Optimization of the production program for output of innovative products of industrial enterprises

Innovations and their implementation largely depend on many parameters of the production stage of the innovation process. These include the goals that the head of an industrial company seeks to achieve, the constraints of capacities and resources typical of production technologies of the enterprise, utilization of available labor potential to the maximum without possible downtime and significant surplus, effective implementation of own products in the production chain in order to manufacture more advanced goods and services, an opportunity to make the production process more stable and flexible with respect to possible risks and unaccounted for factors. All these questions point to the fact that planning the production of innovative products has a number of unresolved issues, which, in turn, determine the relevance of the present study. The aim of the study is to develop a set of mathematical tools that will help optimize the production program for output of innovative products at industrial enterprises. On the basis of scientific works and studies of L.V. Kantorovich, V.V. Leontiev and V.V. Novozhilov, the author designed a mathematical model of linear programming that optimizes the output of innovative products at industrial enterprises. The model takes into account various constraints related to the existing resources and capacities of an enterprise; it also takes into account the use of its own products in the production of other products. On the basis of the model, the author considers an example in which the production of products at industrial organizations is optimized when four local criteria are selected (maximum profit, minimum production costs, maximum profit and profitability of production). When selecting the target function “profitability” the simulated system of inequalities loses the property of linearity (optimality criterion is a fraction). In this regard the author proposes a scheme that reduces this problem to a linear programming problem, and then its detailed algorithm is formed and its application is presented at an illustrative example. The author proposes a scheme of a compromise program that takes into account the discovered manufacturing plans. Further research directions can include the use of the elements of dynamic programming and verification of sustainability of the solutions.