The activity of distribution companies is multifaceted. Ihey establish contacts with producers and consumers, determine the range of prices of medicines, do promotions, hold stocks of pharmaceuticals and take risks in their further selling.

Their internal problems are complicated by the political crisis in the country, decreased purchasing power of national currency, and the rise in interest rates on loans. Therefore the usage of stochastic models of dynamic systems for the research into optimizing the management of pharmaceutical products distribution companies taking into account credit payments is of great current interest.

A stochastic model of the optimal credit strategy of a pharmaceutical distributor in the market of pharmaceutical products has been constructed in the article considering credit payments and income limitations.

From the mathematical point of view the obtained problem is the one of stochastic optimal control where the amount of monetary credit is the control and the amount of pharmaceutical product is the solution curve.

The model allows to identify the optimal cash loan and the corresponding optimal quantity of pharmaceutical product that comply with the differential model of the existing quantity of pharmaceutical products in the form of Ito; the condition of the existing initial stock of pharmaceutical products; the limitation on the amount of credit and profit received from the product selling and maximize the average integral income.

The research of the stochastic optimal control problem involves the construction of the left process of crediting with determination of the shift point of that control, the choice of the right crediting process and the formation of the optimal credit process.

It was found that the optimal control of the credit amount and the shift point of that control are the determined values and don’t depend on the coefficient in the Wiener process and the optimal trajectory of the amount of pharmaceutical product has a stochastic character.

If the coefficient in the Poisson process differs from zero, then there are three modes of crediting (full, partial and absence of crediting), and if the coefficient equals to zero there are two modes of financing (full and the absence of crediting).

Key words: pharmaceutical distributor; optimal control; stochastic model.

DOI: http://dx.doi.org/10.17721/1728-2667.2015/176-11/8

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