253-257.  doi: 10.1093/comjnl/25.3.353.

[27]

J.A. BennellL. Soon Lee and and C.N. Potts, A genetic algorithm for two-dimensional bin packing with due date, International Journal of Production Economics, 145 (2013), 547-560. 

[28]

B. Messaoud, C. Chu and M. L. Espinouse, An approach to solve cutting stock sheets, In Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics, (2004), 5109–5113.

[29]

J.O. Berkey and and P.Y. Wang, Two-dimensional finite bin-packing algorithms, Journal of the Operational Research Society, 38 (1987), 423-429. 

[30]

M. BeyazT. Dokeroglu and A. Cosar, Robust hyper-heuristic algorithms for the offline oriented/non-oriented 2D bin packing problems, Applied Soft Computing, 36 (2015), 236-245. 

[31]

C. Bllum and V. Schmid, Solving the 2D bin packing problem by means of a hybrid evolutionary algorithm, Procedia Computer Science, 18 (2013), 899-908. 

[32]

A. Bòdis, Bin packing with directed stackability conflicts, Acta Universitatis Sapientiae, Informatica, 7 (2015), 31-57. 

[33]

P. Boominathan and S. Rajkumar, Bin packing problems: Comparative analysis of heuristic, International Journal of Pharmacy and Technology, 8 (2016), 13350-13319. 

[34]

I. Borgulya, A hybrid evolutionary algorithm for the offline bin packing problem, Central European Journal of Operations Research, 29 (2021), 425-445.  doi: 10.1007/s10100-020-00695-5.

[35]

A. Bortfeldt and J. Homberger, Packing first, routing second-a heuristic for the vehicle routing and loading problem, Computers and Operations Research, 40 (2013), 873-885. 

[36]

A. Bortfeldt, A genetic algorithm for the two-dimensional strip packing problem with rectangular pieces, European Journal of Operational Research, 172 (2006), 814-837.  doi: 10.1016/j.ejor.2004.11.016.

[37]

M. A. Boschetti and A. Mingozzi, The two-dimensional finite bin packing problem. Part I: New lower bounds for the oriented case, Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 1 (2003), 27-42.  doi: 10.1007/s10288-002-0005-z.

[38]

M. Buljubašić and M. Vasquez, Consistent neighborhood search for one-dimensional bin packing and two-dimensional vector packing, Computers and Operations Research, 76 (2016), 12-21.  doi: 10.1016/j.cor.2016.06.009.

[39]

A. R. Callaghan, A. R. Nair and K. E. Lewis, An extension of the orthogonal packing, In Proceedings of DETC'99: 1999 ASME Design Engineering Technical Conferences, Las Vegas, Nevada, (September 12-15 1999), 1–7.

[40]

A. Caprara, Packing 2-dimensional bins in harmony, In The $43^{rd}$ Annual IEEE Symposium on Foundations of Computer Science, Proceedings, (2002), 490–499. doi: 10.1287/moor.1070.0289.

[41]

M. CasazzaA. Ceselli and In formatica, Exactly solving packing problems with fragmentation, Computers and Operation Research, 75 (2015), 202-213.  doi: 10.1016/j.cor.2016.06.007.

[42]

S. CeschiaA. Schaerf and T. Stützle, Local search techniques for a routing-packing problem, Computers and Industrial Engineering, 66 (2013), 1138-1149. 

[43]

T. ChabotR. LahyaniL. Coelho and J. Renaud, Order picking problems under weight, fragility and category constraints, International Journal of Production Research, 55 (2017), 6361-6379. 

[44]

W.T. ChanF. Y.-L.Ch inD. ZhangG. Ye and Y. Zhang, Online bin packing of fragile objects with application in cellular networks, Journal of Combinatorial Optimization, 14 (2007), 427-435.  doi: 10.1007/s10878-007-9043-y.

[45]

M. Chanaleä and E. Ezugwu, Metaheuristic algorithms for one-dimensional bin-packing problems: A survey of recent advances and applications, Journal of Intelligent Systems, 30 (2021), 636-663. 

[46]

C. Charalambous and K. Fleszar, A constructive bin-oriented heuristic for the two-dimensional bin packing problem with guillotine cuts, Computers and Operations Research, 38 (2011), 1443-1451. 

[47]

A. V. Chekanin, Efficient algorithms for orthogonal packing problems, Computational Mathematics and Mathematical Physics, 53 (2013), 1457-1465.  doi: 10.1134/S0965542513100047.

[48]

M. Chen and W. Huang, A two-level search algorithm for 2D rectangular packing problem, Computers and Industrial Engineering, 53 (2007), 123-136. 

[49]

R. Christopher and P. Nelishia, Combining development and evolution case study: One dimensional bin-packing, In Proceedings of the seventh International Joint Conference on Computational Intelligence (IJCCI 2015), (2015), 188–195.

[50]

H.I. ChristensenA. KhanS. Pokutta and P. Tetali, Approximation and online algorithms for multidimensional bin packing: A survey, Computer Science Review, 24 (2017), 63-79.  doi: 10.1016/j.cosrev.2016.12.001.

[51]

H. I. ChristensenA. KhanS. Pokutta and P. Tetali, Approximation and online algorithms for multidimensional bin packing: A survey, Computer Science Review, 24 (2017), 63-79.  doi: 10.1016/j.cosrev.2016.12.001.

[52]

F. R. K. ChungM. R. Garey and D. S. Johnson, On packing two-dimensional bins, SIAM Journal on Algebraic Discrete Methods, 3 (1982), 66-76.  doi: 10.1137/0603007.

[53]

A. M. Chwatal and S. Pirkwieser, Solving the two-dimensional bin-packing problem with variable bin sizes by greedy randomized adaptive search procedures and variable neighborhood search, In International Conference on Computer Aided Systems Theory. Springer, Berlin, Heidelberg, (2011), 456–463.

[54]

W. Ciscal-TerryM. D. Amico and M. Iori, Bin Packing Problem With General Precedence Constraints, IFAC-PapersOnLine, 48 (2015), 2027-2029. 

[55]

F. ClautiauxA. JougletJ. Carlier and A. Moukrim, A new constraint programming approach for the orthogonal packing problem, Computers and Operations Research, 35 (2008), 944-959.  doi: 10.1016/j.cor.2006.05.012.

[56]

F. ClautiauxJ. Carlier and A. Moukrim, A new exact method for the two-dimensional bin-packing problem with fixed orientation, Operations Research Letters, 35 (2007), 357-364.  doi: 10.1016/j.orl.2006.06.007.

[57]

F. ClautiauxM. Dell'AmicoM. Iori and A. Khanafer, Lower and upper bounds for the bin packing problem with fragile objects, Discrete Applied Mathematics, 163(PART 1) (2014), 73-86.  doi: 10.1016/j.dam.2012.04.010.

[58]

E. G. Coffman, M. R. Garey and D. S. Johnson, Approximation algorithms for bin packing: A survey, in Approximation Algorithms, Ed. by D. Hochbaum (PWS Publishing Company), (1996), 46–93.

[59]

E. G. CoffmanM. R. GareyD. S. Johnson and R. E. Tarjan, Performance bounds for level-oriented two-dimensional packing algorithms, SIAM Journal on Computing, 9 (1980), 808-827.  doi: 10.1137/0209062.

[60]

E. G. CoffmanK. SoM. Hofri and A. C. Yao, A stochastic model of bin-packing, Information and Control, 44 (1980), 105-115.  doi: 10.1016/S0019-9958(80)90050-9.

