Application of maximum principle to optimization of production and storage costs

IF 1.2 4区计算机科学 Q4 AUTOMATION & CONTROL SYSTEMS

Archives of Control Sciences Pub Date : 2023-07-20 DOI:10.24425/acs.2021.139734

L. Popescu, Ramona-Maria Dimitrov

引用次数: 1

Abstract

A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control aﬃne systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.

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应用最大化原理优化生产和储存成本

研究了生产和储存成本的优化问题。这个问题包括制造n种产品，在一些给定的限制下，使总生产和存储成本最小。采用无漂控制仿射系统的框架建立了数学模型。利用李氏几何方法研究了系统的可控性，利用庞特里亚金极大值原理得到了系统的最优解。这证明了经济系统是不可控的，即我们只能生产一定数量的产品。最后给出了一些数值算例，并用图形表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archives of Control Sciences Mathematics-Modeling and Simulation

CiteScore

2.40

自引率

33.30%

发文量

审稿时长

14 weeks

期刊介绍： Archives of Control Sciences welcomes for consideration papers on topics of significance in broadly understood control science and related areas, including: basic control theory, optimal control, optimization methods, control of complex systems, mathematical modeling of dynamic and control systems, expert and decision support systems and diverse methods of knowledge modelling and representing uncertainty (by stochastic, set-valued, fuzzy or rough set methods, etc.), robotics and flexible manufacturing systems. Related areas that are covered include information technology, parallel and distributed computations, neural networks and mathematical biomedicine, mathematical economics, applied game theory, financial engineering, business informatics and other similar fields.