This paper presents three hyper-heuristic approaches for the stochastic open-pit mine production scheduling problem with one processing stream (SMPS) and one of its generalizations, SMPS with multiple processing streams and stockpiles (SMPS+), which aim to optimize the associated mineral value chains. Two of the proposed hyper-heuristic approaches are refined versions of approaches that have been previously proposed in the literature and applied to solve other optimization problems, while the third one is a novel approach that uses some of the ideas of the first two but also includes new features aimed to overcome their weaknesses. The three approaches are simple, fast, and general. Their performance is assessed by comparing them to each other and to other search methodologies from the literature on benchmark instances of various sizes and characteristics. This comparison indicates that the new proposed hyper-heuristic outperforms the two others, providing results that are comparable to or improve on the results obtained by the state-of-the-art problem-specific methods.