2D-Packing with an Application to Stowage in Roll-On Roll-Off Liner Shipping

  • Jone R. HansenEmail author
  • Ivar Hukkelberg
  • Kjetil Fagerholt
  • Magnus Stålhane
  • Jørgen G. Rakke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9855)


Roll-on/Roll-off (RoRo) ships represent the primary source for transporting vehicles and other types of rolling material over long distances. In this paper we focus on operational decisions related to stowage of cargoes for a RoRo ship voyage visiting a given set of loading and unloading ports. By focusing on stowage on one deck on board the ship, this can be viewed as a special version of a 2-dimensional packing problem with a number of additional considerations, such as one wants to place vehicles that belong to the same shipment close to each other to ease the loading and unloading. Another important aspect of this problem is shifting, which means temporarily moving some vehicles to make an entry/exit route for the vehicles that are to be loaded/unloaded at the given port. We present several versions of a new mixed integer programming (MIP) formulation for the problem. Computational results show that the model provides good solutions on small sized problem instances.


Maritime transportation 2D-packing Roll-on Roll-off 



We would like to thank an anonymous referee for many valuable comments and suggestions that led to improvements in the paper.


  1. 1.
    Ambrosino, D., Sciomachen, A., Tanfani, E.: Stowing a containership: the master bay plan problem. Transp. Res. Part A Policy Pract. 38(2), 81–99 (2004)CrossRefGoogle Scholar
  2. 2.
    Andersson, H., Fagerholt, K., Hobbesland, K.: Integrated maritime fleet deployment and speed optimization: case study from roro shipping. Comput. Oper. Res. 55, 233–240 (2015)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Avriel, M., Penn, M., Shpirer, N., Witteboon, S.: Stowage planning for container ships to reduce the number of shifts. Ann. Oper. Res. 76, 55–71 (1998)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dyckhoff, H.: A typology of cutting and packing problems. Eur. J. Oper. Res. 44(2), 145–159 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Hadjiconstantinou, E., Christofides, N.: An exact algorithm for general, orthogonal, two-dimensional knapsack problems. Eur. J. Oper. Res. 83(1), 39–56 (1995)CrossRefzbMATHGoogle Scholar
  6. 6.
    Hopper, E., Turton, B.C.: An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem. Eur. J. Oper. Res. 128(1), 34–57 (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    Hvattum, L.M., Fagerholt, K., Armentano, V.A.: Tank allocation problems in maritime bulk shipping. Comput. Oper. Res. 36(11), 3051–3060 (2009)CrossRefzbMATHGoogle Scholar
  8. 8.
    Kreuzer, E., Schlegel, V., Stache, F.: Multibody simulation tool for the calculation of lashing loads on roro ships. Multibody Sys.Dyn. 18(1), 73–80 (2007)CrossRefzbMATHGoogle Scholar
  9. 9.
    Øvstebø, B.O., Hvattum, L.M., Fagerholt, K.: Optimization of stowage plans for roro ships. Comput. Oper. Res. 38(10), 1425–1434 (2011)CrossRefzbMATHGoogle Scholar
  10. 10.
    Øvstebø, B.O., Hvattum, L.M., Fagerholt, K.: Routing and scheduling of roro ships with stowage constraints. Transp. Res. Part C Emerg. Technol. 19(6), 1225–1242 (2011)CrossRefzbMATHGoogle Scholar
  11. 11.
    Pantuso, G., Fagerholt, K., Wallace, S.W.: Uncertainty in fleet renewal: a case from maritime transportation. Transp. Sci. 50(2), 390–407 (2015)CrossRefzbMATHGoogle Scholar
  12. 12.
    Seixas, M.P., Mendes, A.B., Pereira Barretto, M.R., Da Cunha, C.B., Brinati, M.A., Cruz, R.E., Wu, Y., Wilson, P.A.: A heuristic approach to stowing general cargo into platform supply vessels. J. Oper. Res. Soc. 67(1), 148–158 (2016)CrossRefGoogle Scholar
  13. 13.
    Wäscher, G., Haußner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jone R. Hansen
    • 1
    Email author
  • Ivar Hukkelberg
    • 1
  • Kjetil Fagerholt
    • 1
    • 2
  • Magnus Stålhane
    • 1
  • Jørgen G. Rakke
    • 3
  1. 1.Department of Industrial Economics and Technology ManagementNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Marine Technology Research Institute (MARINTEK)TrondheimNorway
  3. 3.Wallenius Wilhelmsen LogisticsLysakerNorway

Personalised recommendations