[61]

I. CorreiaL. Gouveia and F. Saldanha-da-Gama, Solving the variable size bin packing problem with discretized formulations, Computers and Operations Research, 35 (2008), 2103-13.  doi: 10.1016/j.cor.2006.10.014.

[62]

G. CostaM. DelormeM. IoriE. Malaguti and S. Martello, Training software for orthogonal packing problems, Computers and Industrial Engineering, 111 (2017), 139-147. 

[63]

J.-F. CôtéM. Gendreau and J.-Y. Potvin, An exact algorithm for the two-dimensional orthogonal packing problem with unloading constraints, Operations Research, 62 (2014), 1126-1141.  doi: 10.1287/opre.2014.1307.

[64]

T. G. CrainicL. GobbatoG. Perboli and W. Rei, Logistics capacity planning: A stochastic bin packing formulation and a progressive hedging meta-heuristic, European Journal of Operational Research, 253 (2016), 404-417.  doi: 10.1016/j.ejor.2016.02.040.

[65]

T. G. CrainicL. GobbatoG. PerboliW. ReiJ. P. Watson and D. L. Woodruff, Bin packing problems with uncertainty on item characteristics: An application to capacity planning in logistics, Procedia Social and Behavioral Sciences, 111 (2014), 654-662.  doi: 10.1016/j.ejor.2016.02.040.

[66]

T. G. Crainic, G. Perboli, W. Rei and R. Tadei, Efficient heuristics for the variable size bin packing problem with fixed costs, Cirrelt Tech. Rep., 18 (2010).

[67]

T. G. CrainicG. Perboli and R. Tadei, Extreme point-based heuristics for three-dimensional bin packing, INFORMS Journal on Computing, 20 (2008), 368-384.  doi: 10.1287/ijoc.1070.0250.

[68]

Y. CuiY. Yao and Y. P. Cui, Hybrid approach for the two-dimensional bin packing problem with two-staged patterns, International Transactions in Operational Research, 23 (2016), 539-549.  doi: 10.1111/itor.12188.

[69]

Y. P. Cui and and T. Tang, Sequential heuristic for the two-dimensional bin-packing problem, European Journal of Operational Research, 240 (2015), 43-53.  doi: 10.1016/j.ejor.2014.06.032.

[70]

N. DahmaniS. Krichen and D. Ghazouani, A variable neighborhood descent approach for the two-dimensional bin packing problem, Electronic Notes in Discrete Mathematics, 47 (2015), 117-124.  doi: 10.1016/j.endm.2014.11.016.

[71]

K. Daoden and T. Thaiupathump, Applying shuffled frog leaping algorithm and bottom left fill algorithm in rectangular packing problem, In $7^{th}$ IEEE International Conference on Electronics Information and Emergency Communication (ICEIEC). IEEE, (2017), 136–139.

[72]

S. K. Das, M. Pervin, S. K. Roy and G. W. Weber, Multi-objective solid transportation-location problem with variable carbon emission in inventory management: A hybrid approach, Annals of Operations Research, (2021), 1–27.

[73]

S. K. DasS. K. Roy and G. W. Weber, Heuristic approaches for solid transportation-p-facility location problem, Central European Journal of Operations Research, 28 (2019), 939-961.  doi: 10.1007/s10100-019-00610-7.

[74]

S. K. Das and S. K. Roy, Effect of variable carbon emission in a multi-objective transportation-p-facility location problem under neutrosophic environment, Computers and Industrial Engineering, 132 (2019), 311-324. 

[75]

S. K. DasS. K. Roy and G. W. Weber, An exact and a heuristic approach for the transportation-p-facility location problem, Computational Management Science, 17 (2020), 389-407.  doi: 10.1007/s10287-020-00363-8.

[76]

M. DawandeJ. Kalagnanam and J. Sethuraman, Variable sized bin packing With color constraints, Electronic Notes in Discrete Mathematics, 7 (2001), 154-157. 

[77]

J. L. De Castro SilvaN. Y. Soma and N. Maculan, A greedy search for the three-dimensional bin packing problem: The packing static stability case, International Transactions in Operational Research, 10 (2003), 141-153.  doi: 10.1111/1475-3995.00400.

[78]

M. Dell'Amico, J. C. D. Díaz and M. Iori, The bin packing problem with precedence constraints, $15^{th}$ IFAC Symposium on Information Control in Manufacturing, 60 (2015), 1491–1504. doi: 10.1287/opre.1120.1109.

[79]

M. Dell'AmicoJ. C. D. Díaz and M. Iori, The bin packing problem with precedence constraints, Operations Research, 60 (2012), 1491-1504.  doi: 10.1287/opre.1120.1109.

[80]

M. Delorme, M. Iori and S. Martello, Bin packing and cutting stock problems: Mathematical models and exact algorithms, AIRO 2014 Conference, (2015). doi: 10.1016/j.ejor.2016.04.030.

[81]

T. A. De Queiroz and F. K. Miyazawa, Two-dimensional strip packing problem with load balancing, load bearing and multi-drop constraints, International Journal of Production Economics, 145 (2013), 511-530.  doi: 10.1016/j.dam.2013.08.019.

[82]

W. B. Dowsland, Two and three dimensional packing problems and solution methods, Operational Research Society of New Zeland, 13 (1985), 1-18. 

[83]

H. Dyckhoff, A typology of cutting and packing problems, European Journal of Operational Research, 4 (1990), 145-159.  doi: 10.1016/0377-2217(90)90350-K.

[84]

A. Ekici, Variable-sized bin packing problem with conflicts and item fragmentation, Computers and Industrial Engineering, 163 (2022), 107-844.  doi: 10.1016/j.cor.2020.105113.

[85]

J. El HayekA. Moukrim and S. Negre, New resolution algorithm and pretreatments for the two-dimensional bin-packing problem, Computers and Operations Research, 35 (2008), 3184-3201. 

[86]

S. ElhedhliF. Gzara and Y. F. Yan, A MIP-based slicing heuristic for three-dimensional bin packing, Optimization Letters, 11 (2017), 1547-1563.  doi: 10.1007/s11590-017-1154-5.

[87]

S. ElhedhliL. LiM Gzara and and J. Naoum-Sawaya, A branch-and-price algorithm for the bin packing problem with conflicts, INFORMS Journal on Computing, 23 (2011), 404-415.  doi: 10.1287/ijoc.1100.0406.

[88]

A. Elloumi, H. Kamoun, B. Jarboui and A. Dammak, The classroom assignment problem: Complexity, size reduction and heuristics, Applied Soft Computing Journal, 14(PART C) (2014), 677–686.

[89]

L. Epstein and T. Erlebach, Approximation and online algorithms, Lecture Notes in Computer Science, (2018), 327–347. doi: 10.1007/978-3-030-04693-4.

[90]

L. Epstein and A. Levin, An AFPTAS for variable sized bin packing with general activation costs, Journal of Computer and System Sciences, 84 (2017), 79-96.  doi: 10.1016/j.jcss.2016.07.007.

[91]

L. EpsteinL. M. Favrholdt and J. S. Kohrt, Comparing online algorithms for bin packing problems, Journal of Scheduling, 15 (2012), 13-21.  doi: 10.1007/s10951-009-0129-5.

[92]

L. EpsteinL. M. Favrholdt and A. Levin, Online variable-sized bin packing with conflicts, Discrete Optimization, 8 (2011), 333-343.  doi: 10.1016/j.disopt.2010.11.001.

[93]

L. Epstein and and M. Levy, Dynamic multi-dimensional bin packing, Journal of Discrete Algorithms, 8 (2010), 356-372.  doi: 10.1016/j.jda.2010.07.002.

