Harnessing Uncertainty for Orebody Modelling and Strategic Mine Planning

Transcription

1 Harnessing Uncertainty for Orebody Modelling and Strategic Mine Planning Roussos Dimitrakopoulos Canada Research Chair in Sustainable Mineral Resource Development and Optimization under Uncertainty Department of Mining, Metals and Materials Engineering Keynote speech to AMEC Internal conference, Vancouver, November 2005

2 Overview The economic side of uncertainty Models of geological uncertainly Limits of traditional mine design optimization Shifting the paradigm: Stochastic mine planning Using uncertainty to improve project performance Conclusions - Uncertainty is great!

3 Uncertainty Matters: The Economic Side of Uncertainty Changing the way we do things

4 Uncertainty Matters: Return on Investment is Uncertain, therefore Risky Possibility of not making a return on capital (NPV<0) 0 Reserve NPV, $MM 600 Alternative development plans may have different risk profiles and expected values. Example: Design - can t capture high reserves Design can capture NPV, $MM NPV, $MM 600

5 Risk in Mining: A World Bank Survey 60% of mines had an average rate of production LESS THAN 70% of planned rate In the first year after start up, 70% of mills or concentrators had an average rate of production LESS THAN 70% of design capacity Key contributor to mining risk felt in all downstream phases: Geology and reserves

6 Uncertainty is not a Bad Thing Many managers believe that uncertainty is a problem and should be avoided.. you can take advantage of uncertainty. Your strategic investments will be sheltered from its adverse effects while remaining exposed to its upside potential. Uncertainty will create opportunities and value. Once your way of thinking explicitly includes uncertainty, the whole decision-making framework changes. Martha Amram and Nalin Kulatilaka in Real Options

7 Real Options vs DCF View of Value Current Asset Value $+ Real Options View: Current Value of Option to Produce $0 $- No production NPV = 0 Production NPV > 0 Traditional DCF View (now or never) Contingent Decision Payoff Function (future price known) Future Gold Price

8 Accurate Uncertainty Assessment Needed 1 Probability Unknown, true answer Single, often precise, wrong answer Accurate uncertainty estimation Reserves Reserves The goal of technical evaluation should be to strive for an accurate assessment of uncertainty, not a single precise answer

9 Mining Project Valuation Single estimated model Traditional view Probability 1 Unknown, true answer Single, often precise, wrong answer Reserves Orebody Model Mining Process or Transfer Function Mine Design Production Scheduling Multiple probable models Financial and Production Forecasts Risk oriented view Probability 1 Accurate uncertainty estimation Reserves

10 Quantitative Models of Geological Uncertainty: Stochastic or geostatistical conditional simulations

11 Describing the Uncertainty about a Mineral Deposit Actual but unknown mineral deposit Information about the deposit Probable models of the deposit

12 Describing the Uncertainty about a Gold Deposit Model characteristics: o Large number of blocks o Multiple domains o Resource classes with specific sample selection criteria A gold load

13 Lode 1502 Simulation #1

14 Lode 1502 Simulation #2

15 Lode 1502 Simulation #3

16 Moving Forward in Optimization: Limits of Traditional Mine Design Using Models of Uncertainty

17 Risk Analysis in a Mine Design Objective Quantify the impact of grade uncertainty to tonnage, grades, metal and net present value - net present vnalue vs risk exposure Methodology Mine Design (Scenario)... Mine Design (Scenario X) Multiple simulations Distribution of outcomes for a scenario

18 Open Pit Mine Design and Production Scheduling Intermediate pushbacks Pit Limit

19 Limits of Traditional Modelling The expected project NPV has only 2 4% probability to be realised 25 Probability NPV (m$, i = 8%) Stochastic Orebodies Conventional Pit Shells

20 Limits of Traditional Modelling Discounted Cash Flow Cash Flow (m$ p.a.) First 2 years of production Final year likely to be negative cash flow Production Period (1/4 Year)

21 Probabilities on Pit Limits 100% probability of falling within the pit for a given metal price Pit limit determined conventionally

22 This is Not...

23 Moving Forward.. Step 1 Exploring existing technologies

24 Past Work Open Pit Mine Design Upside Potential / Downside Risk D C F Upside Min acceptable return Downside Value 1 2 Pit design Upside or Downside = [ Value MAR Avg] * probability ( )

25 Past Work Open Pit Mine Design Upside Potential / Downside Risk Pit Design Upside Potential (m$) Downside Potential (m$) CB-1 CB-2 CB-3 CB-1 CB-2 CB

