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GATE MN: Mineral Economics, Mine Planning and Systems Engineering

GATE MN · Work through your exam, one topic at a time.

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Mineral Economics, Mine Planning and Systems Engineering

The final domain links the orebody to money and schedule: reserve and grade estimation, cut-off grade, project cash-flow appraisal, pit and stope planning, and the systems-engineering toolkit of network analysis, linear programming and reliability. Numerical questions here are usually discounted cash flow, PERT timing, or a break-even stripping ratio.

Reserves and planning

  • Resources are classified by geological confidence (measured, indicated, inferred) and converted to reserves only after modifying factors are applied; UNFC and JORC are the usual frameworks.
  • Estimation methods run from polygon and triangle averaging through inverse distance weighting to kriging.
  • Cut-off grade separates ore from waste; it falls when metal price rises or when mining and processing costs fall.
  • Pit limits come from break-even stripping ratio and from optimisation algorithms such as Lerchs-Grossmann; underground layout follows stope and level geometry.

Economics and systems engineering

  • Appraisal tools: cash flow, NPV = sum of CF_t/(1+i)^t, IRR where NPV is zero, payback, depreciation methods, royalty and tax.
  • Networks: CPM and PERT, with expected time t_e = (o + 4m + p)/6 and variance ((p - o)/6)^2; critical path has zero float.
  • Operations research: linear programming, transportation, queueing, simulation, decision trees, EOQ inventory and reliability in series and parallel.

Worked example

Capital of 100 crore at year 0, net inflow 30 crore per year for five years, discount rate 10 percent. Annuity factor = (1 - 1.1^-5)/0.10 = (1 - 0.62092)/0.10 = 3.7908. NPV = -100 + 30 x 3.7908 = -100 + 113.72 = +13.72 crore, so the project is acceptable. For IRR, set 30 x annuity factor = 100, giving a factor of 3.333; interpolating between 15 percent (3.352) and 16 percent (3.274) yields an IRR of about 15.3 percent.

Traps

  • Discounting the first inflow at t = 0 instead of t = 1, which inflates NPV.
  • Reporting the accounting rate of return as the IRR.
  • Using the expected activity time t_e instead of the range in the PERT variance formula.