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1. Riga State Gymnasium No. 1, 8 Raina Boulevard, Riga LV-1050, Latvia;
2. Faculty of Humanities, Leiden University, Rapenburg 70, 2311 EZ Leiden, the Netherlands;
3. Department of Aviation Transport, Transport and Telecommunication Institute, 1 Lomonosov Street, Riga LV-1019, Latvia;
4. Institute of Fundamental Science and Innovative Technologies, Liepaja University, 14 Liela Street, Liepaja LV-3401, Latvia


In this work, we consider a specific problem of optimal planning of maritime transportation of multiproduct cargo by ships of one (so-called “corporate strategy”) or several (so-called “partially corporate strategy”) companies: the core of the problem consists of the existence of the network of intermediate seaports (i.e., transitional seaports), where for every ship arrived the cargo handling is done, and which are situated between the starting and the finishing seaports. In this work, there are mathematical models built from scratch in the form of multi-criterion optimization problem; according to the properties of the criteria and structure of the feasible solution set; are formulated different optimality conditions; are analysed different approaches for finding effective solutions (i.e., Pareto optimal solutions) and for check of the given solutions’ effectiveness. In addition, in this work, there is considered and analysed well-known method of contraction of the Pareto boundary (goal attainment method of Gembicki), then, it is used for reducing the built models to a one-criterion problem of linear programming.


Marine cargo transportation, mathematical modeling, multi-criterion optimization, ill-posedness.

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