DYNAMIC LINEAR MODEL OF MARKETING ON A MULTI-SEGMENT MARKET
S.B. Barabash1, I.A. Bykadorov1,2,3, M.V. Pudova1
1Novosibirsk State University of Economics and Management, Str. Kamenskaya, 56, Novosibirsk, 630099, Russia
2Sobolev Institute of Mathematics SB RAS, Akademik Koptyug Avenue, 4, Novosibirsk, 630090, Russia
3Novosibirsk National Research State University, Str. Pirogova, 2, Novosibirsk, 630090, Russia
Keywords: оптимальное управление, многосекторный рынок, гудвилл, реклама, параметризация, координирующая задача, optimal control, multi-sector market, goodwill, advertising, parameterization, coordinating problem
Abstract
A linear model of optimal control for the marketing of a homogeneous product is considered. The process of production and promotion of the product for the manufacturing firm is divided into two consecutive periods; the first one is devoted to production, while the second one - to the sale of the product. The activities of the firm during these periods (and, consequently, the mathematical description of its activities) are significantly different. The state variables of the model are given by variables characterizing intangible assets (both consumers and sellers), called «goodwills». The firm seeks to maximize profits, subject to not less than a predetermined period of goodwill at the end of the sales level.
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