A nonlinear, two-phase mathematical model of production at a mining facility is proposed. In this model, material flows are represented as two phases (ore and the useful substance contained within it), linked through the concentration of the useful substance. The process of material balance calculation is studied, which represents the solution to an optimization problem with nonlinear constraints at nodes with product accumulation. The solution to this problem is proposed to be sought using the interior point method. Known measured values of useful substance concentrations are considered, as well as the results of indirect measurements, ranges of flow values, stockpiles, and unknown concentration values. The results of test calculations for material balance calculations at a small section of a mining facility are presented.
Savenkova et al. (2026) studied this question.