[94]

L. Epstein and A. Levin, On bin packing with conflicts, SIAM Journal on Optimization, 19 (2008), 1270-1298.  doi: 10.1137/060666329.

[95]

S. ErbayrakV. Özkır and U. Mahir Yıldırım, Multi-objective 3D bin packing problem with load balance and product family concerns, Computers and Industrial Engineering, 159 (2021), 107-518. 

[96]

A. FernàndezC. GilR. Banos and M. G. Montoya, A parallel multi-objective algorithm for two-dimensional bin packing with rotations and load balancing, Expert Systems with Applications, 40 (2013), 5169-5180. 

[97]

H. Firat and N. Alpaslan, An effective approach to the two-dimensional rectangular packing problem in the manufacturing industry, Computers and Industrial Engineering, 148 (2020), 106-687. 

[98]

K. Fleszar, Three insertion heuristics and a justification improvement heuristic for two-dimensional bin packing with guillotine cuts, Computers and Operations Research, 40 (2013), 463-474. 

[99]

D. K. Friesen and M. A. Langston, Variable sized bin packing, SIAM Journal on Computing, 15 (1986), 222-230.  doi: 10.1007/BF01934179.

[100]

G. FuellererR. F. Doerner and M. Iori, Metaheuristics for vehicle routing problems with three-dimensional loading constraints, European Journal of Operational Research, 201 (2010), 751-759. 

[101]

M. Gabay and S. Zaourar, Vector bin packing with heterogeneous bins: Application to the machine reassignment problem, Annals of Operations Research, 242 (2016), 161-194.  doi: 10.1007/s10479-015-1973-7.

[102]

M. GajdaA. TrivellaR. Mansini and D. Pisinger, An optimization approach for a complex real-life container loading problem, Omega, 107 (2022), 102-559. 

[103]

J. Gardeyn and T. Wauters, A goal-driven ruin and recreate heuristic for the 2D variable-sized bin packing problem with guillotine constraints, European Journal of Operational Research, 301 (2022), 432-444.  doi: 10.1016/j.ejor.2021.11.031.

[104]

M. R. GareyR. L. Graham and D. S. Johnson, Resource constrained scheduling as generalized bin packing, Journal of Combinatorial, series A, 21 (1976), 257-298.  doi: 10.1016/0097-3165(76)90001-7.

[105]

M. J. Geiger, Bin packing under multiple objectives - a heuristic approximation approach, In The Fourth International Conference on Evolutionary Multi Criterion Optimization, (2008), 53–56.

[106]

M. GendreauG. Laporte and F. Semet, Heuristics and lower bounds for the bin packing problem with conflicts, Computers and Operations Research, 31 (2004), 347-358.  doi: 10.1016/S0305-0548(02)00195-8.

[107]

J. A. George and D. F. Robinson, A heuristic for packing boxes into a container, Computers and Operations Research, 7 (1980), 147-156. 

[108]

N. Goldberg and S. Karhi, Online packing of arbitrary sized items into designated and multipurpose bins, European Journal of Operational Research, 279 (2019), 54-67.  doi: 10.1016/j.ejor.2019.05.029.

[109]

I. Golan, Performance bounds for orthogonal oriented two-dimensional packing algorithms, SIAM Journal on Computing, 10 (1981), 571-583.  doi: 10.1137/0210042.

[110]

P. Gomez-Meneses and M. Randall, A hybrid extremal optimisation approach for the bin packing problem, In Artificial Life: Borrowing from Biology, Proceedings, (2009), 242–251.

[111]

A. Grange, I. Kacem and S. Martin, Algorithms for the pagination problem, a bin packing with overlapping items, preprint, arXiv: 1605.00558, (2016).

[112]

R. Gupta, S. K. Bose, S. Sundarrajan, M. Chebiyam and A. Chakrabarti, A two stage heuristic algorithm for solving the server consolidation problem with item-item and bin-item incompatibility constraints, Proceedings - 2008 IEEE International Conference on Services Computing, SCC 2008, 2, 2008, 39–46.

[113]

J. N. D. Gupta and J. C. Ho, New heuristic algorithm for the one-dimensional bin-packing problem, Production Planning and Control, 10 (1999), 598-603. 

[114]

F. GzaraS. Elhedhli and B. C. Yildiz, The pallet loading problem: Three-dimensional bin packing with practical constraints, European Journal of Operational Research, 287 (2020), 1062-1074.  doi: 10.1016/j.ejor.2020.04.053.

[115]

E. Hadjiconstantinou and and M. Iori, A hybrid genetic algorithm for the two-dimensional single large object placement problem, European Journal of Operational Research, 183 (2007), 1150-1166.  doi: 10.1016/j.ejor.2005.11.061.

[116]

B. T. HanG. Diehr and and J. S. Cook, Multiple-type, two-dimensional bin packing problems: Applications and algorithms, Annals of Operations Research, 50 (1994), 239-261.  doi: 10.1007/BF02085642.

[117]

K. Hamdi-DhaouiN. Labadie and A. Yalaoui, The bi-objective two-dimensional loading vehicle routing problem with partial conflicts, International Journal of Production Research, 52 (2014), 5565-5582. 

[118]

K. Hamdi-DhaouiN. Labadie and A. Yalaoui, Algorithms for the two dimensional bin packing problem with partial conflicts, RAIRO - Operations Research, 46 (2012), 41-62.  doi: 10.1051/ro/2012007.

[119]

M. Haouari and M. Serairi, Relaxations and exact solution of the variable sized bin packing problem, Computational Optimization and Applications, 48 (2011), 345-368.  doi: 10.1007/s10589-009-9276-z.

[120]

M. Haouari and M. Serairi, Heuristics for the variable sized bin-packing problem, Computers and Operations Research, 36 (2009), 2877-2884.  doi: 10.1016/j.cor.2008.12.016.

[121]

Y. Harrath, A Three-Stage Layer-Based Heuristic to Solve the 3D Bin-Packing Problem under Balancing Constraint, Journal of King Saud University - Computer and Information Sciences, 2021.

[122]

N. Hashim, F. Zulkipli, S. Januri and S. S. R. Shariff, An alternative heuristics for bin packing problem, Proceedings of the 2014 International Conference on Industrial Engineering and Operations Management Bali, Indonesia, (January 7–9 2014), 1560–1568.

[123]

K. Heßler, S. Irnich, T. Kreiter and U. Pferschy, Bin packing with lexicographic objectives for loading weight- and volume-constrained trucks in a direct-shipping system, OR Spectrum, (2021), 1–43. doi: 10.1007/s00291-021-00628-x.

[124]

V. HemmelmayrV. Schmid and C. Blum, Variable neighbourhood search for the variable sized bin packing problem, Computers and Operations Research, 39 (2012), 1097-1108.  doi: 10.1016/j.cor.2011.07.003.

[125]

J. Herrera-FranklinA. Rosete and M. García-Borroto, A fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing, Inteligencia Artificial, 24 (2021), 71-89. 

[126]

M. HifiI. KacemS. Nègre and L. Wu, A linear programming approach for the three-dimensional bin-packing problem, Electronic Notes in Discrete Mathematics, 36(C) (2010), 993-1000. 

[127]

S. HongD. ZhangH. C. LauX. Zeng and Y.W. Si, A hybrid heuristic algorithm for the 2D variable-sized bin packing problem, European Journal of Operational Research, 238 (2014), 95-103.  doi: 10.1016/j.ejor.2014.03.049.

[128]

E. Hopper and B. C. H. Turton, Empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem, European Journal of Operational Research, 128 (2001), 34-57. 

