РАЗРАБОТКА МАТЕМАТИЧЕСКОЙ МОДЕЛИ ДЛЯ ЗАДАЧИ БЕЙПЛАНА С УЧЕТОМ ОЧЕРЕДНОСТИ ЗАГРУЗКИ КОНТЕЙНЕРОВ

Abstract

Compiling a load plan for a containership, which incorporates the maximum number of factors which requires restrictions on placement, consideration of the structural constraints for containers/ a vessel, segregation rules for dangerous cargoes and container loading sequencу in respect of a discharge port. The proposed approach for solving the task on automation of a load plan compilation 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, container loading sequence, compatibility of dangerous cargoes, at the second stage – one calculates safety parameters (stability, operating life, etc.). This paper proposes a Boolean mathematical model of integer linear programming, which takes into consideration the structural features of containers, of a vessel, rules for stowage of hazardous cargoes according to the International Maritime Dangerous Cargoes Code, as well as container loading sequence (sequence of loading containers depending on the port of unloading), as well as a modified additive algorithm for solving a problem on compiling a load plan for a containership. Boolean programming methodology is applied to the problem. The usage simplifies calculations as all variables can only have two values: “0” or “1”. To validate the mathematical model, we have chosen a classic algorithm that relies on the ideas from the general method of branches and boundaries. Its calculations are limited to operations of addition and subtraction. The main idea consists of a systematic enumeration of possible candidate solutions, but the enumeration procedure allows to eliminate the solutions which are not proved to be optimal. Taken into account that this mathematical model on loading a containership has a specific form, this algorithmhas been complemented with tests, which make it possible to reject some solutions without direct checking. The paper gives an example of solving the problem on placing cargoes in the hold, which was obtained through the modified additive algorithm.