The paper investigates the mathematical modeling of anaerobic fermentation for the utilization of animal wastes. It analyzes various approaches to the mathematical modeling of anaerobic digestion processes. However, most of the models previously proposed do not take into account a number of key parameters such as the levels of micro and macronutrientls (such as K, Na, Ca, Mg, Mo, etc.), values of volatile fatty acids, C/N ratio, pH levels, extent of grinding, moisture, and others. This paper proposes a new mathematical model of anaerobic fermentation under industrial scale conditions. The model was developed on the basis of regression analysis and correlation. It found empirical relationships between biogas yield and 26 different parameters. These parameters are measured by appropriate biosensors in industrial production. Some of them have more significant influence on the fermentation process than others. Overall, the developed mathematical model has the potential to provide useful insights into biogas production and can be used to optimize anaerobic fermentation processes.

Manufacturers try to increase their profits, so they improve customer satisfaction, which leads to customer loyalty and increase profits. One of the most important aspects of satisfactory service is the timely delivery of orders. Increasing resource consumption over the past decade has increased researchers' interest in challenges to reducing resource consumption. Proper use of fossil fuels will not only reduce energy consumption, but also reduce emissions. The innovation of this research is to propose a mathematical model considering the constraints related to vehicle speed levels in supply chain scheduling. Considering the relationship between speed and the amount of emissions from fuel in the supply chain-scheduling model, this study intends to reduce the emissions of these gases and also increase customer satisfaction by minimizing delays. The presented nonlinear mixed integer mathematical model is optimized with numerical examples in GAMS is solved and the results are investigated.

Modern requirements for aluminum alloys used in mechanical engineering and aviation include increased strength characteristics and refined microstructure. One of the promising methods for improving the properties of aluminum alloys is rolling on a three-high skew rolling mill, which provides intense plastic deformation and a fine-grained structure. This study describes the results of numerical modeling of the rolling process of aluminum alloy 6082 rods in a three-high skew-type mill. Numerical modeling of alloy 6082 was conducted using the ForgeNxT 2.1 software designed to simulate metal-forming processes, including rolling. The rheological behavior of the material under study was investigated by compression tests using a Gleeble 3800 plastometer (“DSI”, Austin, TX, USA), which enabled the determination of the main parameters of material flow under specified conditions. The process of rolling bars of alloy 6082 on a three-high skew mill was numerically analyzed in the temperature range of 350–400 °C. This allowed for the study of the distribution of stresses, temperatures, and strain rates from the rolling mode. A physical experiment was conducted to validate the results of numerical modeling. The obtained results enabled the identification of rolling modes that promote microstructure refinement and enhance the mechanical properties of the alloy.