DOI: https://doi.org/10.18371/fcaptp.v2i25.136688

TWO-LEVEL BALANCE MODEL OF PRODUCTS DISTRIBUTION BASED ON MARKOV CHAINS

V. I. Lapshyn, V. M. Kuznichenko, T. V. Stetsenko

Abstract


On the basis of one of approaching for models of exchange the two-level balance model of products distribution is created at the use of mathematical theory of probabilistic processes. The participants of nearby overhead and lower channels of commodities distribution in the chains of deliveries can be situated on these levels: producers-consumers, mediators of distribution. A model on the basis of Markov chains allows to determine self-congruent equilibrium relative distributions of finances and commodities monetary at every level accordingly. The relations of amount of the got commodities at bottom level will be saved if volume of deliveries changes at top level proportionally to the equilibrium distribution. In this case every recipient of bottom level knows the part from the distributed products, that assists more effective organization of trade process. The offered methodology is interesting for creation of multilevel channels models of commodities distribution.


Keywords


exchange model; balance; Markov chain.

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References


Blyde, J. (2017). International supply chains and trade agreements. Applied Economics Letters, 1–6. Retreived from: https://doi.org/10.1080/13504851.2017.1409414.

Valras, L. (2000). Elementy chistoy politicheskoy ekonomii [Elements of pure political economy]. Moscow: Izograf [in Russian].

Arrow, K. & Debreu, G. (1954). Existence of Equilibrium for a Competitive Economy. Econometrica, 25, 265–290.

Debreu, G. (1974). Excess Demand Functions. Journal of Mathematical Economics, 1, 15–23.

McKenzie, L. W. (1954). On equilibrium in Graham’s model of world trade and other competitive systems. Econometrica, 22, 146–161.

Sonnenschein, H. (1973). Do Walras identity and continuity characterize the class of community excess demand functions? Journal of Economic Theory. 6, 345–354.

Makarov, V. L. & Rubinov, A. M. & Levin, M. I. (1995). Mathematical Economic Theory: Pure and Mixed Types of Economic Mechanisms. Advanced Textbooks in Economics, Elsevier, North Holland.

Makarov, V. L. (2003). Ischislenie institutov [Calculus of Institutes]. Ekonomika i matematicheskye metody Economics and mathematical methods, 39, 14–32 [in Russian].

Brodskiy, B. E. (2008). Modeli ekonomicheskogo obmena [Models of economic exchange]. Ekonomika i matematicheskiye metody Economics and mathematical methods, 44, 72–89 [in Russian].

Andreev, M. Yu. (2008). Stochasticheskaya zadacha chistogo obmena i aktual’nuyye beskonecheno malyye tseny [Stochastic problem of pure exchange and current infinitesimal prices]. Ekonomika i matematicheskiye metody Economics and mathematical methods, 44, 68–82 [in Russian].

Howard, R. A. (1960). Dynamic Programming and Markov Processes. The MIT Press: Cambridge, MA.

Kemeny, J. G & Snell, J. L. (1976). Finite Markov Chains. Springer-Verlag: New York, Berlin, Heideberg, Tokio.

Zhluktenko, V. I., Nakonechnyi, S. I. & Sanina, S. S. (2002). Stokhastychni protsesy ta modely v ekonomitsi, sotsiolohiyi, ekolohiyi [Stochastic processes and models in economics, sociology, ecology]. Kyiv [in Ukrainian].

Sokolov, G. A. & Chistyakov, N. A. (2005). Teoriya veroyatnostey. Upravlyaemyye tsepi Markova v ekonomike [Probability theory. Managent Markov Chains in the economy]. Moscow [in Russian].

Kuznichenko, V. & Lapshyn, V. & Stetsenko, T. (2014). Stochasticheskiy podhod k analizu lineynoy modeli obmena: Primenenie tsepey Markova v rechenii zadach upravleniya ekonomicheskimi sistemami [The stochastic approach to the analysis of a linear exchange model: Application of Markov Chains in the task of economic systems]. Saarbrücken, Deutschland: Palmarium academic publishing [in Russian].

Kuznichenko, V. M. & Lapshyn, V. I. (2015). Probabilistic approach to the continuous model in the economy. Scientific Bulletin of National Mining University. 5 (149), 137–141.

Kostenko, E., Kuznichenko, V. M. & Lapshyn, V. I. (2016). Deficit model of exchange for continuous processes with external control. Applied Economic Letters, 1–4. Retrieved from: 10.1080/13504851.2016.1250717.

Kuznichenko, V. M. & Lapshyn, V. I. (2017). Generalized Deficit-Having Model of Exchange for Continuous Processes with External Management. Scientific Bulletin of National Mining University, 5 (161), 117–122.

Wilkie, A. D. (1993). Stochastic models for inflation, investments and exchange rates. Conference on Forecasting Inflation and Investment Returns. - Toronto: Canada, 473–509.

