Decision optimization method for coordinated mining and mineral processing production planning considering the uncertain impacts of external environmental factors

Open-pit mining–beneficiation production is highly vulnerable to the uncertain impacts of external environmental factors such as geopolitics, market fluctuations, and extreme weather, leading to volatility in key indicators and deviations from production plans. To improve the stability and economic performance of collaborative mining–beneficiation production planning under complex conditions characterized by the uncertain impacts of external environmental factors, an optimization approach based on Bayesian networks and two-stage stochastic chance-constrained programming is developed. First, a Bayesian network is constructed using monthly production and external environment data from the enterprise to characterize the causal relationships between external environmental factors and key production indicators and to obtain the probability distributions of indicator losses under different combinations of factors. Second, Monte Carlo sampling combined with K-modes clustering is used to generate a finite set of representative scenarios, on the basis of which a two-stage stochastic chance-constrained programming model is formulated: in the first stage, mining and beneficiation plans are jointly determined before the impacts occur; in the second stage, continuous recourse variables adjust key indicators within the impact window, and chance constraints on indicator loss rates together with material balance and capacity constraints are imposed to maximize the total expected profit under the uncertain impacts of external environmental factors. The model is solved using IBM ILOG CPLEX. Using a 12-month mining–beneficiation plan of an open-pit copper mine as a case study, the optimization scheme with recourse increases the annual total expected profit from CNY 2236.77 million to CNY 2720.16 million, an improvement of about 21.6%; the volatility of key production indicators decreases and their average completion rates increase, and the p-values of Wilcoxon signed-rank tests are all below 0.001. Sensitivity analysis shows that relaxing the upper bounds on allowable loss rates and on the violation probabilities of chance constraints increases the total expected profit but also raises the volatility of key indicators and reduces completion rates; variations in recourse costs can trigger switches in recourse strategies between “full remediation” and “boundary remediation”, exhibiting a cost threshold effect. The study establishes a collaborative optimization framework for mining–beneficiation production based on Bayesian networks and two-stage stochastic chance-constrained programming, which can support decision making for the formulation and adjustment of production plans under the uncertain impacts of external environmental factors; future work may model the impact window of external environmental factors as a random variable with an explicit time dimension and incorporate equipment scheduling, inventory, supply chains, and multi-source data and machine learning into the collaborative optimization to enhance the identification of external environmental factors and the modeling of their uncertainty.