### Abstract

Supply chain management occupies a very important place in the activities of any company in a globalized economy and increasing competition in the market. The main goal of supply chain management is to coordinate the work of firms - suppliers of raw materials, firmsmanufacturers and trading companies selling goods on the market. The article studies a continuous mathematical model describing the interaction of the listed firms under conditions of a non-constant rate of supply of some kind of raw materials. It is assumed that the speed of supply of these raw materials can take two possible values, the choice of which is determined by the manufacturer, the manufacturer, the higher rate of supply of raw materials corresponds to the intensive production variant of the product, the slower speed corresponds to the usual production variant. Mathematical modeling is carried out using differential equations. An optimization problem is formulated, which consists in choosing the time point for switching the mode of supply of raw materials from the intensive version to the normal version in order to maximize the income of the manufacturer-manufacturer.

Original language | English |
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Pages (from-to) | 353-361 |

Number of pages | 9 |

Journal | Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya |

Volume | 15 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

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### Scopus subject areas

- Computer Science(all)
- Control and Optimization
- Applied Mathematics

### Cite this

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**Mathematical model of the integrated supply chain.** / Bure, Vladimir M.; Karelin, Vladimir V.; Polyakova, Lyudmila N.; Flegontov, Aleksander V.

Research output

TY - JOUR

T1 - Mathematical model of the integrated supply chain

AU - Bure, Vladimir M.

AU - Karelin, Vladimir V.

AU - Polyakova, Lyudmila N.

AU - Flegontov, Aleksander V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Supply chain management occupies a very important place in the activities of any company in a globalized economy and increasing competition in the market. The main goal of supply chain management is to coordinate the work of firms - suppliers of raw materials, firmsmanufacturers and trading companies selling goods on the market. The article studies a continuous mathematical model describing the interaction of the listed firms under conditions of a non-constant rate of supply of some kind of raw materials. It is assumed that the speed of supply of these raw materials can take two possible values, the choice of which is determined by the manufacturer, the manufacturer, the higher rate of supply of raw materials corresponds to the intensive production variant of the product, the slower speed corresponds to the usual production variant. Mathematical modeling is carried out using differential equations. An optimization problem is formulated, which consists in choosing the time point for switching the mode of supply of raw materials from the intensive version to the normal version in order to maximize the income of the manufacturer-manufacturer.

AB - Supply chain management occupies a very important place in the activities of any company in a globalized economy and increasing competition in the market. The main goal of supply chain management is to coordinate the work of firms - suppliers of raw materials, firmsmanufacturers and trading companies selling goods on the market. The article studies a continuous mathematical model describing the interaction of the listed firms under conditions of a non-constant rate of supply of some kind of raw materials. It is assumed that the speed of supply of these raw materials can take two possible values, the choice of which is determined by the manufacturer, the manufacturer, the higher rate of supply of raw materials corresponds to the intensive production variant of the product, the slower speed corresponds to the usual production variant. Mathematical modeling is carried out using differential equations. An optimization problem is formulated, which consists in choosing the time point for switching the mode of supply of raw materials from the intensive version to the normal version in order to maximize the income of the manufacturer-manufacturer.

KW - Multi-echelon supply chain

KW - Production

KW - Stock level of the goods

UR - http://www.scopus.com/inward/record.url?scp=85074879623&partnerID=8YFLogxK

U2 - 10.21638/11702/spbu10.2019.305

DO - 10.21638/11702/spbu10.2019.305

M3 - Article

AN - SCOPUS:85074879623

VL - 15

SP - 353

EP - 361

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 3

ER -