procyberВестник кибернетикиProceedings in Cybernetics1999-7604Бюджетное учреждение высшего образования Ханты-Мансийского автономного округа – Югры «Сургутский государственный университет»10.35266/1999-7604-2024-4-9procyber-627Research ArticleФИЗИКО-МАТЕМАТИЧЕСКИЕ НАУКИPhysics and MathematicsО математических моделях размещения оборудования при проектировании и реконструкции предприятийOn mathematical models of equipment placement in design and reconstruction of enterpriseshttps://orcid.org/0000-0002-2709-9755ВеремчукН. С.VeremchukN. S.

кандидат физико-математических наук, доцент

Candidate of Sciences (Physics and Mathematics), Docent

n-veremchuk@rambler.ruСибирский государственный автомобильно-дорожный университет; Омский государственный технический университет, ОмскРоссияThe Siberian State Automobile and Highway University; Omsk State Technical University, OmskRussian Federation2024251220242349299Copyright © Веремчук Н.С., 20242024Веремчук Н.С.Veremchuk N.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.vestcyber.ru/jour/article/view/627

Приводится обзор математических моделей размещения технологического оборудования, применяемых при решении задач проектирования и модернизации производственных цехов. Рассматриваются случаи размещения взаимосвязанного оборудования. Построена математическая модель размещения производственных линий и технологического оборудования на них. Линии соединены вертикальным виадуком, через который проводятся коммуникации. На линиях зафиксированы запрещенные зоны, где нельзя располагать другие элементы. Приведены результаты численных экспериментов с применением построенной модели нелинейного программирования и пакета CPLEX. Рассмотрены две серии тестовых примеров, когда расположение виадука фиксировалось и когда находилось его оптимальное размещение. При поиске расположения виадука получилось лучшее значение целевой функции, чем при фиксированном виадуке, но время счета увеличивалось. Модель может быть использована при проектировании и оценке размещения технологических линий с оборудованием в промышленных отраслях.

Abstract. The article provides an overview of mathematical models for the placement of process equipment. These models are used to solve problems of designing and upgrading production shops. Cases of placement of interconnected equipment are considered. A mathematical model for the placement of production lines and process equipment on them is constructed. The lines are connected by a vertical viaduct through which communications are carried out. The model designates prohibited zones on the lines where no other elements can be placed. The results of numerical experiments using the constructed nonlinear programming model and the CPLEX package are presented. The study considers two series of test examples: one with a fixed viaduct location and another determining its optimal placement. A better value of the objective function was obtained when searching for the location of the viaduct, but the calculation time increased. The model can be used in the design and assessment of the process lines placement with equipment in industrial sectors.

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The authors declare that there are no conflicts of interest present.