A material aim when feeding ore blends into a processing facility is to reduce the variability of the properties of the feed material and to maximise the output, or throughput. At the Mining Geology conference of 2019, we presented a paper on optimal blending of coking coal given geological variability. The paper introduced integer-programming techniques to both maximise value and minimise feed or product variability. We discussed an application where the geological uncertainty is characterised using a normal distribution and exact solutions are readily obtainable using second order conic constraints in the mathematical model. Geological uncertainty is not always normally distributed, many properties will be characterised as log normal or some other skewed distribution. For example, copper can be some form of lognormal and Fe in Iron ore has a left skewed distribution. In this paper, we discuss some distribution free techniques to optimise the blends of plant feed or output given a quantified geological uncertainty. We discuss the sample average approximation method and how to set-up and apply the method to an ore blending problem. Evaluating a case study demonstrates that the explicit use of non-normally distributed geological uncertainty can better optimise feed into an ore processing facility and potentially add significant value. The approach is equally applicable to all mining and processing operations that blend material into a processing facility or directly into a saleable product.