Optimization of the production plan by three-criterion modeling

The object of research is the processes of optimizing the production plan according to certain criteria by modeling. One of the most problematic places is the complexity of coordination and taking into account the influence of criteria on the optimal production plan. From the point of view of mathematics, the search for the optimal result can be obtained with different criteria laid down, but from an economic point of view it is important to choose those that are of decisive importance. That is, their weight is important for the consumer in deciding on a purchase and for the manufacturer – in terms of the production capabilities of certain types of products and performance (production efficiency). This problem was solved by solving the three-criterion problem of planning production. The search for a compromise alternative was achieved through a step-by-step solution of the proposed mathematical model for optimizing the production plan according to the most important criteria for the producer and consumer: profit, quality and demand for products of each type, taking into account the known number of units of each resource. The ideal point method, the simplex method and the Lagrange multiplier method are used. The test example provides an algorithm for solving the optimization problem. The result obtained – the three-criterion task of production planning has been solved, which makes it possible to maximize profit from production, product quality and demand for products with known initial resource components. The importance/significance of the developed scientific and methodological approach is confirmed/argued by the fact that the achievement of effective results of the enterprise’s activity directly depends on the optimal production plan. Given the results of the conducted research, out of the many possible alternatives, the enterprise will be able to most efficiently produce the products necessary for the consumer by type and quality. That is, with known resource parameters, the maximum possible positive result is achieved for the manufacturer and for the consumer. The proposed economic and mathematical tools can be used in solving problems of optimizing production in various sectors of the economy.