Question 8 of 27

Question 1.8 (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

1.8.1 — moving-cone rule base (2-D section). Starting from any positive-value block, construct the inverted cone (in 2-D, a triangle) of overlying blocks that must be removed to expose it at the stable wall angle. Sum the candidate block’s value with its overlying cone’s value. If the sum is ≥ 0, the cone is mineable: mark every block in it as part of the pit (cones that overlap already-committed blocks are not double-charged). If negative, leave the block un-mined. Re-scan the whole section (mining one cone can change the marginal cost of a neighbouring one) and repeat to convergence. It is a LOCAL, greedy heuristic, not a global one — its result depends on the order blocks are evaluated.

1.8.2 — why Lerchs–Grossmann is still not fully optimal for a long-life mine. Lerchs–Grossmann (graph-theoretic maximum closure) DOES guarantee the mathematically optimal ULTIMATE pit outline for a given block economic model — but “optimal outline” is not the same as “optimal MINE PLAN”. Over a 10–20+ year life it: (1) ignores the TIME VALUE of money — it maximises undiscounted total pit value, not NPV, so it says nothing about the SEQUENCE (which nested pit envelope/phase to mine when) that actually maximises discounted cash flow; (2) takes the block economic model (metal price, cost, recovery) as FIXED, when these all vary materially over a multi-decade life; (3) ignores mining-rate, blending/grade-control, and equipment-fleet capacity constraints that govern what CAN physically be mined in any given year; and (4) produces a single ultimate pit outline, not the nested series of intermediate pushbacks/phases needed for practical NPV-optimised scheduling (addressed separately by Whittle-style parametric nested-envelope analysis and the phase scheduling problem examined directly in Question 5 of this paper). Lerchs–Grossmann answers “what is the best final hole”, not “in what order and at what discounted value should it be mined”.