[129]

E. Hopper and B. Turton, A genetic algorithm for a 2D industrial packing problem, Computers and Industrial Engineering, 37 (1999), 375-378. 

[130]

E. Hopper and B. Turton, Application of genetic algorithms to packing problems–A review, In Proceedings of the 2nd On-line World Conference on Soft Computing in Engineering Design and Manufacturing, Springer Verlag, London, (1997), 279–288.

[131]

E. Hopper and B. Turton, Empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem, European Journal of Operational Research, 128 (2001), 34-57. 

[132]

Q. HuA. Lim and W. Zhu, The two-dimensional vector packing problem with piecewise linear cost function, Omega (United Kingdom), 50 (2015), 43-53. 

[133]

S.-M. Hwang, C.-Y. Kao and J. T. Horng, On solving rectangle bin packing problems using genetic algorithms, In Systems, Man, and Cybernetics, Humans, Information and Technology, 1994 IEEE International Conference on IEEE, (1994), 1583–1590. doi: 10.1109/21.310541.

[134]

S. Illich and L. While, Multi-objective strip packing, Journal of Advanced Research in Evolutionary Algorithms, 1(April) (2009), 1-26. 

[135]

S. Illich, L. While and L. Barone, Multi-objective strip packing using an evolutionary algorithm, IEEE Congress on Evolutionary Computation, CEC 2007, (2007), 4207–4214.

[136]

S. ImahoriM. Yagiura and T. Ibaraki, Improved local search algorithms for the rectangle packing problem with general spatial costs, European Journal of Operational Research, 167 (2005), 48-67.  doi: 10.1016/j.ejor.2004.02.020.

[137]

S. ImahoriM. Yagiura and T. Ibaraki, Local search algorithms for the rectangle packing problem, Mathematical Programming, 3 (2003), 543-569.  doi: 10.1007/s10107-003-0427-1.

[138]

H. IwasawaY. HuH. Hashimoto and S. Imahori, A heuristic algorithm for the container loading problem with complex loading constraints, Journal of Advanced Mechanical Design, Systems, and Manufacturing, 10 (2016), 1-12. 

[139]

K. Jansen and K-M. Klein, About the structure of the integer cone and its application to bin packing, Mathematics of Operations Research, 45.4 (2020), 1498-1511.  doi: 10.1287/moor.2019.1040.

[140]

K. JansenS. KratschD. Marx and I. Schlotter, Bin packing with fixed number of bins revisited, Journal of Computer and System Sciences, 79 (2013), 39-49.  doi: 10.1016/j.jcss.2012.04.004.

[141]

J JerstichelP. De CausmaeckerF. C. R. Spieksma and G. Vanden Berghe, Exact and heuristic methods for placing ships in locks, European Journal of Operational Research, 235 (2014), 387-398.  doi: 10.1016/j.ejor.2013.06.045.

[142]

L. JunqueiraR. Morabito and D. S. Yamashita, Three-dimensional container loading models with cargo stability and load bearing constraints, Computers and Operations Research, 39 (2012), 74-85.  doi: 10.1016/j.cor.2010.07.017.

[143]

J. Jylänki, A thousand ways to pack the bin-a practical approach to two-dimensional rectangle bin packing, retrived from http://clb.demon.fi/files/RectangleBinPack.pdf, 2010.

[144]

M. A. Kaaouache and S. Bouamama, Solving bin packing problem with a hybrid genetic algorithm for VM placement in cloud, Procedia Computer Science, 60 (2015), 1061-1069. 

[145]

I. Kacem and A. Bekrar, An exact method for the 2d guillotine strip packing problem, Advances in Operations Research, 2009 (2009), 1-20. 

[146]

L. KacprzakJ. Rudy and D. Żelazny, Multi-criteria 3-dimension bin packing problem, Research in Logistics and Production, 5 (2015), 85-94. 

[147]

K. KangI. Moon and H. Wang, A hybrid genetic algorithm with a new packing strategy for the three-dimensional bin packing problem, Applied Mathematics and Computation, 219 (2012), 1287-1299.  doi: 10.1016/j.amc.2012.07.036.

[148]

J. Kang and S. Park, Algorithms for the variable sized bin packing problem, European Journal of Operational Research, 147 (2003), 365-372.  doi: 10.1016/S0377-2217(02)00247-3.

[149]

L. V. Kantorovich, Mathematical methods of organizing and planning production, Management Science, 6 (1960) 363–422. doi: 10.1287/mnsc.6.4.366.

[150]

G. CaKa rloff and H. Y. Rabani, An improved approximation algorithm for two-dimensional bin packing, Journal of Computer and System Sciences, 574 (2000), 564-574. 

[151]

A. KhanaferF. Clautiaux and E. G. Talbi, Tree-decomposition based heuristics for the two-dimensional bin packing problem with conflicts, Computers and Operations Research, 39 (2012), 54-63.  doi: 10.1016/j.cor.2010.07.009.

[152]

A. KhanaferF. Clautiaux and E. G. Talbi, The min-conflict packing problem, Computers and Operations Research, 39 (2012), 2122-2132.  doi: 10.1016/j.cor.2011.10.021.

[153]

A. KhanaferF. Clautiaux and E. G. Talbi, New lower bounds for bin packing problems with conflicts, European Journal of Operational Research, 206 (2010), 281-288.  doi: 10.1016/j.ejor.2010.01.037.

[154]

N.G. Kinnersley and M. Langston, Online variable-sized bin packing, Discrete Applied Mathematics, 22 (1989), 143-148.  doi: 10.1016/0166-218X(88)90089-3.

[155]

R. Korf, A new algorithm for optimal bin packing, Aaai/Iaai, (2002), 731–736.

[156]

R. KorfM. D. Moffitt and M. E. Pollack, Optimal rectangle packing, Annals of Operations Research, 179 (2008), 261-295.  doi: 10.1007/s10479-008-0463-6.

[157]

T. Kucukyilmaza and H. E. Kiziloz, Cooperative parallel grouping genetic algorithm for the one-dimensional bin packing problem, Computers and Industrial Engineering, 125 (2018), 157-170. 

[158]

S. Kumar, V. Rao and D. Tirupati, A heuristic procedure for one dimensional bin packing problem with additional constraints, IIMA Working Papers from Indian Institute of Management Ahmedabad, Research and Publication Department, No WP2003-11-02, (2003).

[159]

A. Laurent and N. Klement, Bin packing problem with priorities and incompatibilities using PSO: Application in a health care community, IFAC PapersOnLine, 52 (2019), 2596-2601. 

[160]

A. Layeb and S. R. Boussalia, A novel quantum inspired cuckoo search algorithm for bin packing problem, International Journal of Information Technology and Computer Science, 4 (2012), 58-67. 

[161]

J. LeeB. Kim and A. L. Johnson, 3 A two-dimensional bin packing problem with size changeable items for the production of wind turbine flanges in the open die forging industry, IIE Transactions, 45 (2012), 1332-1344. 

[162]

S.C.H. LeungX. ZhouD. Zhang and J. Zheng, Extended guided tabu search and a new packing algorithm for the two-dimensional loading vehicle routing problem, Computers and Operations Research, 38 (2011), 205-215.  doi: 10.1016/j.cor.2010.04.013.

[163]

T. W. LeungC. K. Chan and M. D. Troutt, Application of a mixed simulated annealing-genetic algorithm heuristic for the two-dimensional orthogonal packing problem, European Journal of Operational Research, 145 (2003), 530-542.  doi: 10.1016/S0377-2217(02)00218-7.

[164]

R. LewisX. SongK. Dowsland and J. Thompson, An investigation into two bin packing problems with ordering and orientation implications, European Journal of Operational Research, 213 (2011), 52-65.  doi: 10.1016/j.ejor.2011.03.016.

