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

Mathematical models of agricultural production management in high risk environments

“…Since the task of optimizing the production of agricultural products in the face of uncertainty makes it possible to obtain many optimal solutions using different methods, the work of various authors involved in the development and implementation of such tasks is considered. The authors of [4][5][6][7][8][9][10] propose optimization models for solving problems related to business processes, planning, and management under conditions of uncertainty and risk. At the same time, various research objects are described: different business processes [4], production and sales of products by an enterprise [5], a multi-level process for managing an enterprise's production activities in a risk environment [6], planning food production [7 -9] and the use of land resources [10].…”

Algorithm for selecting the winning strategies in the processes of managing the state of the system "supplier – consumer" in the presence of aggressive competitor

“…In addition, when considering the competitiveness of a enterprise in terms of its capability to minimize the price of the product, one should somehow formalize the notion of an innovation activity, introduced into consideration as one of the main factors for enterprise success in the market [13]. One such optimization model of production planning and delivery of diversified products was proposed in paper [14], and this idea was further advanced in [15]. Special features of solutions, proposed in study [15], is that in order to determine the optimal production plans, as well as its delivery to consumers, and investment in production, it is necessary to obtain equilibrium solutions in the duopoly model.…”

“…One such optimization model of production planning and delivery of diversified products was proposed in paper [14], and this idea was further advanced in [15]. Special features of solutions, proposed in study [15], is that in order to determine the optimal production plans, as well as its delivery to consumers, and investment in production, it is necessary to obtain equilibrium solutions in the duopoly model. And they define the equilibrium decisions by Cournot if enterprises decide to release products simultaneously and independently of each other, and by Stakelberg if one manufacturer believes that the competitor would behave as a Cournot duopolist.…”

“…x Such a representation is convenient for practical use when quantifying the opportunities for player 2. For this assessment, it is needed to include in equation (15) the maximally possible (y (2) =4) and the minimally possible (y (2) =1,1) values for an output variable, and to solve the resulting equation relative to ( ) ξ = ϕ ξ , derived in this case, describe the limits of opportunities for player 2 (Fig. 2).…”

“…In the case under consideration, at y (2) <y (1) , player 1 should determine the conditions under which it might have an equal chance with player 2. To this end, it will suffice to equate the right sides of equations (18) and (15) and to solve the resulting equation relative to ( ) x : x , one can choose such…”