Due to the cyclical nature of commodity prices, the profitability of mining projects relies on proper timing. To ensure optimal profits, mines should be brought online at the time, which maximizes the potential value of the asset. In this paper, a coking coal mine construction case is used to demonstrate the effectiveness of scheduling large-scale construction projects with uncertain durations under price cyclicality. Project parameters are obtained stochastically via Monte Carlo sampling, allowing for the influence of uncertainty to be quantified. The critical path method and linear programming are employed to analyze the results and to optimize the construction process, ensuring the maximum value of the mining project. The parameters are repeatedly sampled to obtain distributions of possible project outcomes, allowing for risk and sensitivity quantification. The optimal schedule for construction was determined to be 247 weeks, with a most likely value of $813 million.