Strategic Planning Algorithms

Your product utilizes a range of different algorithms to provide the most practical mine planning solution for the input parameters.

This topic outlines some of the key algorithms that are used to provide these solutions.

Lerchs-Grossmann Algorithm

The algorithm is a significantly improved version of the classic Lerchs-Grossmann method for generating maximum profit pit for given prices and costs. The Lerchs-Grossmann method formulates the ultimate pit problem as a graph and finds a sub-graph (closed tree) that represents the pit, yielding maximum profit. The improvement proposed by D.S. Hochbaum consists in making the LG search for the optimal sub-graph in a particular order driven by a scheme of labeling vertices of the graph.

NPVS employs a variant of the D.S.H. algorithm, called highest-label pseudoflow. Compared with the original LG method, the improvement in running times for larger models is quite significant; a project that required 2 days to complete in versions of Studio NPVS prior to v4.27 is likely to finish in 2-3 hours in version 4.27 or higher.

LG Phases

NPVS utilizes the improved L-G algorithm to generate L-G phases base on parametrizations of prices, costs, or both.

Optimal Extraction Sequence (OES)

NPVS generates OES phase by phase. Within a phase, blocks are ordered by bench and proximity, or by logic known as the lookahead value search.

Towards a practical Final Pit

Your product can remove certain singularities in the final pit that are unacceptable in a practical final pit. With this option enabled, small hills are removed from the surface of the LG pit and the bottom bench in the two principal directions (North-South and West-East for unrotated models) has at least the user-defined mining width.

See Nested LG Pits.

Pushbacks

The Pushback Generator rearranges the OES resulting from pit optimization, to obtain a sequence of pits satisfying the following conditions:

Each bench of the pushback includes only contiguous blocks unless it is made impossible, usually at lower benches, by the shape of the final pit.
Regular boundary at benches; avoid small bumps, depressions, holes etc.
Mining width: pushback boundary either coincides with the final pit wall (earlier pushback boundary) or is separated from it by at least the specified mining width.
Pushback contains ore (alternatively, rock or specific type of ore) tonnage that is as close as possible to the user-specified amount.

The Pushback Generator algorithm is a collection of geometric tools, some similar but not identical to image processing techniques, and problem-specific heuristics. The Pushback Adjustment tool allows you to further customize your pushback sequence. See Pushback Generator: Key Functions.

Scheduler

The search algorithm is based on graph-theoretic concepts. The scheduler divides the model into bins (activities), then finds a sequence of activities that is acceptable in the context of user-defined targets and converts this sequence into a block-by-block OES. See Scheduling Pushbacks.

MAO

A linear-programming-based tool reallocates the scheduler OES to processing destinations and stockpiles in order to meet targets that were impossible to meet under the scheduler model. See What is Material Allocation Optimizer?

MFO

Aims to improve scheduler OES NPV by speeding up mining. The algorithm is an optimization procedure that solves the MAO problem at each iteration. See What is Material Allocation Optimizer?