Large water demands by the mining industry are of increasing concern around the world. The cost of a specific water management regulation is studied for an oil sands mining operation in Canada, where restrictions on water withdrawals vary with fluctuations in the river. A stochastic optimal control problem is formulated for a firm choosing production, water use, and the timing to build a water storage facility, under conditions of uncertain oil prices and uncertain water withdrawal limits. As no closed form solution is available, a stochastic dynamic programming approach is implemented to determine the difference in value and optimal controls for the oil-producing asset, with and without water restrictions. The cost of the restrictions is estimated to be quite small given historical river flow conditions, while cost is shown to increase under drier conditions. A long run marginal cost curve is developed showing the cost of increasing restrictions given expectations about future river conditions and oil prices.

采矿业对水的大量需求越来越受到全世界的关注。针对加拿大的油砂开采作业，研究了特定水资源管理法规的成本，该地区对取水的限制随河流的波动而变化。在不确定的石油价格和不确定的取水限制条件下，为企业选择生产、用水和建造蓄水设施的时间制定了一个随机最优控制问题。由于没有可用的封闭形式解决方案，因此采用随机动态规划方法来确定产油资产的价值差异和最佳控制，无论有无水限制。考虑到历史河流流量条件，限制的成本估计相当小，而成本在干燥条件下会增加。根据对未来河流状况和石油价格的预期，绘制了长期边际成本曲线，显示了增加限制的成本。