[165]

K. LiH. LiuY. Wu and X. Xu, A two-dimensional bin-packing problem with conflict penalties, International Journal of Production Research, 52 (2014), 7223-7238. 

[166]

C. LinJ. R. KangW. Y. Liu and C. C. Li, On two-door three-dimensional container packing problem under home delivery service, Journal of Industrial and Production Engineering, 33 (2016), 205-2014. 

[167]

Q. LiuH. ChengT. TianY. WangJ. LengR. Zhao and L. Wei, Algorithms for the variable-sized bin packing problem with time windows, Computers and Industrial Engineering, 155 (2021), 107-175.  doi: 10.1137/S009753979834669X.

[168]

W. LiuT. Deng and J. Li, Product packing and stacking under uncertainty: A robust approach, European Journal of Operational Research, 277 (2019), 903-917.  doi: 10.1016/j.ejor.2019.03.040.

[169]

Y. LiuC. Chu and K. Wang, A new heuristic algorithm for a class of two-dimensional bin-packing problems, International Journal of Advanced Manufacturing Technology, 57 (2011), 1235-1244. 

[170]

D. S. LiuK. C. TanS. Y. HuangC. K. Goh and W. K. Ho, On solving multiobjective bin packing problems using evolutionary particle swarm optimization, European Journal of operational Research, 190 (2008), 357-382.  doi: 10.1016/j.ejor.2007.06.032.

[171]

F. O. LuizS. I. RenanB. C. LuísaM. LeandroE. M. FabioM. Gabriel and B. C. Claudio, A variable neighborhood search algorithm for the bin packing problem with compatible categories, Expert Systems with Applications, 124 (2019), 209-225. 

[172]

A. LodiM. Monaci and E. Pietrobuoni, Partial enumeration algorithms for two-dimensional bin packing problem with guillotine constraints, Discrete Applied Mathematics, 217 (2017), 40-47.  doi: 10.1016/j.dam.2015.09.012.

[173]

A. LodiS. Martello and D. Vigo, Models and bounds for two-dimensional level packing problems, Journal of Combinatorial Optimization, 8 (2004), 363-379.  doi: 10.1023/B:JOCO.0000038915.62826.79.

[174]

A. LodiS. Martello and M. Monaci, Two-dimensional packing problems: A survey, European Journal of Operational Research, 141 (2002), 241-252.  doi: 10.1016/S0377-2217(02)00123-6.

[175]

A. LodiS. Martello and D. Vigo, Recent advances on two-dimensional bin packing problems, Discrete Applied Mathematics, 123 (2002), 379-396.  doi: 10.1016/S0166-218X(01)00347-X.

[176]

A. LodiS. Martello and D. Vigo, Heuristic algorithms for the three-dimensional bin packing problem, European Journal of Operational Research, 141 (2002), 410-420.  doi: 10.1016/S0377-2217(02)00134-0.

[177]

A. LodiS. Martello and D. Vigo, Approximation algorithms for the oriented two-dimensional bin packing problem, European Journal of Operational Research, 112 (1999), 158-166.  doi: 10.1287/opre.48.2.256.12386.

[178]

A. LodiS. Martello and D. Vigo, Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems, INFORMS Journal on Computing, 11 (1999), 345-357.  doi: 10.1287/ijoc.11.4.345.

[179]

K. Loh, Weight annealing heuristics for solving the two-dimensional bin packing problem outline of presentation two-dimensional bin packing problems, (2009).

[180]

E. López-CamachoH. Terashima-MarinP. Ross and G. Ochoa, A unified hyper-heuristic framework for solving bin packing problems, Expert Systems with Applications, 41 (2014), 6876-6889. 

[181]

D. Mack and A. Bortfeldt, A heuristic for solving large bin packing problems in two and three dimensions, Central European Journal of Operations Research, 20 (2012), 337-354. 

[182]

B. MahvashA. Awasthi and S. Chauhan, A column generation-based heuristic for the three-dimensional bin packing problem with rotation, Journal of the Operational Research Society, 69 (2017), 78-90. 

[183]

M. MaizaA. Labed and M. S. Radjef, Efficient algorithms for the offline variable sized bin-packing problem, Journal of Global Optimization, 57 (2013), 1025-1038.  doi: 10.1007/s10898-012-9989-x.

[184]

M. Maiza and M. S. Radjef, Heuristics for solving the bin-packing, Applied Mathematical Science, 5 (2011), 1739-1752. 

[185]

M. Maiza and C. Guéret, A new lower bound for bin-packing problem with general conflicts graph, $23^{rd}$ European Conference on Operational Research (EURO'XXIII), Bonn, Germany, (2009), 1–5.

[186]

M. Maiza, M. S. Radjef and L. Sais, Efficient lower bounds for packing problems in heterogeneous bins with conflicts constraint, Applied Mathematics and Approximation Theory, Advances in Intelligent Systems and Computing 441, (2016), 263–270.

[187]

A. Malapert, C. Guéret and N. Jussien, Two-dimensional pickup and delivery routing problem with loading constraints, In CPAIOR'08 $1^{st}$ Workshop on Bin Packing and Placement Constraints (BPPC'08), (2008), 1–6.

[188]

S. MartelloM. Monaci and D. Vigo, An exact approach to the strip-packing problem, INFORMS Journal on Computing, 15 (2003), 310-319.  doi: 10.1287/ijoc.15.3.310.16082.

[189]

S. Martello and P. Toth, Lower bounds and reduction procedures for the bin packing problem, Discrete Applied Mathematics, 28 (1990), 59-70.  doi: 10.1016/0166-218X(90)90094-S.

[190]

A. Martinez-SykoraR. Alvarez-ValdesJ. Bennell and J. M. Tamarit, Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts, Omega (United Kingdom), 52 (2015), 15-32. 

[191]

F. Mao, E. Blanco, M. Fu, R. Jain, A. Gupta, S. Mancel and Y. Tian, Small boxes big data: A deep learning approach to optimize variable sized bin packing, 2017 IEEE Third International Conference on Big Data Computing Service and Applications, (2017).

[192]

S. Mezghani, H. Chabchoub and B. Aouni, Manager's preferences in the bi-objectives bin packing problem, In 2013 $5^{th}$ International Conference on Modeling, Simulation and Applied Optimization (ICMSAO). IEEE, (2013), 1–4.

[193]

S. Mezghani and A. Frikha, Heuristics approaches for the industrial storage problem, In 2013 fifth International Conference on Modeling, Simulation and Applied Optimization, ICMSAO, (2013).

[194]

S. Mezghani and A. Frikha, A heuristic approach to the warehouse management problem: A real case study, International Journal of Logistics Systems and Management, 13 (2012), 342-357. 

[195]

S. Mezghani and A. Frikha, Three-dimensional bin packing problem with variable bin length application in industrial storage problem, $4^{th}$ International Conference on Logistics, LOGISTIQUA'2011, (2011), 508–513. doi: 10.1016/j.ejor.2009.05.040.

[196]

G. Miranda, J. De Armas, C. Segura and C. León, Hyperheuristic codification for the multi-objective 2D guillotine strip packing problem, WCCI 2010 - 2010 IEEE World Congress on Computation Intelligence, July, 18-23, Barcelona, Spain, (2010).

[197]

F. MiguelM. FrutosF. Tohmé and M. Méndez, Integrating packing and distribution problems and optimization through mathematical programming, Decision Science Letters, 5 (2016), 317-326. 

