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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Appelgren, L.: A column generation algorithm for a ship scheduling problem. Transp. Sci. 3, 53–68 (1969)
Appelgren, L.: Integer programming methods for a vessel scheduling problem. Transp. Sci. 5, 64–78 (1971)
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)
Bertsimas, D.: A vehicle routing problem with stochastic demand. Oper. Res. 40 (3), 574–585 (1992)
Christiansen, M.: Decomposition of a combined inventory and time constrained ship routing problem. Transp. Sci. 33 (1), 3–16 (1999)
Christiansen, M., Fagerholt, K.: Robust ship scheduling with multiple time windows. Nav. Res. Logist. 49, 611–625 (2002)
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)
Christiansen, M., Nygreen, B.: A method for solving ship routing problems with inventory constraints. Ann. Oper. Res. 81, 357–378 (1998)
Christiansen, M., Nygreen, B.: Modelling path flows for a combined ship routing and inventory management problem. Ann. Oper. Res. 82, 391–412 (1998)
Christiansen, M., Fagerholt, K., Ronen, D.: Ship routing and scheduling: status and perspectives. Transp. Sci. 38 (1), 1–18 (2004)
Crary, M., Nozick, L., Whitaker, L.: Sizing the U.S. destroyer fleet. Eur. J. Oper. Res. 136, 680–695 (2002)
Desrochers, M., Soumis, F.: A generalized permanent labeling algorithm for the shortest path problem with time windows. INFOR 26 (3), 191–211 (1988)
Desrochers, M., Soumis, F.: A reoptimization algorithm for the shortest path problem with time windows. Eur. J. Oper. Res. 35, 242–254 (1988)
Desrochers, M., Desrosiers, J., Solomon, M.: A new optimization algorithm for the vehicle routing problem with time windows. Oper. Res. 40, 342–354 (1992)
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)
Dror, M., Trudeau, P.: Stochastic vehicle routing with modified saving algorithm. Eur. J. Oper. Res. 23, 228–235 (1986)
Dror, M., Laporte, G., Trudeau, P.: Vehicle routing with stochastic demands: properties and solution frameworks. Transp. Sci. 23 (3), 166–176 (1989)
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)
Gunnarsson, H., Ronnqvist, M., Carlsson, D.: A combined terminal location and ship routing problem. J. Oper. Res. Soc. 57, 928–938 (2006)
Hjorring, C., Holt, J.: New optimality cuts for a single-vehicle stochastic routing problem. Ann. Oper. Res. 86, 569–584 (1999)
Irnich, S., Desaulniers, G.: Shortest path problems with resource constraints. Les Cahiers du GERAD G-2004-11 (2004)
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)
Kleywegt, A., Nori, V., Savelsbergh, M.: Dynamic programming approximations for a stochastic inventory routing problem. Transp. Sci. 38, 42–70 (2004)
Mehrez, A., Hung, M., Ahn, B.: An industrial ocean-cargo shipping problem. Decis. Sci. 26 (3), 395–423 (1995)
Ronen, D.: Marine inventory routing: shipments planning. J. Oper. Res. Soc. 53, 108–114 (2002)
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)
Shih, L.H.: Planning of fuel coal imports using a mixed integer programming method. Int. J. Prod. Econ. 51, 243–249 (1997)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
McKinnon, K., Yu, Y. (2016). Solving Stochastic Ship Fleet Routing Problems with Inventory Management Using Branch and Price. In: Pardalos, P., Zhigljavsky, A., Žilinskas, J. (eds) Advances in Stochastic and Deterministic Global Optimization. Springer Optimization and Its Applications, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-29975-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-29975-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29973-0
Online ISBN: 978-3-319-29975-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)