Mathematical modeling of the optimal market of competing goods in conditions of deliveries lags

Poddubny V.V., Romanovich O.V.
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The nonlinear restrictive (with restrictions of the inequalities type) dynamic mathematical model of the committed competition vacant market of many goods in conditions of the goods deliveries time-lag and of the linear dependency of the demand vector from the prices vector is offered. The problem of finding of prices and deliveries of goods into the market which are optimal (from seller’s profit standpoint) is formulated. It is shown the seller’s total profit maximum is expressing by the continuous piecewise smooth function of vector of volumes of deliveries with breakup of the derivative on borders of zones of the goods deficit, of the overstocking and of the dynamic balance of demand and offer of each of goods. With use of the predicate functions technique the computing algorithm of optimization of the goods deliveries into the market is built.

Keywords: mathematical modeling, market of many goods, price, demand, offer, lag of deliveries, discrete time, dynamics, nonlinearity, seller’s profit, piecewise smoothness, optimization algorithm
Citation in English: Poddubny V.V., Romanovich O.V. Mathematical modeling of the optimal market of competing goods in conditions of deliveries lags // Computer Research and Modeling, 2012, vol. 4, no. 2, pp. 431-450
Citation in English: Poddubny V.V., Romanovich O.V. Mathematical modeling of the optimal market of competing goods in conditions of deliveries lags // Computer Research and Modeling, 2012, vol. 4, no. 2, pp. 431-450
DOI: 10.20537/2076-7633-2012-4-2-431-450
URL: http://crm-en.ics.org.ru/journal/article/1901/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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