Case Oriented Paper

Journal of the Operational Research Society

, Volume 58, Issue 9, pp 1167-1177

First online:

Ship routing and scheduling with flexible cargo sizes

  • G BrønmoAffiliated withNorwegian University of Science and Technology Email author 
  • , M ChristiansenAffiliated withNorwegian University of Science and Technology
  • , B NygreenAffiliated withNorwegian University of Science and Technology

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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