Journal of Applied Economic Research
ISSN 2712-7435
The Task of Combinatorial Optimization: the Search for an Optimal Production and Transport Plan When Organizing Production in New Territories
Rogulin R.S., Maksimenko V.I., Zlobina D.V., Zhandarmov V.O., Pugacheva E.S., Matveev V.V.
Abstract
The purpose of this article is to solve one of the tasks of production activities. A company aims to expand individual production facilities and to subsequently determine output and transportation volumes from each of the outlets (local production sites, warehouses, etc.). The hypothesis is that a solution to the production problems can be found in a set of five linear programming problems: the production problem, the center placement problem, the flow problem, the time minimization problem, and the transportation problem. The paper presents the main algorithms for finding optimal solutions, formulates a complex task, builds a model and implements an algorithm for finding optimal solutions. It was shown that such a problem can be formulated in the framework of a complex linear programming problem. The model test is produced on 38 vertices with 16 entry points, 3 exit points. It is shown that such a task can be solved and visualized by means of the Matlab package. Modifications of the model and possible solution algorithms depending on the data sample size are considered. The developed model can be applied at an enterprise or at any production facility where the main task is to search for the optimal combinatorial version of goods, provided that ,first, production costs and the costs of transportation of finished products are minimized and, second, profit is at a maximum. Third, the cost of launching opening new production facilities are kept at a minimum. Such a task corresponds exactly to the economic situation, when the enterprise has yet to expand (open new production sites), and it tries to decide where to produce items from its list of products and determine its output considering the available raw materials and decide on dispatch methods. Such a problem is non-trivial combinatorial in nature.
Keywords
mathematical modeling; linear programming; production; maximum flow; center placement; time minimization; transport problem.
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About Authors
Rogulin Rodion Sergeevich – Assistant, Department of Business Informatics and Economics-Mathematical Methods, School of Economics and Management, Far Eastern Federal University, Vladivostok, Russia (690090, Vladivostok, Sukhanova street, 8); e-mail: rafassiaofusa@mail.ru.
Maksimenko Valery Ivanovich – Candidate of Technical Sciences, Associate Professor, School of Engineering, Far Eastern Federal University, Vladivostok, Russia (690090, Vladivostok, Sukhanova street, 8); e-mail: maximenko.vi@dvfu.ru.
Zlobina Daria Vyacheslavovna – Technician, Department of Food Science and Technology, School of Biomedicine, Far Eastern Federal University, Vladivostok, Russia (690090, Vladivostok, Sukhanova street, 8); e-mail: zlobina.dv@dvfu.ru.
Zhandarmov Vladimir Olegovich – Master Student of the Direction "Cybersecurity", School of Digital Economics, Far Eastern Federal University, Vladivostok, Russia (690090, Vladivostok, Sukhanova street, 8); e-mail: zhandarmov.vo@students.dvfu.ru.
Pugacheva Eva Sergeevna – Technician, School of Biomedicine, Far Eastern Federal University, Vladivostok, Russia (690090, Vladivostok, Sukhanova street, 8); e-mail: pugacheva.es@dvfu.ru.
Matveev Vladislav Victorovich – Laboratory Engineer, School of Biomedicine, Far Eastern Federal University, Vladivostok, Russia (690090, Vladivostok, Sukhanova street, 8); e-mail: matveev.vv@dvfu.ru.
For citation
Rogulin R.S., Maksimenko V.I., Zlobina D.V., Zhandarmov V.O., Pugacheva E.S., Matveev V.V. The Task of Combinatorial Optimization: The Search for an Optimal Production and Transport Plan When Organizing Production in New Territories. Bulletin of Ural Federal University. Series Economics and Management, 2019, Vol. 18, No. 3, 364–377. DOI: 10.15826/vestnik.2019.18.3.018.
Article info
Received June 11, 2019; Accepted June 26, 2019.
DOI: http://dx.doi.org/10.15826/vestnik.2018.17.3.018
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