Skip to main content
SpringerLink
Log in

A constraint programming approach to capacity planning in container vessels

  • Special Issue—Twenty-first century challenges for shipping
  • Published:
Maritime Economics & Logistics Aims and scope

Abstract

A container vessel carries containers of various characteristics, in terms of size, weight, and contents. The cargo load of a container vessel, being subjected to a set of operational conditions and restrictions regarding ship stability and safety, is a fundamental element in decision-making when a shipping line provides logistics services to clients. This study presents a constraint programming-based model for the capacity planning of a container vessel under various operational conditions. The proposed model generates base solutions and is complemented with a rich scenario-based analysis that utilizes real-life ship data of a container vessel operated by a liner shipping company with a significant market presence. Solutions obtained from the model provide insights on containership capacity planning with differing settings and search strategies. Recommendations to container carriers, regarding improved capacity planning, are the highlights of the study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Notes

  1. The cargo mix excludes dangerous cargo as demand for the transportation of dangerous cargoes occurs in an ad hoc manner, which cannot be predicted in advance. Such containers are handled on a case-by-case basis.

  2. By inferior cargo mix, we refer to cargo size and weight that do not optimize the capacity of the vessel.

  3. VGM guidelines require the mandatory verification of the gross mass of packed containers to ensure the safety of ships, seafarers, and shore-side workers from any discrepancy between the declared gross mass and the actual gross mass of a packed container. We refer readers to https://www.imo.org/en/OurWork/Safety/Pages/Verification-of-the-gross-mass.aspx.

  4. The quay crane intensity is an estimation of the number of cranes used to handle a vessel. It is calculated by dividing the total number of container moves by the number of moves the longest crane will perform (Pacino 2018).

  5. The depth-first search strategy is a tree search algorithm such that each instantiation of a decision variable can be thought of as a branch in a search tree. The optimizer works on the subtree of one branch until it has found a solution or has proven that there is no solution in that subtree. The optimizer will not move to work on another section of the tree until the current one has been fully explored. For computational efficiency, the termination criterion for the solution search process will be set to the maximum number of branches. The number of branches generating is limited to 100,000 for the two search strategies. On the other hand, the multipoint search strategy creates a set of solutions using the search points and combines the solutions in the set to produce better solutions. The multipoint search strategy is typically known to be more diversified than depth-first, but it does not necessarily prove the optimality or the inexistence of a solution. This experiment utilizes 50 random search points. The rest of the settings for the two search strategies follow the default configurations of the IBM ILOG CP Optimizer (IBM Documentation 2016). It is typically known that the multipoint search strategy is more efficient, but the depth-first search strategy provides better solutions. The experiment adopts the two search strategies as they could represent the effectiveness and efficiency of searching solutions (Russell and Norvig 2003).

References

  • Allianz Global Corporate & Specialty. 2019. Loss trends—Larger vessels bring bigger losses. https://www.agcs.allianz.com/news-and-insights/expert-risk-articles/larger-vessels-bigger-losses.html. Accessed 30 Sept 2019.

  • Ambrosino, D., D. Anghinolfi, M. Paolucci, and A. Sciomachen. 2009. A new three-step heuristic for the Master Bay Plan Problem. Maritime Economics and Logistics 11: 98–120. https://doi.org/10.1057/mel.2008.19.

    Article  Google Scholar 

  • Ambrosino, D., M. Paolucci, and A. Sciomachen. 2015. Experimental evaluation of mixed integer programming models for the multi-port master bay plan problem. Flexible Service and Manufacturing Journal 27: 263–284.

    Article  Google Scholar 

  • Ambrosino, D., M. Paolucci, and A. Sciomachen. 2017. Computational evaluation of a MIP model for multi-port stowage planning problems. Soft Computing 21 (7): 1753–1763.

    Article  Google Scholar 

  • Ambrosino, D., and A. Sciomachen. 2018. A shipping line stowage-planning procedure in the presence of hazardous containers. Maritime Economics and Logistics. https://doi.org/10.1057/s41278-018-0107-y.

    Article  Google Scholar 

  • Ambrosino, D., A. Sciomachen, and E. Tanfani. 2006. A decomposition heuristics for the container ship stowage problem. Journal of Heuristics 12: 211–233.

    Article  Google Scholar 

  • Araújo, E.J., A.A. Chaves, L.L. de Salles Neto, and A.T. Azevedob. 2016. Pareto clustering search applied for 3D containership loading plan problem. Expert Systems with Applications 44: 50–57.

    Article  Google Scholar 

  • Avriel, M., M. Penn, N. Shpirer, and S. Witteboon. 1998. Stowage planning for container ships to reduce the number of shifts. Annals of Operations Research 76: 55–71.

