A computational framework has been developed that extends stochastic strategic mine planning algorithms, improving the representation of ore selection decisions. Existing algorithms result in block extraction sequences that may violate the mineral processing capacity; under such geological scenarios, the excess ore is subject to a recourse action which is not as profitable as regular processing, hence decreasing the net present value. This decrease has previously been represented as a linear penalty on excess ore, which may be loosely related to stockpiling or outsourcing costs, but is difficult to quantify, and does not accurately represent actual operations. The new framework considers the most typical recourse action, which is to increase the cutoff grade into the mineral process. This approach is demonstrated by hybridizing a Variable Neighborhood Descent (VND) method with a Continuous Knapsack formulation. Sample computations are performed using data from a copper ore deposit, consisting of 9953 blocks, under 20 geological scenarios.