Cargo Stability in the Container Loading Problem - State-of-the-Art and Future Research Directions

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 223)


The purpose of this paper is to present the current understanding and conceptualization of the cargo stability constraint within the context of the Container Loading Problem. This problem is highly relevant in the transportation industry due to the increasing pressure for a more economically, environmentally and socially efficient and sustainable cargo transportation. Stability is one the most important practical relevant constraints in the Container Loading Problem due to its strong influence on the cargo arrangement. Stability is usually divided into stability during loading operations (static) and stability during transportation (dynamic). Two main contributions are made. Firstly, an overview of recent developments in the literature on the two types of stability, static and dynamic, is provided. Secondly, of opportunities for future research are identified.


Container loading Static stability Dynamic stability 



The research was partially supported by ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme within project “POCI-01-0145-FEDER-006961”, and by National Funds through the Portuguese funding agency, FCT – Fundação para a Ciência e a Tecnologia as part of project “UID/EEA/50014/2013”.


  1. 1.
    G. Abdou, M. Elmasry, 3D random stacking of weakly heterogeneous palletization problems. Int. J. Prod. Res. 37(7), 1505–1524 (1999)Google Scholar
  2. 2.
    I. Araya, M.C. Riff, A beam search approach to the container loading problem. Comput. Oper. Res. 43, 100–107 (2014)Google Scholar
  3. 3.
    E.E. Bischoff, Stability aspects of pallet loading. OR Spektrum 13(4), 189–197 (1991)Google Scholar
  4. 4.
    E.E. Bischoff, M.S.W Ratcliff, Issues in the development of approaches to container loading. Omega 23(4), 377–390 (1995)Google Scholar
  5. 5.
    E.E. Bischoff, F. Janetz, M.S.W. Ratcliff. Loading pallets with non-identical items. Eur. J. Oper. Res. 84(3): 681–692 (1995)Google Scholar
  6. 6.
    A. Bortfeldt, H. Gehring, A hybrid genetic algorithm for the container loading problem. Eur. J. Oper. Res. 131(1), 143–161 (2001)Google Scholar
  7. 7.
    A. Bortfeldt, G. Wäscher, Constraints in container loading-a state-of-the-art review. Eur. J. Oper. Res. 229(1), 1–20 (2013)Google Scholar
  8. 8.
    H. Carpenter, W.B. Dowsland, Practical considerations of the pallet-loading problem. J. Oper. Res. Soc. 36(6), 489–497 (1985)Google Scholar
  9. 9.
    S.G. Christensen, Container loading with multi-drop constraints. Int. Trans. Oper. Res. 16(6), 727–743 (2009)Google Scholar
  10. 10.
    A.P. Davies, E.E. Bischoff, Weight distribution considerations in container loading. Eur. J. Oper. Res. 114(3), 509–527 (1999)Google Scholar
  11. 11.
    J.L. de Castro Silva, N.Y. Soma, N. Maculan, A greedy search for the three-dimensional bin packing problem: the packing static stability case. Int. Trans. Oper. Res. 10(2), 141–153 (2003)Google Scholar
  12. 12.
    G. Fuellerer, K.F. Doerner, R.F. Hartl, M. Iori, Metaheuristics for vehicle routing problems with three-dimensional loading constraints. Eur. J. Oper. Res. 201(3), 751–759 (2010)Google Scholar
  13. 13.
    H. Gehring, A. Bortfeldt, A genetic algorithm for solving the container loading problem. Int. Trans. Oper. Res. 4(5–6), 401–418 (1997)Google Scholar
  14. 14.
    M. Gendreau, M. Iori, G. Laporte, S. Martello, A Tabu search algorithm for a routing and container loading problem. Transp. Sci. 40(3), 342–350 (2006)Google Scholar
  15. 15.
