Method of finding equilibrium solutions for duopoly of supply chains taking into account the innovation activity of enterprises

Abstract

We developed and analyzed an economic-mathematical model of duopoly of industrial enterprises-manufacturers with similar nomenclature of products taking into account innovation activity in the field of technologies. It is assumed that enterprises are the links in supply chains, that is, in addition, we examined delivery of the finished goods to the points of consumption. In contrast to the micro-economic theory of the firm, here price competition is investigated at the operational level, that is, when making up plans for the output of products and their delivery to destination points. Innovation activity implies that enterprises invest part of their profit into improvement of the technological process, and, in this case, production expenses of enterprises are the assigned decreasing functions of the investments indicated. In line with the classical theory of the firm, it is considered that the demand function in each point of delivery of finished goods linearly depends on the summary volumes of these goods, delivered from both enterprises. Optimality criterion for supply chains of both plants is the maximum of summary profit, obtained from the sale and delivery of finished products to the points of consumption taking into account expenditures for innovative solutions.We found equilibrium solutions of duopoly by Cournot and Stackelberg. Numerical illustration of the obtained results is given. The obtained results could be used in the process of joint development of marketing, logistic and innovation strategies of enterprises

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