Scandinavian Working Papers in Business Administration
Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science
No 2026/13: Modelling Tramp Shipping Tonne-Miles in an Ever-Changing Market
Nikolaj Bläser (), Búgvi Benjamin Magnussen () and Gabriel Fuentes ()
Additional contact information
Nikolaj Bläser: Dept. of People and Technology, Roskilde University, Postal: Roskilde University , Department of People and Technology, Universitetsvej 1, DK-4000 Roskilde, Denmark
Búgvi Benjamin Magnussen: Dept. of People and Technology, Roskilde University, Postal: Roskilde University , Department of People and Technology, Universitetsvej 1, DK-4000 Roskilde, Denmark
Gabriel Fuentes: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Abstract: The tonne-mile metric serves as a measure to proxy demand for commodity transport in tramp shipping, yet predicting it is challenging due to complex trade route interdependencies and a dynamic geopolitical landscape. This study proposes a methodology for predicting tonne-miles based on trade flow modelling. Leveraging country-level export and import data, we frame tonne-mile estimation as a variant of the Minimum-Cost Flow Problem (MCFP) tailored towards tramp shipping and construct a time-expanded flow network that integrates multiple datasets to capture trade relationships. To evaluate the methodology, we perform a series of experiments across four key Clean Petroleum Product (CPP) commodities, demonstrating the ability of the model to reconstruct tonne-miles over a four-year historical period with a 2.1% Mean Absolute Percentage Error (MAPE). Finally, we showcase our method’s utility as a decision-support tool by estimating future tonne-miles under several market scenarios utilising projected country-level export and import data. The framework can be used to estimate tonne-miles per commodity segment both regularly and during disruptions, such as geopolitical tensions.
Keywords: Tonne-miles; Trade flow modelling; Tramp shipping; Minimumcost flow problem; Time-expanded flow network
Language: English
15 pages, September 30, 2026
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