“Pit Optimization” is a mysterious catch-all term used by mining engineers, financiers, and geologists. You input a bunch of economic variables into various Black-Box algorithms and with a click of a button, and 20-30 minutes, out spits a pit shell that is “optimized.” From this shell, you can tell the world how much metal is economic and then run some mine plans to figure out the economic reality for the project. My interest in digging into this topic a bit deeper was spurred by the realization that experienced industry leaders were treating the Nevada Net Proceeds Tax differently.
What is Whittle? What is Lerchs-Grossman?
Lerch-Grossman is the name of a modeling approach for solving open-pit optimization. It was developed in 1965 and implemented in the 1980’s by Jeff Whittle. The algorithm uses block dependencies to determine which blocks must be mined out as a group (i.e. if you mine G you must mine B, C, and D). The graphical relationship between blocks is determined by slope parameters (i.e. if you are using a very shallow slope than mining G may necessitate the mining of A through E).
Figure 1: Dependency Example (source: CONSTRUCTION ECONOMIC ORE BODY MODELS FOR OPEN PIT OPTIMIZATION, D. Whittle)
I like to think about optimization in a backwards fashion. Flip the topography upside down and whatever falls out is the optimized pit. Instead of gravity, you have revenue, this is the force propelling the ore out of the ground. In the opposite direction, let’s call it friction, we have costs; forces that go against the revenue generated by the ore. Like any physics equation, the fundamental forces need to be correct and well thought out.
With this explanation in mind, let’s think about a tricky situation. Below you’ll see excerpts from two technical reports. Both open-pit mines located in Nevada. One accounts for the State’s Net Proceeds Tax, one does not. So who is right here?
Well, the calculation of the net proceeds tax looks like you can deduct just about every expense that occurs during mining so the tax is more of a net profit royalty. Thinking about the flipped topo, the net proceeds tax only applies to blocks that actually generate a profit. So, as my beautiful the drawing shows, the tax applies after the blocks have “fallen out.” The tax applies to a component of the profit, so there is no way that there can be enough force to push the blocks back up. Therefore, I just can’t see why the Net Proceeds Tax would be included in the determination of the ultimate resource. Looks like Mine 2 has it right.
Figure 2: NNPT Calc, Source: https://nevadataxpayers.org/wp-content/uploads/2016/10/minerals-tax-2007-08.pdf
In playing devil’s advocate, I wonder if the tax should be used in the determination of interim pit phases? Imagine you have two phases, one high profit, one low profit. Does this change your thinking? It still shouldn’t matter. As long as the second phase is above breakeven, it should be mined.
Ok, so for now, I think the case is closed. NNPT and NPI royalties should not be included as cost factors in open pit optimization.