## Двоетапна транспортна задача з невідомими потребами споживачів

 dc.contributor.author Стецюк, Петро dc.contributor.author Хом'як, Ольга dc.contributor.author Ляшко, Володимир dc.date.accessioned 2023-03-30T03:35:56Z dc.date.available 2023-03-30T03:35:56Z dc.date.issued 2022 dc.description The work investigates a mathematical model of a two-stage transportation problem for finding the most economical plan for the transportation of homogeneous products from suppliers to consumers, where the demands of consumers are unknown, taking into account constraints on their lower and upper bounds. It is an extension of the classic two-stage transportation problem, where products are transported from suppliers to consumers only through intermediate points. Intermediary firms and various storage facilities (warehouses) can be such intermediate points. The relationship of the developed mathematical model with the two-stage continuous-discrete problem of optimal partitioning-distribution, which is characterized by the presence of two stages, is investigated. The problem consists in determining the areas of collection of the continuously distributed resource (raw material) by enterprises of the first stage and the volumes of transportation of the processed product from the enterprises of the first stage to consumers (points of the second stage), in order to minimize the total costs of transportation of the resource from suppliers to consumers through processing points (collection points, storage points). The material of the article is presented in two sections. Section 1 describes the mathematical model of the two-stage transportation problem with unknown consumer demands and provides the necessary and sufficient conditions for the compatibility of the system of linear constraints. It is shown that its special case coincides with the classic two-stage transportation problem. Section 2 provides a description of the model problem of optimal partitioning-distribution for the continuous area Ω and the discrete analog of the model problem. The results of computational experiments for a rectangular area Ω = {x = (x(1), x(2)) : 0 ≤ x(1) ≤ 1, 0 ≤ x(2) ≤ 1} with discretizations by grids 31 × 31 and 500 × 500 are presented. Optimal plans for transportation of processed product from points of the first stage to points of the second stage for both grids were found. The average time spent by the Gurobi solver to solve problems for the second grid, where the number of variables equals 250018 and the number of constraints equals 250009, is a few seconds on modern PCs. en_US dc.description.abstract Досліджено математичну модель двоетапної транспортної задачі з невідомими потребами споживачів та заданими їхніми нижніми й верхніми межами. Її частковим випадком є класична двоетапна транспортна задача, яка визначає найбільш економічний план перевезення продукції від постачальників до споживачів через проміжні пункти. Наведено умови сумісності систем лінійних обмежень відповідних задач лінійного програмування. Розглянуто модельну задачу оптимального розбиття множини та наведено результати обчислювальних експериментів із використанням солвера Gurobi. uk_UA dc.identifier.citation Стецюк П. І. Двоетапна транспортна задача з невідомими потребами споживачів / Стецюк П. І., Хом'як О. М., Ляшко В. І. // Наукові записки НаУКМА. Комп'ютерні науки. - 2022. - Т. 5. - С. 92-96. - https://doi.org/10.18523/2617-3808.2022.5.92-96 uk_UA dc.identifier.issn 2617-3808 dc.identifier.issn 2617-7323 dc.identifier.uri https://doi.org/10.18523/2617-3808.2022.5.92-96 dc.identifier.uri https://ekmair.ukma.edu.ua/handle/123456789/24861 dc.language.iso uk dc.relation.source Наукові записки НаУКМА. Комп'ютерні науки uk_UA dc.status first published en_US dc.subject двоетапна транспортна задача uk_UA dc.subject задача лінійного програмування uk_UA dc.subject Gurobi uk_UA dc.subject оптимальне розбиття множини uk_UA dc.subject стаття uk_UA dc.subject two-stage transportation problem en_US dc.subject linear programming problem en_US dc.subject Gurobi en_US dc.subject optimal set partition en_US dc.title Двоетапна транспортна задача з невідомими потребами споживачів uk_UA dc.title.alternative Two-stage transportation problem with unknown consumer demands en_US dc.type Article en_US
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