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
Highlights
At present, the concept of supply chain management has been disseminated
That is why of interest is the study into economic-mathematical models of competition, which would be a synthesis of innovative policies of enterprises and logistics management concept
We developed and examined an economic-mathematical model of duopoly, which takes into account a possibility to deduct a portion of the profit of competing enterprises-manufacturers on innovative activity
Summary
The concept of supply chain management has been disseminated. This creates many problems associated with modeling the interaction between the elements of the chain. Principles were developed to construct economic solutions for the companies-duopolies generated by such concepts as the Cournot equilibrium, the Stackelberg equilibrium, the Nash equilibrium, cartel agreements [1]. As it is well-known [2], one of the main factors of success of an enterprise in the market is the intention to achieve market advantages based on innovative activity. That is why it is a relevant task to construct and analyze optimization models, which would take into account simultaneously the impact of innovation activity of enterprises on their gaining competitive advantages and the use of the logistic concept of supply chains
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