Simulation statistical modeling of the market of one goods with the optimal deterministic strategy of the delivery of goods under condition of stochastic demand

The simulation model of the inertial market of one goods is considered under conditions of delivery time-lag and casual fluctuations of the purchase requirement under the optimal deterministic strategy of the supply of goods to the market. The mathematical description of the market is given by the restrictive (because of restrictions of inequalities type) dynamic model with the time-lag of control taking into account casual fluctuations of the purchase requirement. It was shown that the optimal (in the sense of the maximum profit of the seller) strategy of the goods delivery to the market is determining by the market conditions (commodity deficit, overstocking of the market, or the dynamic balance state of the market). The algorithm of the finding of optimum deterministic strategy of the delivery of goods to the market is constructed with using of the forecasting deterministic model of the market. The simulation modeling and statistical analysis of the market dynamics are organized with simultaneous use of the stochastic model and of the forecasting deterministic model. The statistical simulation of the model behavior is performed; average values, variances, and auto-correlation functions for all variables of the model are investigated. It is shown that in view of non-linearity of the model the casual fluctuations of demand shift the statistical equilibrium of the market from its deterministic equilibrium.