[198]

A. Moura and A. Bortfeldt, A two-stage packing problem procedure, International Transactions in Operational Research, 0 (2016), 1-16.  doi: 10.1111/itor.12251.

[199]

A.E.F. MuritibaM. IoriE. Malaguti and P. Toth, Algorithms for the bin packing problem with conflicts, INFORMS Journal on Computing, 22 (2010), 401-415.  doi: 10.1287/ijoc.1090.0355.

[200]

B. Naderi and M. Yazdani, A real multi-objective bin packing problem: A case study of an engine assembly line, Arabian Journal for Science and Engineering, 39 (2014), 5271-5277. 

[201]

N. Ntene and J. H. van Vuuren, A survey and comparison of guillotine heuristics for the 2D oriented offline strip packing problem, Discrete Optimization, 6 (2009), 174-188.  doi: 10.1016/j.disopt.2008.11.002.

[202]

J. F. OliveiraA. Neuenfeldt JúniorE. Silva and M. A. Carravilla, A survey on heuristics for the two-dimensional rectangular strip packing problem, Pesquisa Operacional, 36 (2016), 197-226. 

[203]

F. G. OrtmannN. Ntene and J. H. van Vuuren, New and improved level heuristics for the rectangular strip packing and variable-sized bin packing problems, European Journal of Operational Research, 203 (2010), 306-315.  doi: 10.1016/j.ejor.2011.06.022.

[204]

T. Osogami and H. Okano, Local search algorithms for the bin packing problem and their relationships to various, Heuristics, 9 (2003), 29-49. 

[205]

C. PaquayS. Limbourg and M. Schyns, A tailored two-phase constructive heuristic for the three-dimensional multiple bin size bin packing problem with transportation constraints, European Journal of Operational Research, 267 (2018), 52-64.  doi: 10.1016/j.ejor.2017.11.010.

[206]

C. Paquay, M. Schyns and S. Limbourg, Three dimensional bin packing problem applied to air cargo, In Proceedings of the $4^{th}$ International Conference on Information Systems, Logistics and Supply Chain Creative Logistics For an Uncertain World, (2012), 1–6.

[207]

K. ParkS. Park and W. Kim, A heuristic for an assembly line balancing problem with incompatibility, range, and partial precedence constraints, Computers and Industrial Engineering, 32 (1997), 321-332. 

[208]

F. Parre{ñ}oR. Alvarez-ValdesJ. F. Oliveira and J. M. Tamarit, A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing, Annals of Operations Research, 179 (2010), 203-220.  doi: 10.1007/s10479-008-0449-4.

[209]

S. PatelK. Patel and V. Agrawal, Effectiveness of FireFly algorithm in solving bin packing problem, International Journal of Advanced Research in Computer Science and Software Engineering, 3 (2013), 402-405. 

[210]

J. Pereira, Procedures for the bin packing problem with precedence constraints, European Journal of Operational Research, 17 (2015), 48-1.  doi: 10.1016/j.ejor.2015.10.048.

[211]

J. Pereira and M. Vilà, Variable neighborhood search heuristics for a test assembly design problem, Expert Systems with Applications, 42 (2015), 4805-4817. 

[212]

N. Pillay, A study of evolutionary algorithm selection hyper-heuristics for the one-dimensional bin-packing problem, South African Computer Journal, 48 (2012), 31-40. 

[213]

C.-M. PinteaC. Pascan and M. Hajdu-Macelaru, Comparing several heuristics for a packing problem, International Journal of Advanced Intelligence Paradigms, 4 (2012), 268-277. 

[214]

D. Pisinger and M. Sigurd, Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem, INFORMS Journal on Computing, 19 (2007), 36-51.  doi: 10.1287/ijoc.1060.0181.

[215]

D. Pisinger and M. Sigurd, The two-dimensional bin packing problem with variable bin sizes and costs, Discrete Optimization, 2 (2005), 154-167.  doi: 10.1016/j.disopt.2005.01.002.

[216]

S. Polyakovskiy and R. M'Hallah, Just-in-time two-dimensional bin packing, Omega, 102 (2021), 102-311. 

[217]

S. Polyakovskiy and R. M'Hallah, A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates, European Journal of Operational Research, 266 (2018), 819-839.  doi: 10.1016/j.ejor.2017.10.046.

[218]

S. Polyakovsky and R. M'Hallah, An agent-based approach to the two-dimensional guillotine bin packing problem, European Journal of Operational Research, 192 (2009), 767-781. 

[219]

J. Puchinger and G. R. Raidl, Models and algorithms for three-stage two-dimensional bin packing, European Journal of Operational Research, 183 (2007), 1304-1327.  doi: 10.1016/j.ejor.2005.11.064.

[220]

M. Quiroz-CastellanosL. Cruz-ReyesJ. Torres-JimenezS. C. GomezJ. F. HuacujaA. Héctor and C. F. Alvim, A grouping genetic algorithm with controlled gene transmission for the bin packing problem, Computers and Operations Research, 55 (2014), 52-64.  doi: 10.1016/j.cor.2014.10.010.

[221]

R. G. van Vuuren and J. H. van Rakotonirainy, Improved metaheuristics for the two-dimensional strip packing problem, Applied Soft Computing, 92 (2020), 106-268. 

[222]

A. G. RamosJ. F. Oliveira and M. P. Lopes, A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions, International Transactions in Operational Research, 23 (2016), 215-238.  doi: 10.1111/itor.12124.

[223]

K. RaphaelD. Mauro and I. Manuel, Bin packing problem with general precedence constraints, Journal of Chemical Information and Modeling, 53 (2013), 1689-1699. 

[224]

M. RemicG. Žerovnik and J. Žerovnik, An experimental comparison of some heuristics for cardinality constrained bin packing problem, Business Systems Research, 3 (2012), 57-63. 

[225]

J. RenY. Tian and T. Sawaragi, A tree search method for the container loading problem with shipment priority, European Journal of Operational Research, 214 (2011), 526-535. 

[226]

M. G. C. Resende and J. F. Gonçalve, A hybrid heuristic for the constrained two-dimensional non-guillotine orthogonal cutting problem, AT & T Labs Research Technical Report, (2006).

[227]

M. C. RiffX. Bonnaire and B. Neveu, A revision of recent approaches for two-dimensional strip-packing problems, Engineering Applications of Artificial Intelligence, 22 (2009), 833-837. 

[228]

P. Ross, J. G. Marin-Blazquez, S. Schulenburg and E. Hart, Learning a procedure that can solve hard bin-packing problems: A new GA-based approach to hyper-heuristics, In Genetic and Evolutionary Computation Conference (GECCO), (2003), 1295–1306.

[229]

P. Ross, S. Schulenburg, J. G. Marin-Blazquez and E. Hart, Hyper-heuristics: learning to combine simple heuristics in bin-packing problems, In Proceedings of the 12th annual conference on Genetic and evolutionary computation, (2002), 942–948.

[230]

R. Sadykov and F. Vanderbeck, Bin packing with conflicts: A generic branch-and-price algorithm, INFORMS Journal on Computing, 25 (2013), 244-255.  doi: 10.1287/ijoc.1120.0499.

[231]

R.D. Saraiva, N. Nepomuceno and P. R. Pinheiro, A layer-building algorithm for the three-dimensional multiple bin packing problem: A case study in an automotive company, In IFAC Proceedings Volumes (IFAC-PapersOnline), (2015). 490–495.

[232]

M. Sathe, O Schenk and H. Burkhart, Solving bi-objective many-constraint bin packing problems in automobile sheet metal forming processes, In International Conference on Evolutionary Multi-Criterion Optimization. Springer Berlin Heidelberg, (2009), 246–260.

