Minimizing overstowage in master bay plans of large container ships

  • Shih-Liang ChaoEmail author
  • Pi-Hung Lin
Original Article


This study proposes a mathematical model that minimizes overstowage in class-based master bay plans for large container ships. With the advantage of an underlying multi-commodity network structure, solutions are obtained within reasonable computation time in the case of 14,000-TEU ships. In addition, changeable bay configuration patterns due to different container sizes—an important but rarely discussed issue—are efficiently addressed by adding specially designed arcs and side constraints. Our model can support container stowage planners by providing a flexible and efficient approach for allocating ship slots to containers of different lengths when preparing class-based master bay plans for large container ships.


Containers Liner shipping Stowage planning Multi-commodity networks 



The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this work under Contract No. NSC 101-2410-H-019-023.


  1. Alvarez, J. 2006. A heuristic for vessel planning in a reach stacker terminal. Journal of Maritime Research III (1): 3–16.Google Scholar
  2. Ambrosino, D., M. Paolucci, and A. Sciomachen. 2015. Experimental evaluation of mixed integer programming models for the multi-port master bay plan problem. Flexible Services and Manufacturing Journal 27 (2–3): 263–284.CrossRefGoogle Scholar
  3. Ambrosino, D., M. Paolucci, and A. Sciomachen. 2017. Computational evaluation of a MIP model for multi-port stowage planning problems. Soft Computing 21: 1753–1763.CrossRefGoogle Scholar
  4. Ambrosino, D., M. Paolucci, and A. Sciomachen. 2018. Shipping liner company stowage plans: An optimization approach. In Advanced concepts, methodologies and technologies for transportation and logistics, ed. J. Żak, Y. Hadas, and R. Rossi, 405–420. Cham: Springer International Publishing. Scholar
  5. Aslidis, A.H. 1989. Combinatorial algorithms for stacking problems. Ph.D. Dissertation, Massachusetts Institute of Technology.Google Scholar
  6. Avriel, M., and M. Penn. 1993. Exact and approximate solutions of the container ship stowage problem. Computers & Industrial Engineering 25 (1–4): 271–274.CrossRefGoogle Scholar
  7. Avriel, M., M. Penn, and N. Shpirer. 2000. Container ship stowage problem: complexity and connection to the coloring of circle graphs. Discrete Applied Mathematics 103 (1–3): 271–279.CrossRefGoogle Scholar
  8. Avriel, M., M. Penn, N. Shpirer, and S. Witteboon. 1998. Stowage planning for container to reduce the number of shifts. Annals of Operations Research 76: 55–71.CrossRefGoogle Scholar
  9. Christensen, J.M., and D. Pacino. 2017. A matheuristic for the Cargo Mix Problem with block stowage. Transportation Research Part E: Logistics and Transportation Review 97: 151–171.CrossRefGoogle Scholar
  10. Ding, D., and M.C. Chou. 2015. Stowage planning for container ships: A heuristic algorithm to reduce the number of shifts. European Journal of Operational Research 246 (1): 242–249.CrossRefGoogle Scholar
  11. Iris, C., and D. Pacino. 2015. A survey on the ship loading problem. In 6th International conference on computational logistics (ICCL 2015), vol. 9335, ed. F. Corman, S. Voß, and R.R. Negenborn, 238–251., Lecture notes in computer science Cham: Springer International Publishing.Google Scholar
  12. Jensen, R.M., and M.L. Ajspur. 2018. The standard capacity model: Towards a polyhedron representation of container vessel capacity. In Computational logistics, vol. 11184, ed. R. Cerulli, A. Raicone, and S. Voß, 175–190., Lecture notes in computer science Cham: Springer.CrossRefGoogle Scholar
  13. Kim, K., and J. Bae. 1998. Re-marshalling export containers in port container terminals. Computers and Industry Engineering 35: 655–658.CrossRefGoogle Scholar
  14. Kim, K., and H. Kim. 1999a. Segregating space allocation models for container inventories in port container terminals. International Journal of Production Economics 59(1–3): 415–423.Google Scholar
  15. Kim, K., and K. Kim. 1999b. An optimal routing algorithm for a transfer crane in port container terminals. Transportation Science 33: 17–33.CrossRefGoogle Scholar
  16. Kim, K., Y. Park, and K. Ryu. 2000. Deriving decision rules to locate export containers in container yards. European Journal of Operational Research 124: 89–101.CrossRefGoogle Scholar
  17. Malawski, M., K. Figiela, M. Bubak, E. Deelman, and J. Nabrzyski. 2014. Cost optimization of execution of multi-level deadline-constrained scientific workflows on clouds. In Parallel processing and applied mathematics (PPAM 2013), ed. R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Waśniewski., Lecture notes in computer science Berlin: Springer.Google Scholar
  18. Monaco, M.F., M. Sammarra, and G. Sorrentino. 2014. The terminal-oriented ship stowage planning problem. European Journal of Operational Research 239 (1): 256–265.CrossRefGoogle Scholar
  19. Pacino, D., A. Delgado, R.M. Jensen, and T. Bebbington. 2012. An accurate model for seaworthy container vessel stowage planning with ballast tanks. In Computational logistics, vol. 7555, ed. H. Hu, X. Shi, R. Stahlbock, and S. Voß, 17–32., Lecture notes in computer science Cham: Springer International Publishing.CrossRefGoogle Scholar
  20. Steenken, D., S. Voß, and R. Stahlbock. 2004. Container terminal operation and operations research—A classification and literature review. OR Spectrum 26 (1): 3–49.CrossRefGoogle Scholar
  21. Webster, W.C., and P. Van Dyke. 1970. Container loading. A container allocation model: I—introduction background, II—strategy, conclusions. In Proceedings of computer-aided ship design engineering summer conference, University of Michigan.Google Scholar
  22. Wilson, I.D., and P.A. Roach. 1999. Principles of combinatorial optimization applied to container-ship stowage planning. Journal of Heuristics 5 (4): 403–418.CrossRefGoogle Scholar
  23. Wilson, I.D., and P.A. Roach. 2000. Container stowage planning—A methodology for generating computerized solutions. Journal of Operational Research Society 51 (11): 1248–1255.CrossRefGoogle Scholar
  24. Wilson, I.D., P.A. Roach, and J.A. Ware. 2001. Container stowage pre-planning: Using search to generate solutions, a case study. Knowledge-Based Systems 14 (3–4): 137–145.CrossRefGoogle Scholar
  25. Xiao, X., M.Y.H. Low, F. Liu, S.Y. Huang, W.J. Hsu, and Z.P. Li. 2009. An efficient block-based heuristic method for stowage planning of large containerships with crane split consideration. In Proceedings of the International Conference on Harbor, Maritime & Multimodal Logistics Modeling and Simulation, pp. 93–99.Google Scholar

Copyright information

© Springer Nature Limited 2019

Authors and Affiliations

  1. 1.Department of Shipping and Transportation ManagementNational Taiwan Ocean UniversityKeelungTaiwan
  2. 2.Center of Excellence for Ocean EngineeringNational Taiwan Ocean UniversityKeelungTaiwan

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