基于金属价格不确定性的地下矿生产计划风险分析

针对采用无底柱分段崩落法生产的地下金属矿山的生产计划编制问题，通过构建以净现值（NPV）最大为目标函数并满足生产能力及空间顺序等约束条件的混合整数规划模型，用于确定各个采场之间开采的先后顺序，其中金属价格的变化不仅影响计划编制结果而且使计划的风险显著增大。根据金属历史价格分布，运用几何布朗运动（GBM）模型预测15条金属价格走势曲线，通过求解生产计划的混合整数规划模型，得到不同价格走势下的生产计划结果，然后根据GBM模型预测更多金属价格走势曲线并分析不同计划结果下的净现值、上涨潜力、风险下限、条件风险价值（CVaR）和风险价值（VaR），最终运用熵值法确定金属价格不确定条件下收益高且风险小的生产计划。经实例验证，此方法科学可行，减少了传统手工方法编制生产计划时受到的价格风险的影响，实现资源低风险高效开采，对指导矿山的实际生产具有重要的意义。

Risk Analysis of Underground Mine Production Scheduling Based on Metal Price Uncertainty

For the underground metal mine production planning optimization in sublevel caving method，the mixed integer programming model was built with the function of maximizing the net present value （NPV） constraint condition of the production capacity and space order to determine the stope mining sequence.The metal price changes not only affect the planning result，but also it is difficult to determine the risk of plan and can bring great economic losses in mining enterprises.According to the distribution of metal history price，using the geometric Brownian motion（GBM） model to predict 15 metal price trend curve，the production plan for different price trend curve was gutted by solving the mixed integer programming model，finally the more metal prices curve was predicted by using the GBM model again and analysis the net present value.Upside potential，downside risk，conditional value at risk （CVaR） and the value at risk （VaR） of different planning also was analyzed.Finally by using entropy method to determine the price of metal high yield under uncertainty and risk of small production plan.Verification by the concrete example that the method is scientific and feasible，can reduce the risk of the price when use traditional manual method to prepare production plan，realize low risk high efficiency mining resources，and has an important significance for actual production of the mine.