Stochastic Open Pit Mine Production Scheduling Incorporating Price h - - PowerPoint PPT Presentation

▶
stochastic open pit mine production scheduling
SMART_READER_LITE
LIVE PREVIEW

Stochastic Open Pit Mine Production Scheduling Incorporating Price h - - PowerPoint PPT Presentation

Jan 21, 2023 31 likes •147 views

Stochastic Open Pit Mine Production Scheduling Incorporating Price h d li i i Uncertainties Uncertainties Manas Ranjan Sethi & Snehamoy Chatterjee Department of Mining Engineering Department of Mining Engineering National Institute of

slide-1
SLIDE 1

Stochastic Open Pit Mine Production h d li i i Scheduling Incorporating Price Uncertainties Uncertainties

Manas Ranjan Sethi

&

Snehamoy Chatterjee Department of Mining Engineering Department of Mining Engineering National Institute of Technology, Rourkela

slide-2
SLIDE 2

Introduction

  • Mine production scheduling is an assignment

bl problem

  • Aim to maximizes profit
  • No algorithm is available to solve large scale mine

scheduling problem scheduling problem

  • Number of approximate algorithms are available
slide-3
SLIDE 3

Iron ore price

160 180 120 140 160

Price in US$

80 100

per metric tonne

20 40 60

Year

1980 1985 1990 1995 2000 2005 2010 2015

Year

Fig: ‐Iron ore price chart: 1982‐2011 Source: Index Mundi commodity price www.indexmundi.com/commodities/?commodity=iron‐ore&months=360

slide-4
SLIDE 4

Stochastic production scheduling

, 1 1 1

Maximize (1 )

s T S N s i i t t t i

c Z x r  

  

1 1 1 (1

)

t s i

r

  

, ,

subject to 0, , , ,

s s i t j t i

x x j i N s S t T      

s s

x x i N s S t T     

,

{0,1}, , ,

s i t

x i N s S t T    

, 1 ,

0, , ,

i t i t

x x i N s S t T

   

, 1

, , ,

S s i t s

x S i N s S t T

   

1 1 1 N st st st i i i

a x b

N 1 s 2 2 1 N st st st i i i

a x b

is the set of successor blocks of block

i

i  is the economic value of block for simulation is the number of blocks in the block model

i s i

c i s N

is the amount of ore from a block

  • f simulation

at time

st

a x s t

1 2 1

is the amount of ore from a block of simulation at time is the amount of waste from a block of simulation at time is the amount of ore production constraint from simulatio

i i st i i st

a x s t a x s t b n at time s t

st 2 is the amount of waste production constraint from simulation at time

is the total number of production periods is the number of simulation; is interest rate

st

b s t T S r

slide-5
SLIDE 5

Constructing graph

1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3

Three simulation with economic value of blocks

c1

1

c2

1

c3

1

c4

1

c5

1

c6

1

c7

1

c8

1

c9

1

c10

1

c11

1

c12

1

c13

1

c14

1

c15

1

c1

2

c2

2

c3

2

c4

2

c5

2

c6

2

c7

2

c8

2

c9

2

c10

2

c11

2

c12

2

c13

2

c14

2

c15

2

c1

3

c2

3

c3

3

c4

3

c5

3

c6

3

c7

3

c8

3

c9

3

c10

3

c11

3

c12

3

c13

3

c14

3

c15

3

c1

1

c2

1

c3

1

c4

1

c5

1

c6

1

c7

1

c8

1

c9

1

c10

1

c11

1

c12

1

c13

1

c14

1

c15

1

c1

2

c2

2

c3

2

c4

2

c5

2

c6

2

c7

2

c8

2

c9

2

c10

2

c11

2

c12

2

c13

2

c14

2

c15

2

c1

3

c2

3

c3

3

c4

3

c5

3

c6

3

c7

3

c8

3

c9

3

c10

3

c11

3

c12

3

c13

3

c14

3

c15

3 11 12 13 14 15 11 12 13 14 15 11 12 13 14 15 11 12 13 14 15 11 12 13 14 15 11 12 13 14 15

Economic value of blocks of three simulations after multiplying 

d1

1

d2

1

d3

1

d4

1

d5

1

d6

1

d7

1

d8

1

d9

1

d10

1

d1

2

d2

2

d3

2

d4

2

d5

2

d6

2

d7

2

d8

2

d9

2

d10

2

d1

3

d2

3

d3

3

d4

3

d5

3

d6

3

d7

3

d8

3

d9

3

d10

3

d1

1

d2

1

d3

1

d4

1

d5

1

d6

1

d7

1

d8

1

d9

1

d10

1

d1

2

d2

2

d3

2

d4

2

d5

2

d6

2

d7

2

d8

2

d9

2

d10

2

d1

3

d2

3

d3

3

d4

3

d5

3

d6

3

d7

3

d8

3

d9

3

d10

3

p y g 

6 7 8 9 10

d11

1

d12

1

d13

1

d14

1

d15

1 6 7 8 9 10

d11

2

d12

2

d13

2

d14

2

d15

2

d6 d7 d8 d9 d10 d11

3

d12

3

d13

3

d14

3

d15

3 6 7 8 9 10

d11

1

d12

1

d13

1

d14

1

d15

1 6 7 8 9 10

d11

2

d12

2

d13

2

d14

2

d15

2

d6 d7 d8 d9 d10 d11

3

d12

3

d13

3

d14

3

d15

3

Suppose economic value of blocks are

2 5

  • 2

2

  • 2

3 6 1 4 2 1 3

  • 1
  • 2
  • 2

1 4 3 5 1

  • 6

1

  • 3

3

  • 2

2 1 1 3 11 2 5

  • 2

2

  • 2

3 6 1 4 2 1 3

  • 1
  • 2
  • 2

1 4 3 5 1

  • 6

1

  • 3

3

  • 2

2 1 1 3 11

Suppose economic value of blocks are

  • 3

6

  • 1

4

  • 2
  • 5

8 4

  • 7
  • 4
  • 1

4 3 5

  • 1
  • 3

6 7 7

  • 3
  • 2
  • 1

1 3 11

  • 1

1 1 3 10

  • 3

6

  • 1

4

  • 2
  • 5

8 4

  • 7
  • 4
  • 1

4 3 5

  • 1
  • 3

6 7 7

  • 3
  • 2
  • 1

1 3 11

  • 1

1 1 3 10

slide-6
SLIDE 6

Constructing graph

Merged graph

Source

3 9 11 10

3 6 9 6 5 2 6 3 6 9 6 5 2 6

3 9 10 15 4 12 11 5 10 12 10

6 6 2 6 6 10 1 4 1 12 11 3 6 6 2 6 6 10 1 4 1 12 11 3 9 15 12 10 7 10 7 9 15 12 10 7 10 7

6 6 1 6 1 2 6 3 7

Sink

9 7

slide-7
SLIDE 7

Case Study

  • A Iron ore deposit
  • Slope angle is 45 degree
  • 100 simulated ore body models
  • Price simulation was done using SGS algorithm
slide-8
SLIDE 8

Variogram Model

Nugget No of structure Sill Type Max Med Min 1 0.63 Spherical 100 70 27

slide-9
SLIDE 9

3‐D view of Pit

slide-10
SLIDE 10

Conclusions

  • Production scheduling was performed by

incorporating price uncertainty incorporating price uncertainty

  • The algorithm is computationally fast, so can

handle large orebody model

  • No ultimate pit and pushback generation is
  • u t

ate p t a d pus bac ge e at o s required in this algorithm

  • 5% more NPV can be generated as compared to

conventional method conventional method

slide-11
SLIDE 11

THANK YOU