[233]

A. SavićT. Šukilović and V. Filipović, Solving the two-dimensional packing problem with m- M calculus, Journal of Operations Research, 21 (2011), 93-102.  doi: 10.2298/YJOR1101093S.

[234]

P. Schaus and Y. Deville, A global constraint for bin-packing with precedences: Application to the assembly line balancing problem, In Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, (July 13-17), 369–374.

[235]

X ScheplerA. RossiE. Gurevsky and A. Dolgui, Solving robust bin-packing problems with a branch-and-price approach, European Journal of Operational Research, 297 (2021), 795-1192.  doi: 10.1016/j.ejor.2021.05.041.

[236]

A. SchollR. Klein and C. Jürgens, Bison: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem, Computers and Operations Research, 24(7) (1997), 627-645. 

[237]

M. Serairi and M. Haouari, A computational study of lower bounds for the two dimensional bin packing problem, Electronic Notes in Discrete Mathematics, 36(C) (2010), 891-897. 

[238]

E. SilvaJ.F. Oliveira and G. Wäscher, 2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problems, European Journal of Operational Research, 237 (2014), 846-856.  doi: 10.1016/j.ejor.2014.02.059.

[239]

K. Sim, E. Hart and B. Paechter, A hyper-heuristic classifier for one dimensional bin packing problems: Improving classification accuracy by attribute evolution, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7492 LNCS(PART 2), (2012), 48–357.

[240]

A. Soke and Z. Bingul, Hybrid genetic algorithm and simulated annealing for two-dimensional non-guillotine rectangular packing problems, Engineering Applications of Artificial Intelligence, 19 (2006), 557-567. 

[241]

U. Sommerweiß, Heuristics for the rectangle packing problem, Partially supported by BMBF, registration number 03-TE7DRE-8, 3 (1996), 1-21. 

[242]

D. Stathis, I. Vourkas and G. C. Sirakoulis, Solving AI problems with memristors: A case study for optimal bin packing, In PCI'14, October 02 - 04 2014, Athens, Greece, (2014), 1–6.

[243]

Y. Tao and F. Wang, An effective tabu search approach with improved loading algorithms for the 3L-CVRP, Computers and Operations Research, 55 (2015), 127-140.  doi: 10.1016/j.cor.2013.10.017.

[244]

J. TernoG. ScheithauerU. Sommerweiß and J. Riehme, An efficient approach for the multi-pallet loading problem, European Journal of Operational Research, 123 (2000), 372-381.  doi: 10.1016/S0377-2217(99)00263-5.

[245]

T. TianW. ZhuA. Lim and L. Wei, The multiple container loading problem with preference, European Journal of Operational Research, 248 (2016), 84-94.  doi: 10.1016/j.ejor.2015.07.002.

[246]

T. A. M. Toffolo, E. Esprit, T. Wauters and G. Vanden Berghe, A two-dimensional heuristic decomposition approach to a three-dimensional multiple container loading problem, European Journal of Operational Research, (2016), 1–26. doi: 10.1016/j.ejor.2016.07.033.

[247]

N. VakhaniaaJ. A. Hernandezb and C. Zavala, A single-machine scheduling problem to minimize the maximum lateness is tightly related with a variation of bin packing problem with different bin, Ciência e Técnica Vitivinícola, 30 (2015), 0-15. 

[248]

J. M. V. De Carvalho, LP models for bin packing and cutting stock problems, European Journal of Operational Research, 141 (2002), 253-273.  doi: 10.1016/S0377-2217(02)00124-8.

[249]

J. P. L. Viegas, S. M. Vieira, J. M. C. Sousa and E. M. P. Henriques, Metaheuristics for the 3D bin packing problem in the steel industry, Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014, (2014), 338–343.

[250]

N. WangJ. S. WangY. X. Zhang and T. Z. Li, Two-dimensional bin-packing problem with rectangular and circular regions solved by genetic algorithm, IAENG International Journal of Applied Mathematics, 51 (2021), 1-11. 

[251]

Y. Wang and L. Chen, Two-dimensional residual-space-maximized packing, Expert Systems with Applications, 42 (2015), 3297-3305. 

[252]

B. Wang, J. Liu and Y. Y. M. Keech, A constructive heuristic for two-dimensional bin packing, Proceedings of the 2012 2nd International Conference on Computer and Information Applications (ICCIA 2012), (2012), 210–213.

[253]

G. WäscherH. Haußner and H. Schumann, An improved typology of cutting and packing problems, European Journal of Operational Research, 183 (2007), 1109-1130. 

[254]

S. Watanabe, T. Hiroyasu and M. Miki, Multi-objective rectangular packing problem and its applications, In Evolutionary Multi-Criterion Optimization, Proceedings, (2003), 565–577.

[255]

L. WeiZ. ZhangD. Zhang and A. Lim, A variable neighborhood search for the capacitated vehicle routing problem with two-dimensional loading constraints, European Journal of Operational Research, 243 (2015), 798-814. 

[256]

L. WeiW. C. OonW. Zhu and A. Lim, A goal-driven approach to the 2D bin packing and variable-sized bin packing problems, European Journal of Operational Research, 224 (2013), 110-121.  doi: 10.1016/j.ejor.2012.08.005.

[257]

L. WeiW. C. OonW. Zhu and A. Lim, A skyline heuristic for the 2D rectangular packing and strip packing problems, European Journal of Operational Research, 215 (2011), 337-346.  doi: 10.1016/j.ejor.2011.06.022.

[258]

M. WittemanQ. Deng and B. F. Santos, A bin packing approach to solve the aircraft maintenance task allocation problem, European Journal of Operational Research, 294 (2021), 365-376.  doi: 10.1016/j.ejor.2021.01.027.

[259]

L. WongL. S. Lee and U. P. M. Serdang, Heuristic placement routines for two-dimensional bin packing problem, Journal of Mathematics and Statistics, 5 (2009), 334-341. 

[260]

L. WuX. LiC. Liu and W. Xiao, NHACR: A novel heuristic approach for 2D rectangle packing area minimization problem with central rectangle, Engineering Applications of Artificial Intelligence, 103 (2021), 104-291. 

[261]

Y. WuW. LiM. Goh and R. Souza, Three dimensional bin packing problem with variable bin height, European Journal of Operational Research, 202 (2010), 347-355.  doi: 10.1016/j.ejor.2009.05.040.

[262]

L. Xueping, Z. Zhaoxia and K. Zhang, A genetic algorithm for the three-dimensional bin packing problem with heterogeneous bins, In Proceedings of the 2014 Industrial and Systems Engineering Research Conference, (2014).

[263]

Y. YaoC. Lai and Y. Cui, A constructive heuristic for the two-dimensional bin packing based on value correction, International Journal of Computer Applications in Technology, 55 (2017), 12-21. 

[264]

A. Yarimcam, S. Asta, E. Ozcan and A. J. Parkes, Heuristic generation via parameter tuning for online bin packing, In IEEE SSCI 2014 - 2014 IEEE Symposium Series on Computational Intelligence - EALS 2014: 2014 IEEE Symposium on Evolving and Autonomous Learning Systems, Proceedings, (2014), 102–108.

[265]

R. Yesodha and T. Amudha, Bio-inspired metaheuristics for bin packing problems, International Journal of Emerging Technologies in Computational and Applied Sciences (IJETCAS), 1961 (2013), 329-333. 

[266]

Y. Yuan, Y.J. Li and Y. Q. Wang, An improved ACO algorithm for the bin packing problem with conflicts based on graph coloring model, In International Conference on Management Science and Engineering - Annual Conference Proceedings, (2014), 3–9.

