生产调度问题的一种求解算法

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI:10.1134/S1990478924040173

N. P. Savenkova, A. Yu. Mokin, A. A. Dryazhenkov, L. A. Artemyeva

{"title":"生产调度问题的一种求解算法","authors":"N. P. Savenkova, A. Yu. Mokin, A. A. Dryazhenkov, L. A. Artemyeva","doi":"10.1134/S1990478924040173","DOIUrl":null,"url":null,"abstract":"<p> A mathematical model of raw materials processing is proposed. The production consists of\nunits processing raw materials, storage tanks, and mixing units. The processing units are assumed\nto operate in one of two known modes. Switching from one mode to another can be carried out no\nmore than once. The problem of finding the optimal capacity of production at each of units, as\nwell as the time of switching units from one operating mode to another is formulated in a form of\ndiscrete optimization problem. The solution of this problem should ensure an achievement of the\nspecified production plan. A method for its solution is proposed, including a transition to\na convex statement, as well as an algorithm for discretizing the obtained control.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"839 - 849"},"PeriodicalIF":0.5800,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Algorithm to Search for a Solution\\nto a Production Scheduling Problem\",\"authors\":\"N. P. Savenkova, A. Yu. Mokin, A. A. Dryazhenkov, L. A. Artemyeva\",\"doi\":\"10.1134/S1990478924040173\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> A mathematical model of raw materials processing is proposed. The production consists of\\nunits processing raw materials, storage tanks, and mixing units. The processing units are assumed\\nto operate in one of two known modes. Switching from one mode to another can be carried out no\\nmore than once. The problem of finding the optimal capacity of production at each of units, as\\nwell as the time of switching units from one operating mode to another is formulated in a form of\\ndiscrete optimization problem. The solution of this problem should ensure an achievement of the\\nspecified production plan. A method for its solution is proposed, including a transition to\\na convex statement, as well as an algorithm for discretizing the obtained control.\\n</p>\",\"PeriodicalId\":607,\"journal\":{\"name\":\"Journal of Applied and Industrial Mathematics\",\"volume\":\"18 4\",\"pages\":\"839 - 849\"},\"PeriodicalIF\":0.5800,\"publicationDate\":\"2025-07-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1990478924040173\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924040173","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}

引用次数: 0

摘要

提出了原料加工过程的数学模型。生产由原料处理单元、储罐和混合单元组成。假定处理单元以两种已知模式中的一种运行。从一种模式切换到另一种模式只能执行一次以上。求解各机组的最优生产能力问题，以及机组从一种工作模式切换到另一种工作模式所需的时间问题，用离散优化问题的形式表述。该问题的解决应确保完成规定的生产计划。提出了一种求解方法，包括向凸命题的过渡，以及对得到的控制进行离散化的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An Algorithm to Search for a Solution to a Production Scheduling Problem

A mathematical model of raw materials processing is proposed. The production consists of units processing raw materials, storage tanks, and mixing units. The processing units are assumed to operate in one of two known modes. Switching from one mode to another can be carried out no more than once. The problem of finding the optimal capacity of production at each of units, as well as the time of switching units from one operating mode to another is formulated in a form of discrete optimization problem. The solution of this problem should ensure an achievement of the specified production plan. A method for its solution is proposed, including a transition to a convex statement, as well as an algorithm for discretizing the obtained control.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.