Strategy for selecting optimal volumes of production activities with iterative learning

The problem of optimal control of production activities with iterative learning is considered. In the process of mastering new products, introducing new technologies and innovations at industrial enterprises, the effect of iterative learning is manifested, which leads to a reduction in time spent on manufacturing products while increasing the cumulative production volume. The goal of solving the problem is to reduce labor costs of industrial enterprises during the development of new products, the introduction of new technologies and innovations. The problem is formalized mathematically as a continuous-time optimal control task for a production system. The dynamics of change in the production system are described by an ordinary differential equation. Minimization of the integral growth rate of labor costs for production is considered as an optimality criterion. The original problem is reduced to the task of minimizing the integral natural logarithm of labor costs. An analytical solution to the problem is found using Pontryagin's maximum principle. A strategy for selecting optimal production volumes for any learning model has been determined. Optimal production volumes are selected in inverse proportion to the specific labor costs (labor intensity) for manufacturing products. It is shown that when choosing optimal production volumes, labor costs for manufacturing products are constant over the entire planning horizon.