Journal of the Operational Research Society

, Volume 58, Issue 9, pp 1167–1177 | Cite as

Ship routing and scheduling with flexible cargo sizes

Case Oriented Paper


Here, we describe a real planning problem in the tramp shipping industry. A tramp shipping company may have a certain amount of contract cargoes that it is committed to carry, and tries to maximize the profit from optional cargoes. For real long-term contracts, the sizes of the cargoes are flexible. However, in previous research within tramp ship routing, the cargo quantities are regarded as fixed. We present an MP-model of the problem and a set partitioning approach to solve the multi-ship pickup and delivery problem with time windows and flexible cargo sizes. The columns are generated a priori and the most profitable ship schedule for each cargo set–ship combination is included in the set partitioning problem. We have tested the method on several real-life cases, and the results show the potential economical effects for the tramp shipping companies by utilizing flexible cargo sizes when generating the schedules.


sea transport scheduling integer programming 


  1. Archetti CM, Savelsbergh MWP and Speranza MG (2006). Worst-case analysis for split delivery routing problems. Transport Sci 40: 226–234.CrossRefGoogle Scholar
  2. Bausch D, Brown G and Ronen D (1998). Scheduling short-term marine transport of bulk products. Maritime Pol Mngt 25: 335–348.CrossRefGoogle Scholar
  3. Brønmo G, Christiansen M, Fagerholt K and Nygreen B (2005). A multi-start local search heuristic for ship scheduling—a computational study. Comput Oper Res, available online June 28th 2005. 17pp.Google Scholar
  4. Brown G, Graves W and Ronen D (1987). Scheduling ocean transportation of crude oil. Mngt Sci 33: 335–346.CrossRefGoogle Scholar
  5. Campbell AM (2006). The vehicle routing problem with demand range. Ann Opns Res, forthcoming, 18pp.Google Scholar
  6. Campbell AM, Clarke LW and Savelsbergh MWP (2002). Inventory rouing in practice. In: Toth P and Vigo D (Eds). The Vehicle Routing Problem. SIAM: Philadelphia 309–330.CrossRefGoogle Scholar
  7. Campbell AM and Savelsbergh MWP (2004). Delivery volume optimization. Transport Sci 38: 210–233.CrossRefGoogle Scholar
  8. Christiansen M and Fagerholt K (2002). Robust ship scheduling with multiple time windows. Naval Res Logist 49: 611–625.CrossRefGoogle Scholar
  9. Christiansen M, Fagerholt K and Ronen D (2004). Ship routing and scheduling: status and perspectives. Transport Sci 38: 1–18.CrossRefGoogle Scholar
  10. Christiansen M and Nygreen B (1998a). A method for solving ship routing problems with inventory constraints. Ann Opns Res 81: 357–378.CrossRefGoogle Scholar
  11. Christiansen M and Nygreen B (1998b). Modelling path flows for a combined ship routing and inventory management problem. Ann Opns Res 82: 391–412.CrossRefGoogle Scholar
  12. Desaulniers G, Desrosiers J and Solomon M (eds) (2005). Column Generation. Springer, GERAD: Montréal, Canada, ISBN 0-387-25485-4.Google Scholar
  13. Desrosiers J, Dumas Y, Solomon M and Suomis F (1995). Time constrained routing and scheduling. In: Ball M, Magnanti T, Monna C and Nemhauser G (Eds). Handbooks in Operations Research and Management Science: Network Routing. North Holland, Amsterdam 35–139.Google Scholar
  14. Dror M, Laporte G and Trudeau P (1994). Vehicle routing with split deliveries. Discrete Appl Math 50: 239–254.CrossRefGoogle Scholar
  15. Fagerholt K and Christiansen M (2000a). A combined ship scheduling and allocation problem. J Opl Res Soc 51: 834–842.CrossRefGoogle Scholar
  16. Fagerholt K and Christiansen M (2000b). A travelling salesman problem with allocation, time window and precedence constraints—an application to ship scheduling. Int Trans Opns Res 7: 231–244.CrossRefGoogle Scholar
  17. Fisher ML and Rosenwein MB (1989). An interactive optimization system for bulk-cargo ship scheduling. Naval Res Logist 36: 27–42.CrossRefGoogle Scholar
  18. Flatberg T, Haavardtun H, Kloster O and Løkketangen A (2000). Combining exact and heuristic methods for solving a vessel routing problem with inventory constraints and time windows. Ricerca Operativa 29: 55–68.Google Scholar
  19. Ho SC and Haugland D (2004). A tabu search heuristic for the vehicle routing problem with time windows and split deliveries. Comput Opl Res 31: 1947–1964.CrossRefGoogle Scholar
  20. Kim S-H and Lee K-K (1997). An optimisation-based decision support system for ship scheduling. Comput Indust Eng 33: 689–692.CrossRefGoogle Scholar
  21. Lawrence SA (1972). International Sea Transport: The Years Ahead. Lexington Books: Lexington, MA.Google Scholar
  22. Persson JA and Göthe-Lundgren M (2005). Shipment planning at oil refineries using column generation and valid inequalities. Eur J Opl Res 163: 631–652.CrossRefGoogle Scholar
  23. Ronen D (2002). Marine inventory routing: shipments planning. J Opl Res Soc 53: 108–114.CrossRefGoogle Scholar
  24. Sherali HD, Al-Yakoob SM and Hassan MM (1999). Fleet management models and algorithms for an oil tanker routing and scheduling problem. IIE Trans 31: 395–406.Google Scholar
  25. Westerlund A, Göthe-Lundgren M and Larsson T (2005). A column generation scheme for the fixed fleet heterogeneous vehicle routing problem. Paper IV In: Westerlund A. Accelerating column generation schemes—applications to routing problems. Dissertation No. 978, Linköping Studies in Science and Technology, University of Linköping, Sweden.Google Scholar

Copyright information

© Palgrave Macmillan Ltd 2006

Authors and Affiliations

  1. 1.Norwegian University of Science and TechnologyTrondheimNorway

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