MATHEMATICAL MODELING OF A MULTI-STAGE PROCESS IN FOOD PRODUCTION

Modern civilization is characterized by rapid growth in computational capabilities and the widespread adoption of digital technologies. In this context, robots, intelligent devices, and AI-based software systems are increasingly used in industry and scientific research. Informatization is actively penetrating the food industry, which has traditionally relied on empirical approaches and has accumulated large volumes of experimental data that now require mathematical modeling and computer-based analysis. This study presents a mathematical model of a multi-stage bread-making process formulated as a system of nonlinear differential equations with concentrated parameters. The model describes key technological stages, including raw material preparation, fermentation, cutting and shaping, baking, and product output. Each stage is represented as a dynamic subsystem with temperature-dependent transition intensities. A parameterization of kinetic coefficients is proposed that accounts for the basic process rates and their sensitivity to temperature variations. It is shown that the control problem of the technological process can be reduced to a Volterra integral equation of the second kind with an analytical solution. Based on this result, a controllability criterion establishes relationships among baking time, temperature regimes, initial raw material reserves, and required production volume. Numerical experiments confirm applicability for optimization and digital twin development in the food industry.