    J.F. Gonçalves, M.G. Resende, A parallel multi-population biased random-key genetic algorithm for a container loading problem. Comput. Oper. Res. 39, 179–190 (2012)Google Scholar
  16. 16.
    IMO/ILO/UNECE, IMO/ILO/UNECE Code of Practice for Packing of Cargo Transport Units, vol. 4 (International Maritime Organization, 2014)Google Scholar
  17. 17.
    L. Junqueira, R. Morabito, On solving three-dimensional open-dimension rectangular packing problems. Eng. Optim. 49(5), 733–745 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    J.L. Lin, C.H. Chang, J.Y. Yang, A study of optimal system for multiple-constraint multiple-container packing problems, in Advances in Applied Artificial Intelligence, vol. 4031, Lecture Notes in Computer Science, ed. by M. Ali, R. Dapoigny (Springer, Berlin, 2006), pp. 1200–1210Google Scholar
  19. 19.
    D. Mack, A. Bortfeldt, H. Gehring, A parallel hybrid local search algorithm for the container loading problem. Int. Trans. Oper. Res. 11, 511–533 (2004)Google Scholar
  20. 20.
    D. Männel, A. Bortfeldt, A hybrid algorithm for the vehicle routing problem with pickup and delivery and three-dimensional loading constraints. Eur. J. Oper. Res. 254(3), 840–858 (2016)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    A. Moura, J.F. Oliveira, A GRASP approach to the container-loading problem. IEEE Intell. Syst. 20(4), 50–57 (2005)Google Scholar
  22. 22.
    B.K.A. Ngoi, M.L. Tay, E.S. Chua, Applying spatial representation techniques to the container packing problem. Int. J. Prod. Res. 32(1), 111–123 (1994)Google Scholar
  23. 23.
    F. Parreño, R. Alvarez-Valdes, J.M. Tamarit, J.F. Oliveira, A maximal-space algorithm for the container loading problem. INFORMS J. Comput. 20(3), 412–422 (2008)Google Scholar
  24. 24.
    A.G. Ramos, J.F. Oliveira, J.F. Gonçalves, M.P. Lopes, Dynamic stability metrics for the container loading problem. Transp. Res. Part C: Emerg. Technol. 60, 480–497 (2015)CrossRefGoogle Scholar
  25. 25.
    A.G. Ramos, J.F. Oliveira, J.F. Gonçalves, M.P. Lopes, A container loading algorithm with static mechanical equilibrium stability constraints. Transp. Res. Part B: Methodol. 91, 565–581 (2016)CrossRefGoogle Scholar
  26. 26.
    A.G. Ramos, J.F. Oliveira, M.P. Lopes, A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions. Int. Trans. Oper. Res. 23(1–2), 215–238 (2016)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    A.G. Ramos, J. Jacob, J.F. Justo, J.F. Oliveira, R. Rodrigues, A.M. Gomes, Cargo dynamic stability in the container loading problem - a physics simulation tool approach. Int. J. Simul. Process Model. 12(1), 29–41 (2017)CrossRefGoogle Scholar
  28. 28.
    C.D. Tarantilis, E.E. Zachariadis, C.T. Kiranoudis, A hybrid metaheuristic algorithm for the integrated vehicle routing and three-dimensional container-loading problem. IEEE Trans. Intell. Transp. Syst. 10(2), 255–271 (2009)Google Scholar
  29. 29.
    G. Wäscher, H. Hauß ner, H. Schumann, An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007)Google Scholar
  30. 30.
    D. Zhang, Y. Peng, S.C. Leung, A heuristic block-loading algorithm based on multi-layer search for the container loading problem. Comput. Oper. Res. 39(10), 2267–2276 (2012)Google Scholar
  31. 31.
    W. Zhu, A. Lim, A new iterative-doubling Greedy–Lookahead algorithm for the single container loading problem. Eur. J. Oper. Res. 222(3), 408–417 (2012)Google Scholar

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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.INESC TEC and CIDEM, School of EngineeringPolytechnic of PortoPortoPortugal
  2. 2.INESC TEC and Faculty of EngineeringUniversity of PortoPortoPortugal

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