Goswami, S. & Chakraborti, A. (2014). Кinеtіс Ехсhаngе Моdеl іп Есоnоmісs апd Sосіоlogу. ARXIV e-print (arXiv:1408.1365), 1–19.

Leontief, W. (1936). Quantitative Input and Output Relations in the Economic System of the United States. Review of Economics and Statistics, 18, 3, 105–125.


GOST Style Citations


Blyde J. International supply chains and trade agreements [Electronic resource] / J. Blyde, V. Faggioni // Applied Economics Letters. – 2017. – November, 29. – Р. 1–6. – Avilable from : https://doi.org/10.1080/13504851.2017.1409414.

Вальрас Л. Элементы чистой политической экономии / Л. Вальрас. – Москва : Изограф, 2000. – 448 с.

Arrow K. Existence of Equilibrium for a Competitive Economy / K. Arrow, G. Debreu // Econometrica. - 1954. - Vol. 25. - P. 265–290.

Debreu G. Excess Demand Functions / G. Debreu // Journal of Mathematical Economics. - 1974. - Vol. 1. - P. 15–23.

McKenzie L.W. On equilibrium in Graham’s model of world trade and other competitive systems / L.W. McKenzie // Econometrica. - 1954. - Vol. 22. - P. 146–161.

Sonnenschein H. Do Walras’ identity and continuity characterize the class of community excess demand functions? / H. Sonnenschein // Journal of Economic Theory. - 1973. - Vol. 6. - P. 345– 354.

Makarov V. L. Mathematical Economic Theory: Pure and Mixed Types of Economic Mechanisms / V. L. Makarov, A. M. Rubinov, M. I. Levin // Advanced Textbooks in Economics. – 1995. – Elsevier, North Holland. - 610 p.

Макаров В. Л. Исчисление институтов / В. Л. Макаров // Экономика и математические методы. - 2003. - Т. 39, Вып. 2. - С. 14–32.

Бродский Б. Е. Модели экономического обмена // Б. Е. Бродский / Экономика и математические методы. - 2008. - Т. 44, № 4. - С. 72–89.

Андреев М. Ю. Стохастическая задача чистого обмена и актуальные бесконечно малые цены / М. Ю. Андреев // Экономика и математические методы. - 2008. - Т. 44, № 2. - С. 68–82.

Howard R. A. Dynamic Programming and Markov Processes / R. A. Howard. - The MIT Press : Cambridge, MA., 1960. - 136 p.

Kemeny J. G. Finite Markov Chains / J. G. Kemeny, J. L. Snell. - Springer-Verlag : New York, Berlin, Heideberg, Tokio, 1976. - 224 p.

Жлуктенко В. І. Стохастичні процеси та моделі в економіці, соціології, екології / В. І. Жлуктенко, С. І. Наконечний, С. С. Савіна. - Київ, 2002. – 226 c.

Соколов Г. А. Теория вероятностей. Управляемые цепи Маркова в экономике / Г. А. Соколов, Н. А. Чистяков. - Москва, 2005. - 248 c.

Кузниченко, В. М. Стохастический подход к анализу линейной модели обмена: Применение цепей Маркова в решении задач управления экономическими системами / В. М. Кузниченко, В. И. Лапшин, Т. В. Стеценко. - Saarbrücken, Deutschland : Palmarium academic publishing, 2014. – 66 p.

Kuznichenko, V. M. Probabilistic approach to the continuous model in the economy / V. M. Kuznichenko, V. I. Lapshyn // Scientific Bulletin of National Mining University. -2015. – № 5 (149). - P. 137–141.

Kostenko E. Deficit model of exchange for continuous processes with external control [Electronic resource] / E. Kostenko, V. M. Kuznichenko, V. I. Lapshyn // Applied Economic Letters. - 2016. - 2016. – Published online 07 Julау, 1–4. – Available at : 10.1080/13504851.2016.1250717.

Kuznichenko V. M. Generalized Deficit-Having Model of Exchange for Continuous Processes with External Management / V. M. Kuznichenko, V. I. Lapshyn // Scientific Bulletin of National Mining University. - 2017. – № 5 (161). - P. 117–122.

Wilkie A.D. Stochastic models for inflation, investments and exchange rates / A. D. Wilkie // Conference on Forecasting Inflation and Investment Returns. - Toronto : Canada. - 1993. - P. 473–509.

Goswami S. Кinеtіс Ехсhаngе Моdеl іn Есоnоmісs апd Sосіоlogу / S. Goswami, A. Chakraborti // ARXIV e-print (arXiv:1408.1365). - 2014. - P. 1–19.

Leontief W. Quantitative Input and Output Relations in the Economic System of the United States / W. Leontief // Review of Economics and Statistics. - 1936. - Vol. 18, № 3. - P. 105–125.

 





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ISSN (print) 2306-4994, ISSN (on-line) 2310-8770