M. Boychuk, PhD in Physics and Mathematics, Associate Professor, O. Yaroshenko, PhD in Economics, Associate Professor Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine STOCHASTIC MODELING OF OPTIMIZED CREDIT STRATEGY OF A DISTRIBUTING COMPANY ON THE PHARMACEUTICAL MARKET

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

  1. Bortnytskyi V. A., 2012. Prospects for the pharmaceutical industry as a system of innovative building systems. Formation of market relations in Ukraine, 10, pp. 154-159.
  2. Karpyshyn N., 2009. Ways to optimize financial provision of healthcare in Ukraine. World Finance, 4, pp. 99-104.
  3. Dremova N. B., 2005. Development of methodology of marketing research in pharmacy. “Man and his health” Kursk scientific and practical bulletin, 1, pp. 62-76.
  4. Palasiuk, B. M., 2013. Using simulation for improving inventory management distribution company in the market pharmaceutical industry. Management, economics and quality assurance in pharmacy, 2(28), pp. 85-93.
  5. Posylkina, O. V., Khromyh, A. G. and Novytska, Yu. Ye., 2014. Modern approaches to the management of stocks in the wholesale pharmaceutical companies. Access mode: http://dspace.nuph.edu.ua/handle/123456789/6222
  6. Tryhub M. V. and Yasynskyi V. V., 2001. Control of nonlinear stochastic systems. Journal of Automation and Information Sciences, 2, pp. 72-81.
  7. Habasov R., Kyryllova F. M. and Kostiukova O. Y., 1995. Synthesis of optimal controls for dynamic systems with incomplete and uncertain information about their states. Access mode: http://mi.mathnet.ru/rus/tm/v211/p140
  8. Tretiakov V. E., Tselyshcheva Y. V., and Shyshkyn H. Y., 1992. The optimal control of systems with incomplete and incorrect information Access mode: http://mi.mathnet.ru/eng/timm397
  9. Krasovskyi N.N., Tarasova S.Y., Tretiakov V.E. and Shyshkyn H.Y., 1986. Control with information deficit. Problems of control and information theory, 15 (3), pp. 1-13.
  10. Ka-Veng Yuen, James L Beck, 2003. Reliability-based robust control for uncertain dynamical systems using feedback of incomplete noisy response measurements. Earthquake engineering and structural dynamics, 32, pp. 751-770. DOI: 10.1002/eqe.247
  11. Quincampoix M. and Veliov V.M., 2004. Optimal control of uncertain systems with incomplete information for the disturbances.SlAM Journal on Control and Optimization, Vol. 43, No. 4, pp. 1373-1399. DOI: 10.1137/S0363012903420863
  12. Serhyenko I. V., Kozeratskaia L. N. and Lebedeva T. T., 1995. Investigation of the stability and parametric analysis of discrete optimization problems. Kyiv: Naukova dumka, 170 p.
  13. Sergienko I.V., Deineka V.S., 2005. Optimal Control of Distributed Systems with Conjugation Conditions. New York: Kluwer Akademic Publishers, 400 p.
  14. Ayda-zade K.R. and Ragimov A.B., 2007. Solution of optimal control problem in class of piecewise-constant functions. Avtomatika i Vychislitel’naya Tekhnika, 41 (1), pp. 27-36. DOI: 10.3103/S0146411607010038.
  15. Skorokhod A. V., 1990. Lectures on the theory of random processes. Kyiv: Lybid, 168 p.
  16. Andreeva E. A., Kolmanovskiy E. B. and Shayhet L. E., 1992. Management systems with aftereffect. Moskva: Nauka, 336 p.
  17. Boichuk M. and Semchuk A., 2013. Stochastic modeling of the full cycle of single-commodity macroeconomic growth. Cybernetics and Systems Analysis, 2, pp.156-163.
  18. Boichuk M. and Semchuk A., 2013. Stochastic modeling of the full cycle of optimal ecological and economic dynamic. Journal of Automation and Information Sciences, 2, pp.125-139.
  19. Boichuk M. and Semchuk A., 2011. A stochastic model of the optimal economics with ecological and economic criterion and lag. Formation of market economy in Ukraine: scientific journal, 25, pp. 12-27.
  20. Hrygorkiv V.S. and Yaroshenko O.I., 2007. Modeling of optimum credit strategy of realtor. Economic cybernetics : scientific journal, 1-2(43-44), pp. 4-9.
  21. Boichuk M.V. and Yaroshenko O.I., 2015. Credit strategy optimization of a distributing company on the pharmaceutical market. Scientific journal of Bukovyna State University of Finance and Economics, pp. 258-263.
  22. Yurchenko I. V., Yasynska L., Yasynskyi V., 2002. Methods of stochastic modeling systems. – Chernivtsi: Prut, 416 p.
  23. I.and Skorohod A.V., 1977. Controlled random processes. – Kyiv: Naukova dumka, 251 p.
  24. Magnus Ya.R., Katyishev P.K. and PeresetskiyA.A. Econometrics. Basic course. – Moskva: Delo, 248 p.


  • pdf 176_8
    File size: 351 kB Downloads: 69