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On continuous models of current stock of divisible productions

Pages: 601 - 613, Issue Special, September 2011

 Abstract        Full Text (303.8K)              

Sharif E. Guseynov - Institute of Mathematical Sciences and Information Technologies, University of Liepaja, Transport and Telecommunication Institute, 1 Lomonosov Street, Riga LV-1019, Latvia (email)
Eugene A. Kopytov - Transport and Telecommunication Institute, 1 Lomonosov Street, Riga LV-1019, Latvia (email)
Edvin Puzinkevich - Transport and Telecommunication Institute, 1 Lomonosov Street, Riga LV-1019, Latvia (email)

Abstract: In the given paper we investigate the problem of constructing continuous and unsteady mathematical models, to determine the volumes of current stock of divisible productions, in one or several interconnected warehouses using the apparatus of mathematical physics and continuum principle. It is assumed that production distribution and replenishment is continuous. The constructed models are stochastic, and have di erent levels of complexity, adequacy and application potential. The simple model is constructed using the theory of ODE, for construction of more complex models the theory of PDE is applied. Also using additional conditions for the finite-diff erenced model for determination of random volume of divisible homogeneous production is constructed, and this nite di erenced mathematical model makes it possible to determine one of the possible trajectories of the random quantity. All constructed models can be used for on-line monitoring of the dynamics of the random productions volumes.

Keywords:  Inventory control model, current stock, divisible production, stochastic equations of mathematical physics
Mathematics Subject Classification:  Primary: 90B05, 90B30; Secondary: 49J20

Received: August 2010;      Revised: April 2011;      Published: October 2011.