Open-Pit Block-Sequencing Formulations: A Tutorial

A classical problem in the mining industry for open-pit mines involves scheduling the production of notional three-dimensional production blocks, each containing a predetermined amount of ore and waste. That is, given operational resource constraints on extraction and processing, we seek a net present value-maximizing schedule of when, if ever, to extract each block in a deposit. We present a version of the problem, which some literature refers to as (CPIT). This constrained ultimate pit limit problem (i.e., open-pit production-scheduling problem variant) produces a sequence of blocks to extract given minimum and maximum bounds on production and processing capacity, and geospatial precedences. Our tutorial demonstrates methods to expedite solutions for instances of this model through variable definition, preprocessing, algorithmic choice, and the provision of an initial feasible solution. As such, our paper is relevant for any mining practitioner interested in production scheduling, and any operations researcher interested in a basic introduction before extending the boundaries of algorithmic development in this area.