Planning the production of innovative products based on linear programming

Innovation activity is primarily associated with the production of new products and services and release them in the market. In the context of globalization of the Russian Federation and its integration into the world economic system, domestic industrial enterprises more and more often have to compete with foreign companies. This encourages Russian organizations to adjust their production scheme. The problem of production and sales of products and services, particularly those that are innovative, currently has no single and clear solution, which leads to the existence of many methods and algorithms to achieve optimal solutions using mathematical tools, and those that are purely theoretical. The purpose of this paper is to build an optimization model for the production process of innovative products. The paper discusses in detail the mathematical model of input-output balance developed by V.V. Novozhilov and the industrial task developed by L.V. Kantorovich. The author highlights their features that must be incorporated in the models for managing innovative activity of enterprises. The paper contains a detailed elaboration of the example of application of these algorithms in the production activity of an organization on the basis of which an optimum plan of production of innovative products and products of the old product range is calculated. The production program that was developed substantiated the costs of the resources allocated in the task. Further research directions may include the search for additional optimality criteria such as revenue, cost, profitability, and finding compromises between them.