    Article  Google Scholar 

  • Azevedo, A.T., L.L. de Salles Netob, A.A. Chaves, and A.C. Moretti. 2018. Solving the 3D stowage planning problem integrated with the quay crane scheduling problem by representation by rules and genetic algorithm. Applied Soft Computing 65: 495–516.

    Article  Google Scholar 

  • Bockmayr, A., and J. Hooker. 2005. Constraint programming. In Handbooks in Operations Research and Management Science, ed. K. Aardal, G. Nemhauser, and R. Weismantel, 559–600. Elsevier Science & Technology: North Holland.

    Google Scholar 

  • Chao, S.L., and P.H. Lin. 2021. Minimizing overstowage in master bay plans of large container ships. Maritime Economics and Logistics 23: 71–93. https://doi.org/10.1057/s41278-019-00126-6.

    Article  Google Scholar 

  • Chou, C.C., and P.Y. Fang. 2021. Applying expert knowledge to containership stowage planning: An empirical study. Maritime Economics and Logistics 23: 4–27. https://doi.org/10.1057/s41278-018-0113-0.

    Article  Google Scholar 

  • Christensen, J., and D. Pacino. 2017. A matheuristic for the cargo mix problem with block stowage. Transportation Research Part E 97: 151–171.

    Article  Google Scholar 

  • Christensen, J., A. Erera, and D. Pacino. 2019. A rolling horizon heuristic for the stochastic cargo mix problem. Transportation Research Part E 123: 200–220.

    Article  Google Scholar 

  • Delgado, A. (2013) Models and algorithms for container vessel stowage optimization. PhD Dissertation, IT University of Copenhagen, Denmark.

  • Delgado, A., R.M. Jensen, K. Janstrup, T.H. Rose, and K.H. Andersen. 2012. A Constraint Programming model for fast optimal stowage of container vessel bays. European Journal of Operational Research 220: 251–261.

    Article  Google Scholar 

  • 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: 242–249.

    Article  Google Scholar 

  • Dubrovsky, O., G. Levitin, and M. Penn. 2002. A genetic algorithm with a compact solution encoding for the container ship stowage problem. Journal of Heuristics 8: 585–599.

    Article  Google Scholar 

  • Gent, I.P., K.E. Petrie, and J.-F. Puget. 2006. Symmetry in constraint programming. In Handbook of Constraint Programming, ed. F. Rossi, P. van Beek, and T. Walsh, 329–368. Amsterdam: Elsevier.

    Chapter  Google Scholar 

  • Ge, J., M. Zhu, M. Sha, T. Notteboom, W. Shi, and X. Wang. 2019. Towards 25,000 TEU vessels? A comparative economic analysis of ultra-large containership sizes under different market and operational conditions. Maritime Economics and Logistics. https://doi.org/10.1057/s41278-019-00136-4.

    Article  Google Scholar 

  • Glave, T., M. Joerss, and S. Saxon. 2014. The hidden opportunity in container shipping. McKinsey & Company, https://www.mckinsey.com/business-functions/strategy-and-corporate-finance/our-insights/the-hidden-opportunity-in-container-shipping. Accessed 30 Sept 2019.

  • Helo, P., H. Paukku, and T. Sairanen. 2018. Containership cargo profiles, cargo systems, and stowage capacity: key performance indicators. Maritime Economics and Logistics. https://doi.org/10.1057/s41278-018-0106-z.

    Article  Google Scholar 

  • IBM Documentation. 2016. Using alternative search types. https://www.ibm.com/support/knowledgecenter/SSSA5P_12.7.1/ilog.odms.cpo.help/CP_Optimizer/User_manual/topics/tune_altSearch.html. Accessed 23 Aug 2021.

  • Imai, A., K. Sasaki, E. Nishimura, and S. Papadimitriou. 2006. Multi-objective simultaneous stowage and load planning for a container ship with container rehandle in yard stacks. European Journal of Operational Research 171: 373–389.

    Article  Google Scholar 

  • International Transport Forum. 2015. The Impact of Mega-Ships: Case-Specific Policy Analysis. OECD, Paris. https://www.itf-oecd.org/sites/default/files/docs/15cspa_mega-ships.pdf. Accessed 10 Dec 2020.

  • Iris, Ç., J. Christensen, D. Pacino, and S. Ropke. 2018. Flexible ship loading problem with transfer vehicle assignment and scheduling. Transportation Research Part B 111: 113–134.

    Article  Google Scholar 

  • Kang, J.-G., and Y.-D. Kim. 2002. Stowage planning in maritime container transportation. Journal of the Operational Research Society 53: 415–426.

    Article  Google Scholar 

  • Kos, S., and Z. Zenzerović. 2007. Model of optimal cargo transport structure by full container ship on predefined sailing route. Promet Traffic Traffico 16 (1): 15–20. https://doi.org/10.7307/ptt.v16i1.568.

    Article  Google Scholar 

  • Larsen, R., and D. Pacino. 2021. A heuristic and a benchmark for the stowage planning problem. Maritime Economics and Logistics 23: 94–122. https://doi.org/10.1057/s41278-020-00172-5.

