375
5 CONCLUSION
This paper presented a new mathematical formulation to model the short-term production
scheduling problem of mineral value chains comprising of multiple mines. The model presented here aims to closely meet the quality and quantity requirements of all the processing
plants in each period subject to the technical and operational constraints. In addition, a
genetic algorithm based heuristic technique was also presented herein to solve industrial scale
instances of the problem within a reasonable amount of time. The presented model and the
Figure 3. Details of material flow to processing plants given by genetic algorithm.
165
gj' 160
~
~
B 155
0
~ 150
"
~ 145
~
~ 140
135
~-~-~~·
2 3 4 5 6 7 8 9 1011 12
Time Period (Months)
- - - - · Upper
Tokmncc
- - - Targer
101111<1!,'\:
n:quin,111CD1
(a). Tonnage sent to Plant-!
64
-.. ·-- -~ t-<:- --~,
63
!\,.-'~
~ ....
- - - - • Lower
~62
'l'olu:mce
~
1/
- + - Avelllgc
~ 61
Gmdc
- - - - · UI'T"'r
~
-- --~·
Tolcr<~ncc
- - - Target
60
Grnde
59
I 2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(c). Average Fe(%) sent to Plant- I
4.5
4
3.5
~ 3
N
Q 2.5
C./)
2
1.5
/ ..... .... I\
~
J
- + - Average
Grade
- - - - • UpJl'l'r
!"o lernrJCe
- - - Target
Gnldc
I 2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(e). Average Si02 (%)sent to Plant-1
5.5
5
4.5
'i. 4
;::;- 3.5
~ 3
;;: 2.5
2
1.5
t-
Tokr-.m..x:
- + - A,·crasc
Gn"k
- - - - · Upper
Tol~mn""
- - - Target
Grade
1 2 3 4 5 6 7 8 9 10 11 12
Time Period (Months)
(g). Average A l203 (%)sent to Plant- !
910
~ 890
"
B 870
..'l
6 850
" ~ 830
- - - - • Upper
HH---f---f-+-+-+-+++-1
TokTancc
Tolerance
- + - Tun!
Mat..-ial
"
~ 8 10 ..,. ........... ~~~~ ...... ..,.--- :;::;:;,
r~
n:quin:mcor
790
2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(b). Tonnage sent to Plant-2
62.5
62
6 1.5
~ 6 1
~60.5
60
59.5
59
~
""
1/
!'. ~
- - - - • Lower
Tulcra~lcc
- + - A ,·cr~gc
Grode
- - - - · Upp<.<
fo lerance
1arget
Grade
2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(d). Average Fe(%) sent to Plant-2
6.5
6
5.5
~ 5
N
Q4.5
C./)
4
3.5
3
1 /
v
.... ~
- + - Av..-age
Grade
- - - - • lJPf"'r
Tolcr:mcc
- - - Targ:<'l
Grade
I 2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(f). Average Si02 (%)sent to Plant-2
5.5
4.5
----· W,• :.:r
~ 4 1-+-+-+-+-+-+-+-+-+-H _...,._ ::. ~:;:c
;::::'3.5
Grade
~ 3
----· ~~~:n~
;;: 2.25 -::~~~~~*$~~l--- ' "' ' "
~
Grade
1.5
2 3 4 5 6 7 8 9 1011 12
Time Period (Months)
(h). Average Al203 (%)sent to Plant-2
5 CONCLUSION
This paper presented a new mathematical formulation to model the short-term production
scheduling problem of mineral value chains comprising of multiple mines. The model presented here aims to closely meet the quality and quantity requirements of all the processing
plants in each period subject to the technical and operational constraints. In addition, a
genetic algorithm based heuristic technique was also presented herein to solve industrial scale
instances of the problem within a reasonable amount of time. The presented model and the
Figure 3. Details of material flow to processing plants given by genetic algorithm.
165
gj' 160
~
~
B 155
0
~ 150
"
~ 145
~
~ 140
135
~-~-~~·
2 3 4 5 6 7 8 9 1011 12
Time Period (Months)
- - - - · Upper
Tokmncc
- - - Targer
101111<1!,'\:
n:quin,111CD1
(a). Tonnage sent to Plant-!
64
-.. ·-- -~ t-<:- --~,
63
!\,.-'~
~ ....
- - - - • Lower
~62
'l'olu:mce
~
1/
- + - Avelllgc
~ 61
Gmdc
- - - - · UI'T"'r
~
-- --~·
Tolcr<~ncc
- - - Target
60
Grnde
59
I 2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(c). Average Fe(%) sent to Plant- I
4.5
4
3.5
~ 3
N
Q 2.5
C./)
2
1.5
/ ..... .... I\
~
J
- + - Average
Grade
- - - - • UpJl'l'r
!"o lernrJCe
- - - Target
Gnldc
I 2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(e). Average Si02 (%)sent to Plant-1
5.5
5
4.5
'i. 4
;::;- 3.5
~ 3
;;: 2.5
2
1.5
t-
Tokr-.m..x:
- + - A,·crasc
Gn"k
- - - - · Upper
Tol~mn""
- - - Target
Grade
1 2 3 4 5 6 7 8 9 10 11 12
Time Period (Months)
(g). Average A l203 (%)sent to Plant- !
910
~ 890
"
B 870
..'l
6 850
" ~ 830
- - - - • Upper
HH---f---f-+-+-+-+++-1
TokTancc
Tolerance
- + - Tun!
Mat..-ial
"
~ 8 10 ..,. ........... ~~~~ ...... ..,.--- :;::;:;,
r~
n:quin:mcor
790
2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(b). Tonnage sent to Plant-2
62.5
62
6 1.5
~ 6 1
~60.5
60
59.5
59
~
""
1/
!'. ~
- - - - • Lower
Tulcra~lcc
- + - A ,·cr~gc
Grode
- - - - · Upp<.<
fo lerance
1arget
Grade
2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(d). Average Fe(%) sent to Plant-2
6.5
6
5.5
~ 5
N
Q4.5
C./)
4
3.5
3
1 /
v
.... ~
- + - Av..-age
Grade
- - - - • lJPf"'r
Tolcr:mcc
- - - Targ:<'l
Grade
I 2 3 4 5 6 7 8 9 10 II 12
Time Period (Months)
(f). Average Si02 (%)sent to Plant-2
5.5
4.5
----· W,• :.:r
~ 4 1-+-+-+-+-+-+-+-+-+-H _...,._ ::. ~:;:c
;::::'3.5
Grade
~ 3
----· ~~~:n~
;;: 2.25 -::~~~~~*$~~l--- ' "' ' "
~
Grade
1.5
2 3 4 5 6 7 8 9 1011 12
Time Period (Months)
(h). Average Al203 (%)sent to Plant-2