Mathematical model of the integrated supply chain

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, firms-manufacturers 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.