    Article  Google Scholar 

  • Lee, C.B., J. Wan, W. Shi, and K. Li. 2014. A cross-country study of competitiveness of the shipping industry. Transport Policy 35: 366–376.

    Article  Google Scholar 

  • Low, M.Y.H., M. Zeng, W.J. Hsu, S.Y. Huang, F. Liu, and C.A. Win. 2011. Improving safety and stability of large containerships in automated stowage planning. IEEE Systems Journal 5: 50–60.

    Article  Google Scholar 

  • Merk, O. (2018) Container ship size and port relocation. International Transport Forum Discussion Paper, No. 2018–10, International Transport Forum, OECD, Paris. http://dx.doi.org/https://doi.org/10.1787/d790ae41-en.

  • Monaco, M.F., M. Sammarra, and G. Sorrentino. 2014. The terminal-oriented ship stowage planning problem. European Journal of Operational Research 239: 256–265.

    Article  Google Scholar 

  • Pacino, D. (2012) Fast Generation of Container Vessel Stowage Plans: Using mixed integer programming for optimal master planning and constraint based local search for slot planning. PhD Dissertation, IT University of Copenhagen, Denmark.

  • Pacino, D. 2018. Crane Intensity and Block Stowage Strategies in Stowage Planning. In Computational Logistics. ICCL 2018. Lecture Notes in Computer Science, ed. R. Cerulli, A. Raiconi and S. Voß. Cham: Springer, vol. 11184. https://doi.org/10.1007/978-3-030-00898-7_12.

  • Parreño, F., D. Pacino, and R. Alvarez-Valdes. 2016. A GRASP algorithm for the container stowage slot planning problem. Transportation Research Part E 94: 141–157.

    Article  Google Scholar 

  • Perunovic, Z., and J. Vidic-Perunovic. 2011. Innovation in the maritime industry. In Proceedings of the 22nd Annual POM Conference: Operations management, 29 April–2 May 2011, Reno, NV, United States.

  • Régin, J.-C. 2004. Global constraints and filtering algorithms. In Constraint and Integer Programming Operations Research/Computer Science Interfaces Series 27, ed. M. Milano, 89–135. Boston, MA: Springer.

    Chapter  Google Scholar 

  • Russell, S.J., and P. Norvig. 2003. Problem-solving. In Artificial Intelligence: A Modern Approach, 2nd ed., 59–193. New Jersey: Prentice Hall.

    Google Scholar 

  • Sciomachen, A., and E. Tanfani. 2007. A 3D-BPP approach for optimising stowage plans and terminal productivity. European Journal of Operational Research 183 (3): 1433–1446.

    Article  Google Scholar 

  • Ting, S., and G. Tzeng. 2004. An optimal containership slot allocation for liner shipping revenue management. Maritime Policy and Management 31 (3): 199–211.

    Article  Google Scholar 

  • UNCTAD. 2020. Review of Maritime Transport 2020. United Nations publication, Sales No. E.20.II.D.31, New York and Geneva. https://unctad.org/system/files/official-document/rmt2020_en.pdf.

  • Wilson, I.D., and P.A. Roach. 1999. Principles of combinatorial optimization applied to container-ship stowage planning. Journal of Heuristics 5: 403–418.

    Article  Google Scholar 

  • Wilson, I.D., and P.A. Roach. 2000. Container stowage planning: a methodology for generating computerised solutions. Journal of the Operational Research Society 51: 1248–1255.

    Article  Google Scholar 

  • Wu, W. (2014) An analysis of the profitability of container shipping lines. Proceedings of the International Forum on Shipping, Ports and Airports (IFSPA) 2014: Sustainable Development in Shipping and Transport Logistics, 519–527.

Download references

Acknowledgements

The authors would like to express their appreciation for the invaluable advice from a major industry partner, especially their highly experienced captains, in developing the research problem, as well as the constructive comments from anonymous referees and editors of MEL, which greatly improved the quality of this work. This research was funded by the Maritime and Port Authority of Singapore (MPA) Research Fellowship Grant.

Author information

Authors and Affiliations

  1. Deaprtment of Industrial Systems Engineering and Management, National University of Singapore, 1 Engineering Drive 2, Singapore, 117576, Singapore

    Byung Kwon Lee

  2. Lee Kong Chian School of Business, Singapore Management University, 50 Stamford Road, Singapore, 178899, Singapore

    Joyce M. W. Low

Authors
  1. Byung Kwon Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joyce M. W. Low
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joyce M. W. Low.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, B.K., Low, J.M.W. A constraint programming approach to capacity planning in container vessels. Marit Econ Logist 24, 415–438 (2022). https://doi.org/10.1057/s41278-021-00208-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/s41278-021-00208-4

Keywords

Search

Navigation