Building a Model of Supply Chains Duopoly Taking Into Account the Marketing and Innovative Activities of Manufacturing Enterprises

This paper reports the construction and analysis of the economic and mathematical model of the duopoly of supply chains, based on the model of optimization of plans for the release and delivery of multi-range articles, taking into consideration the marketing and innovative activities of industrial enterprises. Demand for goods is supposed to be an increasing function of advertising costs. In this case, marketing investments affect only the base selling prices of articles and do not affect competitive discounts. The explicit form of this dependence can be established as a result of marketing research. It is also assumed that investments in innovative technological projects could reduce industrial costs; production costs are decreasing functions of the size of the investment. It is believed that the demand function is linearly dependent on the total volume of output produced. The criterion of optimality for supply chains is the maximum of the total profit received from the sale and delivery of finished products to points of consumption, taking into consideration the costs of production and advertising. As a result of this study, equilibrium solutions of the duopoly according to Cournot and Stackelberg were found. That has made it possible to determine the optimal values of product volumes for output, the size of investment investments, as well as product advertising costs. The model helped study the impact of investment deductions and advertising costs on the acquisition of competitive advantages by manufacturing enterprises. A numerical illustration of the results obtained is given. The proposed approach could be used to build and analyze dynamic optimization models taking into consideration the innovation and marketing activities of enterprises, as well as to study other market structures