[267]

G Zhang and R. E. Burkard, A new version of on-line variable-sized bin packing, Discrete Applied Mathematics, 72 (1997), 193-197.  doi: 10.1016/S0166-218X(96)00018-2.

[268]

Z. ZhangS. GuoW. ZhuW. C. Oon and A. Lim, Space defragmentation heuristic for 2D and 3D bin packing problems, IJCAI International Joint Conference on Artificial Intelligence, 3 (2011), 699-704.  doi: 10.1016/j.ejor.2012.05.031.

[269]

D. ZhangL. S. C. H. Shi and T. Wu, A priority heuristic for the guillotine rectangular packing problem, Information Processing Letters, 116 (2016), 15-21. 

[270]

X. Zhao and H. Shen, Online algorithms for 2D bin packing with advice, Neurocomputing, 189 (2016), 25-32. 

[271]

D. Zhu, Max-min bin packing algorithm and its application in nano-particles filling, Chaos, Solitons & Fractals, 89 (2016), 83-90. 

[272]

W. ZhuZ. ZhangW. C. Oon and A. Lim, Space defragmentation for packing problems, European Journal of Operational Research, 222 (2012), 452-462.  doi: 10.1016/j.ejor.2012.05.031.

[273]

A. ZudioD. H. da Silva CostaB. P. MasquioI. M. Coelho and P. E. D. Pinto, BRKGA/VND hybrid algorithm for the classic three-dimensional bin packing problem, Electronic Notes in Discrete Mathematics, 66 (2018), 175-182.  doi: 10.1016/j.endm.2018.03.023.

Figure 1.  Example of bin packing
Figure 2.  The distribution of problem types according to addressed characteristics (Dimensionality, constraints, No constraints)
Figure 3.  % of BPP constraints through the years
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)}
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)}
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
Year Number of papers
1980-1989 10
1990-1999 14
2000-2004 23
2005-2009 40
2010-2014 83
2015-2022 80
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
2.1.2.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
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
2.1.2.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
Table 4.  Number of papers where the constraint types have been discussed
Constraints type Number of papers ($ N=250 $)
No constraints 122
Orientation 64
Guillotine 33
Precedence 28
Fragility 11
Stability 14
Conflicts 29
Constraints type Number of papers ($ N=250 $)
No constraints 122
Orientation 64
Guillotine 33
Precedence 28
Fragility 11
Stability 14
Conflicts 29
Table 5.  Number of papers where the constraint types have been discussed
Number of Constraints 0 1 2 3 4 5 6
Number of papers ($ N=232 $) 122 84 32 7 2 0 0
Number of Constraints 0 1 2 3 4 5 6
Number of papers ($ N=232 $) 122 84 32 7 2 0 0
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
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
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
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
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
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
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
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
[1]

Wenxun Xing, Feng Chen. A-shaped bin packing: Worst case analysis via simulation. Journal of Industrial and Management Optimization, 2005, 1 (3) : 323-335. doi: 10.3934/jimo.2005.1.323

[2]

Mao Chen, Xiangyang Tang, Zhizhong Zeng, Sanya Liu. An efficient heuristic algorithm for two-dimensional rectangular packing problem with central rectangle. Journal of Industrial and Management Optimization, 2020, 16 (1) : 495-510. doi: 10.3934/jimo.2018164

[3]

Chuanxin Zhao, Lin Jiang, Kok Lay Teo. A hybrid chaos firefly algorithm for three-dimensional irregular packing problem. Journal of Industrial and Management Optimization, 2020, 16 (1) : 409-429. doi: 10.3934/jimo.2018160

[4]

Ankhbayar Chuluunbaatar, Burmaa Galaa, Enkhbat Rentsen. Application of sphere packing theory in financial management. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022092

[5]

Shinji Imahori, Yoshiyuki Karuno, Kenju Tateishi. Pseudo-polynomial time algorithms for combinatorial food mixture packing problems. Journal of Industrial and Management Optimization, 2016, 12 (3) : 1057-1073. doi: 10.3934/jimo.2016.12.1057

[6]

Georg Vossen, Torsten Hermanns. On an optimal control problem in laser cutting with mixed finite-/infinite-dimensional constraints. Journal of Industrial and Management Optimization, 2014, 10 (2) : 503-519. doi: 10.3934/jimo.2014.10.503

[7]

Ernesto A. Lacomba, Mario Medina. Oscillatory motions in the rectangular four body problem. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 557-587. doi: 10.3934/dcdss.2008.1.557

[8]

Yi Jiang, Chuan Luo, Shenggui Ling. An efficient cutting plane algorithm for the smallest enclosing circle problem. Journal of Industrial and Management Optimization, 2017, 13 (1) : 147-153. doi: 10.3934/jimo.2016009

[9]

Elena Celledoni, Markus Eslitzbichler, Alexander Schmeding. Shape analysis on Lie groups with applications in computer animation. Journal of Geometric Mechanics, 2016, 8 (3) : 273-304. doi: 10.3934/jgm.2016008

[10]

Barbara Kaltenbacher, Gunther Peichl. The shape derivative for an optimization problem in lithotripsy. Evolution Equations and Control Theory, 2016, 5 (3) : 399-430. doi: 10.3934/eect.2016011

[11]

Lekbir Afraites, Chorouk Masnaoui, Mourad Nachaoui. Shape optimization method for an inverse geometric source problem and stability at critical shape. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 1-21. doi: 10.3934/dcdss.2021006

[12]

Ruiheng Cai, Feng-kuang Chiang. A laser-cutting-centered STEM course for improving engineering problem-solving skills of high school students in China. STEM Education, 2021, 1 (3) : 199-224. doi: 10.3934/steme.2021015

[13]

Jaroslav Haslinger, Raino A. E. Mäkinen, Jan Stebel. Shape optimization for Stokes problem with threshold slip boundary conditions. Discrete and Continuous Dynamical Systems - S, 2017, 10 (6) : 1281-1301. doi: 10.3934/dcdss.2017069

[14]

Masataka Shibata. Asymptotic shape of a solution for the Plasma problem in higher dimensional spaces. Communications on Pure and Applied Analysis, 2003, 2 (2) : 259-275. doi: 10.3934/cpaa.2003.2.259

[15]

Alberto Bressan, Sondre Tesdal Galtung. A 2-dimensional shape optimization problem for tree branches. Networks and Heterogeneous Media, 2021, 16 (1) : 1-29. doi: 10.3934/nhm.2020031

[16]

John Sebastian Simon, Hirofumi Notsu. A shape optimization problem constrained with the Stokes equations to address maximization of vortices. Evolution Equations and Control Theory, 2022  doi: 10.3934/eect.2022003

[17]

E. Minguzzi. A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena. Journal of Geometric Mechanics, 2015, 7 (4) : 473-482. doi: 10.3934/jgm.2015.7.473

[18]

Mourad Azi, Mohand Ouamer Bibi. Optimal control of a dynamical system with intermediate phase constraints and applications in cash management. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 279-291. doi: 10.3934/naco.2021005

[19]

Arezu Zare, Mohammad Keyanpour, Maziar Salahi. On fractional quadratic optimization problem with two quadratic constraints. Numerical Algebra, Control and Optimization, 2020, 10 (3) : 301-315. doi: 10.3934/naco.2020003

[20]

Nidhal Gammoudi, Hasnaa Zidani. A differential game control problem with state constraints. Mathematical Control and Related Fields, 2022  doi: 10.3934/mcrf.2022008

2021 Impact Factor: 1.411

Metrics

  • PDF downloads (127)
  • HTML views (256)
  • Cited by (0)

[Back to Top]