2010
HMS 2010 Proceeding
Stochastic ODE and PDE models of current stock of divisible productions
Authors: Eugene Kopytov, Sharif Guseynov, Edvin Puzinkevich
Abstract
In the given paper we investigate the problem of constructing continuous and unsteady mathematical models for determine the volumes of current stock of divisible productions in one or several interconnected warehouses using apparatus of mathematical physics and continuum principle. It is assumed that time of production distribution and replenishment is continuous. The constructed models are stochastic, and have different levels of complexity, adequacy and application potentials. The simple model is constructed using the theory of ODE, for construction of more complex models it is applied the theory of PDE. Besides, provided some additional conditions the finite- differenced model for determination of random volume of divisible homogeneous production is constructed, and this finite differenced mathematical model makes possible to determine one of possible trajectories of the random quantity. All constructed models can be used for on-line monitoring of the dynamics of the productions random volumes.
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