Treffer: Network optimization for the design of underground mines

Efficient methods to model and optimize the design of open-cut mines have been known for many years. The design of the infrastructure of underground mines has a similar potential for optimization and strategic planning. In this article we discuss the use of network optimization to tackle this problem. The idea is to design a connected system of declines, ramps, drives, and possibly shafts, to minimize capital development and haulage costs over the lifetime of a mine. This can be modeled as a variation on the Steiner problem, with suitable metric and constraints. These constraints include: an upper bound on the absolute gradient of arcs in the embedded network (typically 1/7), turning circle restrictions for navigability, and obstacle avoidance. Here we give an overview of the literature, focussing on our published work. We investigate the way in which this design problem can be modeled as a network optimization problem that accurately reflects the real costs involved while remaining mathematically tractable. Our approach is to first establish a fundamental model, which principally captures the development costs of the mine, and to study its geometric properties. We then outline more complicated generalized models, which add extra costs and constraints to the fundamental model but are still solvable.