Using Precedence Constraints to Model the Geometry of Optimal Mining Envelopes

Precedence constraints are broadly used in mathematical models and algorithms for mine planning to model, for example, slope angles in open pit operations or connectivity in underground mines. Unfortunately, these constraints do not capture relevant geometrical aspects for the design of the mine like minimum bottom space of pits or smoothness of the economic envelope in block caves. In this work, we present different approaches that utilize precedence constraints generating economic envelops that are more suitable for design purposes. The numerical experiences show that the proposed techniques produce high value envelops with better geometrical properties and that the methods proposed can be computed efficiently.