26 Moving Forward.. Step 2 Re-writing optimizers

27 Models of Uncertainty in Optimization Integer Programming An objective function Maximise (c 1 x 11 +c 2 x ) Subject to c 1 x 11 +c 2 x b 1 c 1 c 2 c 3 Period 1 Orebody model c 4 c = constant X 11 = binary variable c 1 x 1p +c 2 x 2p +. b p Period p

28 Stochastic Integer Programming The objective function now.. s 11 s 21 s 1 3 Maximise (s 11 x 11 +s 21 x s 12 x 11 +s 22 x 21 +.) s 1 s 11 4 s 21 s 1 3 Subject to s 11 s s 1 21 s 1 3 s 4 1n s 2n 1 s n 3 s 11 x 11 +s 21 x b 4 1 Period 1 s 1 4 Simulated model 1 Simulated model 2 Simulated model r s 11 x 1p +s 21 x 2p +. b 1 s 12 x 1p +s 22 x 2p +. b 1 s 1r x 1p +s 2r x 2p +. b 1 Period p

29 Uncertainty Will Create Opportunities and Value Higher NPV for less risk

30 Base Case: Geological Risk Assessment of Ore Production Mt Uncertainty in Ore Production - Base Case Schedule 70% Mt 60% Ore Production Mt Mt Mt Mt Mt 13.9% 13.5% 8.7% 18.2% Avrg. Deviation Target Ore Production Maximum Ore Expected Ore Minimum Ore 12.7% 12.4% 12.5% 10.8% 11.4% 12.4% 10.4% 12.3% 9.0% 11.9% 14.5% 12.3% 12.9% 50% 40% 30% 20% 10% Average Deviation (%) Mt Period 0%

31 Risk-based: Assessment in Ore Production Mt Uncertainty in Ore Production - Risk-based Schedule 70% Ore Production Mt Mt Mt Mt Mt Avrg. Deviation Target Ore Production Maximum Ore Expected Ore Minimum Ore 60% 50% 40% 30% 20% Average Deviation (%) Mt 10% Mt 0.5% 3.0% 1.2% 0.7% 3.5% 1.9% 0.2% 2.7% 1.6% 0.0% 0.6% 0.4% 0.1% 0.0% 0.7% Period 0%

32 Uncertainty is Good: Base case vs Risk-based NPV Multistage combinatorial optimization Risk-Based Difference 28% Traditional and Risk Traditional Expected Year

33 Uncertainty is Good: Discounting Geological Risk The discounting goes along with production sequencing

34 SIP - Production Scheduling Model Objective function P U - E{(NPV) + } i= 1 M + (SV) (P) q s= 1 N Max [ E{(NPV) } b t= 1 i= 1 t s t t t i MCi * si t s t i t i Mill & dump Part 1 Part 2 Stockpile input Part 3 Stockpile output M - (c d + c d )] s= 1 ty ty ty ty u su l sl Part 4 Risk management

35 Stochastic Integer Programming - SIP Deviation 1 A production schedule Orebody Model 1 Orebody Model 2 Ore Grade 1 Metal Ore Grade 2 Metal -TARGET [ ] Deviation 2 -TARGET [ ] Deviation R Orebody Model R Ore Grade R Metal -TARGET [ ]

36 Cross-Sectional Views of the Schedules SIP Whittle Four-X Periods

37 Managing Risk Between Periods 3 3 Deviations from metal production target Metal quantity (1000 Kg) Periods C t =C t-1 * RDF t-1 RDF t =1/(1+r) t RDF risk discounting factor r orebody risk discount rate

38 Case Study on a Large Gold Mine The SIP specific information Orebody risk discounting rate 20 % Cost of shortage in ore production 10,000 /t Cost of excess ore production 1,000 /t Cost of shortage in metal production 20 /gr Cost of excess metal production 20 /gr Number of simulated orebody models 15

39 Deviations from Production Targets -20 Metal Production Metal quantity (1000 Kg) SIP model WFX Periods

40 6 Stockpile s Profile Tonnes (million) Available ore at the end of each period SIP model WFX Tonnes (million) Ore taken out from the stockpile Periods

41 Uncertainty is Good: Traditional vs Risk-Based Stochastic Integer Programming $ (million) Periods $723 M Risk Based $609 M Traditional Difference = 17% Cumulative NPV values SIP model WFX Average NPV values SIP model WFX Geological Risk Discounting= 20%

42 Some conclusions. uncertainty is (not) a problem and should be avoided? you can take advantage of uncertainty..uncertainty will create opportunities and value. once your way of thinking explicitly includes uncertainty, the whole decision-making framework changes. We need: Stochastic mine planning and NEW mathematical models

43 And It is all about good people: Education and training in a long term sense

44 Please join us!