Функции Доц. д-р Владимир Димитров e-mail: [email protected] Web: cht_co.tripod.com Wap: .
Doychin Boyadzhiev, Zlatko Varbanov, Alexander Peltekov...
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Doychin Boyadzhiev, Zlatko Varbanov, Alexander Peltekov * , Mariusz Kozlowski, Zlatogor Minchev IN COOPERATION WITH KCM AD, PLOVDIV*
Transcript of Doychin Boyadzhiev, Zlatko Varbanov, Alexander Peltekov...
Doychin Boyadzhiev, Zlatko Varbanov, Alexander Peltekov*, Mariusz Kozlowski, Zlatogor Minchev
IN COOPERATION WITH KCM AD, PLOVDIV*
ZINC HYDROMETALLURGY DEMO VIDEO
PROBLEM DEFINITION
METHODOLOGY & SOFTWARE SELECTION
RESULTS
DISCUSSION
THE MAIN GOAL IS TO OPTIMIZE THE CHARGING PROCESS OF THE ZINC METALLURGY FOLLOWING THE INPUT COMPONENTS MIXTURE
(“CONCENTRATE” – “CHARGE”) TECHNOLOGICAL PRICE - CT
L(x) =
CT = C1 - C2 - C3,
CTj - price of the j-th concentrate; xj – quantity of the j-th concentrate
→ CTj * xj → min,
Further on, for simplicity CTj and its three components are denoted
without the j-th index.
C1 – depends on the Zn contents in the concentrate as follows:
IF [(1-p) * Zn < q THEN (Zn-q) * Cd /100) ELSE p * Zn * Cd /100 ]
Cd – daily price of Zn on London Metal Exchange (LME)
p – final agreed Zn content at official LME (85%)
q – minimum deduction of Fe at the official LME (8%)
Where:
C2 – the correction that depends on the difference
between Cd and Cavg of the Zn:
Cd – daily price of Zn on London Metal Exchange (LME)
C2 = Eavg – (Cavg - Cd) / 10; Eavg – average expenses for 1 tone concentrate processing and transport, Eavg = 2000 $
C3 – penalty for Fe contents in the concentrate:
[IF Fe < q THEN 0 ELSE (Fe- q)* s]
q – minimum deduction of Fe at the official LME (8%)
s – the penalty for 1 % Fe contents in the concentrate, s = 2$
LINEAR OPTIMIZATION - assuming that the components mixture is a linear combination of the concentrate components
MS EXCEL SOLVER – well-known and commonly available
Input concentrate components n, n=21
LINEAR OPTIMIZATION INTEGER LINEAR OPTIMIZATION
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3.9
2
Tota
l Pri
ce (
CT)
49
3.1
8
Tota
l Pri
ce (
CT)
The Integer optimization provides results that require discretization change in accordance with the real production system mechanical capabilities improvements.
No Boundary Conditions of
the charge components
min Price = 543.55 $/t
Linea
r m
od
el
No Boundary Conditions of
the charge components
min Price = 549.61 $/t Lin
ear In
t mo
del
divisib
le on
1%
No Boundary Conditions of
the charge components
min Price = 558.03 $/t
Linea
r Int m
od
el d
ivisible o
n 5
%
No Boundary Conditions of
the charge components
min Pb+Cu+SiO2= 4.40 %
Linea
r m
od
el
No Boundary Conditions of
the charge components
Linea
r Int m
od
el d
ivisible o
n 1
%
No Boundary Conditions of
the charge components
Linea
r Int m
od
el d
ivisible o
n 5
%
Price < 560 $/t
min Pb+Cu+SiO2= 4.88 %
Price < 560 $/t
Price < 560 $/t
min Pb+Cu+SiO2= 5.15 %
I
No Boundary Conditions of
the charge components
min Pb+Cu+SiO2= 4.40 %
Linea
r m
od
el
No Boundary Conditions of
the charge components
Linea
r Int m
od
el d
ivisible o
n 1
%
No Boundary Conditions of
the charge components
Linea
r Int m
od
el d
ivisible o
n 5
%
Price < 560 $/t
min Pb+Cu+SiO2= 4.88 %
Price < 560 $/t
Price < 560 $/t
min Pb+Cu+SiO2= 5.15 %
No Boundary Conditions of
the charge components
min Fe = 7.64 %
Linea
r m
od
el
No Boundary Conditions of
the charge components
Linea
r Int m
od
el d
ivisible o
n 1
%
No Boundary Conditions of
the charge components
Linea
r Int m
od
el d
ivisible o
n 5
%
Price < 560 $/t
Price < 560 $/t
Price < 560 $/t
Pb+Cu+SiO2 < 5.20 %
Pb+Cu+SiO2 < 5.20 %
Pb+Cu+SiO2 < 5.20 %
min Fe = 7.82 %
min Fe = 7.98 %
II
No Boundary Conditions of
the charge components
min Price = 543.55 $/t
Linea
r m
od
el
No Boundary Conditions of
the charge components
min Price = 549.61 $/t Lin
ear In
t mo
del
divisib
le on
1%
No Boundary Conditions of
the charge components
min Price = 558.03 $/t
Linea
r Int m
od
el d
ivisible o
n 5
%
Lower & Upper Boundary Conditions
Linea
r m
od
el
Lower & Upper Boundary Conditions
Linea
r Int m
od
el d
ivisible o
n 1
%
Lower & Upper Boundary Conditions
Linea
r Int m
od
el d
ivisible o
n 5
%
min Price = 548.83 $/t
min Price = 553.41 $/t
No feasible solution
III
The developed mathematical model based on liner programming techniques for industrial support of zinc metallurgy charging process successfully demonstrated the practical problems between theoretical and practical industrial requirements meeting. Evidently the integer liner programming is a good tool for industrial application together with MS Excel software. Unfortunately, not always a feasible solution is possible to be found
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