考虑外部环境因素不确定性影响的采选协同生产计划决策优化方法

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

  • 摘要: 露天矿山采选生产易受地缘政治、市场波动、极端天气等外部环境因素影响,导致关键指标波动和计划偏离。为提高复杂外部环境条件下采选协同生产计划的稳定性和经济性,构建基于贝叶斯网络与两阶段随机机会约束规划的优化方法。首先,利用企业月度生产与外部环境数据构建贝叶斯网络,刻画外部环境因素与关键生产指标之间的因果关系,获得不同因素组合下指标损失的概率分布。其次,采用蒙特卡洛采样与K-modes聚类生成有限个典型场景,在此基础上构建两阶段随机机会约束规划模型:第1阶段在影响发生前联合决策采矿与选矿计划,第2阶段在影响窗口内通过连续补救变量调整关键指标,并引入指标损失率机会约束、物料平衡与能力约束,以最大化外部环境因素不确定性影响下的总期望收益。模型采用IBM ILOG CPLEX求解。以某露天铜矿12个月采选计划为例,在多源外部环境影响场景下,引入补救机制的优化方案将年度总期望利润由223677万元提高至272016万元,增幅约21.6%;关键生产指标的波动性下降、平均完成率上升,Wilcoxon符号秩检验的p值均小于0.001。灵敏度分析表明:放宽允许损失率和机会约束失效概率上限可以提高总期望收益,但增加关键指标波动性、降低完成率;补救成本变化可诱发补救策略在“完全补救”和“边界补救”之间的切换,呈现成本阈值效应。研究形成了“贝叶斯网络+两阶段随机机会约束规划”的采选协同优化框架,可为在复杂外部环境下制定和调整生产计划提供决策支持;未来可将外部环境影响窗口建模为随机变量并纳入时间维度描述,同时将设备调度、库存和供应链等环节及多源数据和机器学习纳入协同优化,以提升外部环境因素识别和不确定性建模能力。

     

    Abstract: 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.

     

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