Construction of a mathematical model and a method for arranging hazardous cargoes on a containership




containerships, load plan, Boolean mathematical model, dangerous cargoes, additive algorithm


Compiling a load plan for a containership, which takes into account the maximum number of factors, requires consideration of the structural constraints for containers and a vessel, restrictions on placement, as well as segregation rules for cases of dangerous cargoes.

Accounting for restrictions on placing containers with hazardous cargoes, the so-called IMO containers (IMO – International Maritime Organization), appears important given the current tendency towards the increased volumes of hazardous cargo transportation.

The proposed approach for solving the task on automating the compilation of a load plan aboard a containership implies dividing the task into two stages. At the first stage, one calculates the permissible arrangement of containers taking into consideration the structural limitations and compatibility of dangerous cargoes, at the second stage – one calculates safety parameters (stability, durability, etc.).

This paper proposes a Boolean mathematical model of integer linear programming, which takes into consideration the structural features of containers, of a vessel, as well as rules for placing hazardous cargoes according to the IMDG Code (International Maritime Dangerous Cargoes Code), as well as a modified additive algorithm for solving a problem on compiling a load plan for a containership. To validate the mathematical model, we have chosen a classic algorithm that relies on the ideas from the general method of branches and boundaries. Given that the derived mathematical model for a problem on loading a containership by dangerous cargoes has a specific form, this algorithm was complemented with tests, which make it possible to reject some solutions without direct check.

The paper gives an example of solving the problem on placing cargoes in the hold taking into consideration the structural constraints for containers and the rules for placing dangerous cargoes in accordance with the IMDG Code, which was obtained through the modified additive algorithm

Author Biographies

Kyrylo Kamieniev, National University "Odessa Maritime Academy" Didrikhsona str., 8, Odessa, Ukraine, 65029

Postgraduate student

Department of Shipping

Alla Kamienieva, National University "Odessa Maritime Academy" Didrikhsona str., 8, Odessa, Ukraine, 65029

PhD, Associate Professor

Department of Theory of Automatic Control and Computing

Mykola Tsymbal, National University "Odessa Maritime Academy" Didrikhsona str., 8, Odessa, Ukraine, 65029

Doctor of Technical Sciences, Professor

Department of Shipping


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How to Cite

Kamieniev, K., Kamienieva, A., & Tsymbal, M. (2019). Construction of a mathematical model and a method for arranging hazardous cargoes on a containership. Eastern-European Journal of Enterprise Technologies, 6(3 (102), 20–27.



Control processes