Geodesic
Loading optimization of an ordered set of aircrafts
Matematičeskoe modelirovanie, Tome 32 (2020) no. 4, pp. 43-56.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper deals with the problem of optimal loading of the air vehicles set, ordered in accordance with the given priority rules. The regarded problem is formalized as a mixedinteger linear programming task. Proposed formalization requires twice less binary variables to formalize the conditions for the absence of the intersections of loaded objects in comparison with approaches, regarded in literature. The exact solution technology, designed in the form of a public web-service, is presented. Features and practical significance of the developed technology are described.
Keywords: aircraft loading, container packing, mixed-integer linear programming. 
@article{MM_2020_32_4_a3,
     author = {I. P. Bogdanov and V. A. Sudakov and N. B. Toporov},
     title = {Loading optimization of an ordered set of aircrafts},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {43--56},
     publisher = {mathdoc},
     volume = {32},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_4_a3/}
}
TY  - JOUR
AU  - I. P. Bogdanov
AU  - V. A. Sudakov
AU  - N. B. Toporov
TI  - Loading optimization of an ordered set of aircrafts
JO  - Matematičeskoe modelirovanie
PY  - 2020
SP  - 43
EP  - 56
VL  - 32
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2020_32_4_a3/
LA  - ru
ID  - MM_2020_32_4_a3
ER  - 
%0 Journal Article
%A I. P. Bogdanov
%A V. A. Sudakov
%A N. B. Toporov
%T Loading optimization of an ordered set of aircrafts
%J Matematičeskoe modelirovanie
%D 2020
%P 43-56
%V 32
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2020_32_4_a3/
%G ru
%F MM_2020_32_4_a3
I. P. Bogdanov; V. A. Sudakov; N. B. Toporov. Loading optimization of an ordered set of aircrafts. Matematičeskoe modelirovanie, Tome 32 (2020) no. 4, pp. 43-56. http://geodesic.mathdoc.fr/item/MM_2020_32_4_a3/

[1] E. E. Bischoff, M. S.W. Ratcliff, “Issues in the development of approaches to container loading”, Omega, The International Journal of Management Science, 23:4 (1995), 377–390 | DOI

[2] A. Bortfeldt, G. W?scher, “Constraints in container loading A state-of-the-art review”, European Journal of Operational Research, 229:1 (2013), 1–20 | DOI | MR | Zbl

[3] J. Egeblad, C. Garavelli, S. Lisi, D. Pisinger, “Heuristics for container loading of furniture”, European Journal of Operational Research, 200:3 (2010), 881–892 | DOI | MR | Zbl

[4] C. Paquay, M. Schyns, S. Limbourg, “A mixed integer programming formulation for the three-dimensional bin packing problem deriving from an air cargo application”, International Transactions in Operational Research, 23:1-2 (2016), 187–213 | DOI | MR | Zbl

[5] M. R. Garey, D. S. Johnson, Computers and intractability: a guide to the theory of NP-completeness, W. H. Freeman and Company, San Francisco, 1979 | MR | Zbl

[6] V. V. Psiola, “O priblizhennom reshenii trekhmernoi zadachi ob upakovke na osnove evristik”, Intellektualnye sistemy, 11:1–4 (2007), 83–100

[7] M. Eley, “A bottleneck assignment approach to the multiple container loading problem”, OR Spectrum, 25:1 (2003), 45–60 | DOI | MR | Zbl

[8] A. Lim, H. Ma, J. Xu, X. Zhang, “An iterated construction approach with dynamic prioritization for solving the container loading problems”, Expert Systems with Applications, 39:4 (2012), 4292–4305 | DOI

[9] Z. Jin, T. Ito, K. Ohno, “The three-dimensional bin packing problem and its practical algorithm”, JSME International Journal Series, 46:1 (2003), 60–66 | DOI

[10] C. H. Che, W. Huang, A. Lim, W. Zhu, “The multiple container loading cost minimization problem”, European Journal of Operational Research, 214:3 (2011), 501–511 | DOI | Zbl

[11] C. S. Chen, S. M. Lee, Q. S. Shen, “An analytical model for the container loading problem”, European Journal of Operational Research, 80:1 (1995), 68–76 | DOI | Zbl

[12] M. Padberg, “Packing small boxes into a big box”, Mathematical Methods of Operations Research, 52:1 (2000), 1–21 | DOI | MR | Zbl

[13] H. T. Hong Ha, N. Nananukul, “Air cargo loading management system for logistics forwarders”, Proceedings of 2016 International Conference on Urban Planning, Transport and Construction Engineering, ICUPTCE'16 (Pattaya, Jan. 2–3, 2016), 51–58

[14] L. Junqueira, R. Morabito, D. S. Yamashita, “Three-dimensional container loading models with cargo stability and load bearing constraints”, Computers Operations Research, 39:1 (2012), 74–85 | DOI | MR | Zbl

[15] V. P. Osipov, V. A. Sudakov, Kombinirovannyi metod podderzhki priniatiia mnogokriterialnyh reshenii, Keldysh Institute preprints, 2015, 21 pp.

[16] B. Korte, J. Vygen, Combinatorial optimization: theory and algorithms, Springer-Verlag, Berlin–Heidelberg, 2006 | MR

[17] T. C. Hu, Integer programming and network flows, Addison-Wesley Publishing Company, Reading, Massachusetts, 1970 | MR

[18] J. T. Linderoth, T. K. Ralphs, “Noncommercial software for mixed-integer linear programming”, Integer Programming: Theory and Practice, Operations Research Series, CRC Press, 2005, 253–303 | MR

[19] T. Achterberg, “SCIP: solving constraint integer programs”, Mathematical Programming Computation, 1:1 (2009), 1–41 | DOI | MR | Zbl

[20] H. Pollaris, K. Braekers, A. Caris, G. K. Janssens, S. Limbourg, “Vehicle routing problems with loading constraints: state-of-the-art and future directions”, OR Spectrum, 37:2 (2015), 297–330 | DOI | MR | Zbl