Application of maximum principle to optimization of production and storage costs

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...

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Bibliographic Details
Published inArchives of control sciences Vol. 31; no. 4; pp. 865 - 881
Main Authors Popescu, Liviu, Dimitrov, Ramona
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter Poland 01.01.2021
Polish Academy of Sciences
Subjects
Control theory
Controllability
Economics
Graphical representations
Inventory control
Mathematical models
Maximum principle
optimal control
Optimization
pontryagin maximum principle
Process controls
Product returns
production and storage
Production costs
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Summary: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.
ISSN:1230-2384
2300-2611
DOI:10.24425/acs.2021.139734