Advertisement

Solving Stochastic Ship Fleet Routing Problems with Inventory Management Using Branch and Price

  • Ken McKinnonEmail author
  • Yu Yu
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 107)

Abstract

This chapter describes a stochastic ship routing problem with inventory management. The problem involves finding a set of least cost routes for a fleet of ships transporting a single commodity when the demand for the commodity is uncertain. Storage at supply and consumption ports is limited and inventory levels are monitored in the model. Consumer demands are at a constant rate within each time period, and in the stochastic problem, the demand rate for a period is not known until the beginning of that period. The demand situation over the time periods is described by a scenario tree with corresponding probabilities. A decomposition formulation is given and it is solved using a Branch and Price framework. A master problem (set partitioning with extra inventory constraints) is built, and the subproblems, one for each ship, are solved by stochastic dynamic programming and yield the columns for the master problem. Each column corresponds to one possible tree of actions for one ship giving its schedule loading/unloading quantities for all demand scenarios. Computational results are given showing that medium sized problems can be solved successfully.

Keywords

Stochastic Dynamic Programming Branch and Price Ship Routing Inventory Management. 

References

  1. 1.
    Appelgren, L.: A column generation algorithm for a ship scheduling problem. Transp. Sci. 3, 53–68 (1969)CrossRefGoogle Scholar
  2. 2.
    Appelgren, L.: Integer programming methods for a vessel scheduling problem. Transp. Sci. 5, 64–78 (1971)CrossRefGoogle Scholar
  3. 3.
    Bendall, H., Stent, A.: A scheduling model for a high speed containership service: a hub and spoke short-sea application. J. Marit. Econ. 3 (3), 262–277 (2001)CrossRefGoogle Scholar
  4. 4.
    Bertsimas, D.: A vehicle routing problem with stochastic demand. Oper. Res. 40 (3), 574–585 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Christiansen, M.: Decomposition of a combined inventory and time constrained ship routing problem. Transp. Sci. 33 (1), 3–16 (1999)CrossRefzbMATHGoogle Scholar
  6. 6.
    Christiansen, M., Fagerholt, K.: Robust ship scheduling with multiple time windows. Nav. Res. Logist. 49, 611–625 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Christiansen, C., Lysgaard, J.: A branch-and-bound algorithm for the capacitated vehicle routing problem with stochastic demands. Oper. Res. Lett. 35, 773–781 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Christiansen, M., Nygreen, B.: A method for solving ship routing problems with inventory constraints. Ann. Oper. Res. 81, 357–378 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Christiansen, M., Nygreen, B.: Modelling path flows for a combined ship routing and inventory management problem. Ann. Oper. Res. 82, 391–412 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Christiansen, M., Fagerholt, K., Ronen, D.: Ship routing and scheduling: status and perspectives. Transp. Sci. 38 (1), 1–18 (2004)CrossRefGoogle Scholar
  11. 11.
    Crary, M., Nozick, L., Whitaker, L.: Sizing the U.S. destroyer fleet. Eur. J. Oper. Res. 136, 680–695 (2002)Google Scholar
  12. 12.
    Desrochers, M., Soumis, F.: A generalized permanent labeling algorithm for the shortest path problem with time windows. INFOR 26 (3), 191–211 (1988)zbMATHGoogle Scholar
  13. 13.
    Desrochers, M., Soumis, F.: A reoptimization algorithm for the shortest path problem with time windows. Eur. J. Oper. Res. 35, 242–254 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Desrochers, M., Desrosiers, J., Solomon, M.: A new optimization algorithm for the vehicle routing problem with time windows. Oper. Res. 40, 342–354 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Desrosiers, J., Dumas, Y., Solomon, M., Soumis, F.: Time constrained routing and scheduling. In: Network Routing. Handbooks in Operations Research and Management Science, vol. 8, pp. 35–139. North-Holland, Amsterdam (1995)Google Scholar
  16. 16.
    Dror, M., Trudeau, P.: Stochastic vehicle routing with modified saving algorithm. Eur. J. Oper. Res. 23, 228–235 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Dror, M., Laporte, G., Trudeau, P.: Vehicle routing with stochastic demands: properties and solution frameworks. Transp. Sci. 23 (3), 166–176 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Gendreau, M., Laporte, G., Seguin, R.: An exact algorithm for the vehicle routing problem with stochastic demands and customers. Transp. Sci. 29 (2), 143–156 (1995)CrossRefzbMATHGoogle Scholar
  19. 19.
    Gunnarsson, H., Ronnqvist, M., Carlsson, D.: A combined terminal location and ship routing problem. J. Oper. Res. Soc. 57, 928–938 (2006)CrossRefzbMATHGoogle Scholar
  20. 20.
    Hjorring, C., Holt, J.: New optimality cuts for a single-vehicle stochastic routing problem. Ann. Oper. Res. 86, 569–584 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Irnich, S., Desaulniers, G.: Shortest path problems with resource constraints. Les Cahiers du GERAD G-2004-11 (2004)Google Scholar
  22. 22.
    Irnich, S., Villeneuve, D.: The shortest-path problem with resource constraints and k-cycle elimination for k ≥ 3. INFORMS J. Comput. 18 (3), 391–406 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Kleywegt, A., Nori, V., Savelsbergh, M.: Dynamic programming approximations for a stochastic inventory routing problem. Transp. Sci. 38, 42–70 (2004)CrossRefGoogle Scholar
  24. 24.
    Mehrez, A., Hung, M., Ahn, B.: An industrial ocean-cargo shipping problem. Decis. Sci. 26 (3), 395–423 (1995)CrossRefGoogle Scholar
  25. 25.
    Ronen, D.: Marine inventory routing: shipments planning. J. Oper. Res. Soc. 53, 108–114 (2002)CrossRefzbMATHGoogle Scholar
  26. 26.
    Sherali, H., Al-Yahoob, S., Hassan, M.: Fleet management models and algorithms for an oil-tanker routing and scheduling problem. IIE Trans. 31, 395–406 (1999)Google Scholar
  27. 27.
    Shih, L.H.: Planning of fuel coal imports using a mixed integer programming method. Int. J. Prod. Econ. 51, 243–249 (1997)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of MathematicsUniversity of EdinburghEdinburghUK

Personalised recommendations