mine.gms : Opencast Mining
This model finds an optimal extraction schedule for an opencast mine
with a side angle of 45 degrees and square plots. The extraction blocks
are identified by level, row and column number, with the surface blocks
having level number one.
Reference:
- Williams, H P, Model Building in Mathematical Programming. John Wiley and Sons, 1978.
Small Model of Type: LP
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$Title Opencast Mining (MINE,SEQ=39)
$Ontext
This model finds an optimal extraction schedule for an opencast mine
with a side angle of 45 degrees and square plots. The extraction blocks
are identified by level, row and column number, with the surface blocks
having level number one.
Williams, H P, Model Building in Mathematical Programming. John Wiley
and Sons, 1978.
$Offtext
Set l identifiers for level row and column labels / 1*4 /;
Alias(l,i,j);
Table conc(l,i,j) estimated ore concentration (percent metal)
1 2 3 4
1.1 1.5 1.5 1.5 .75
1.2 1.5 2.0 1.5 .75
1.3 1.0 1.0 .75 .50
1.4 .75 .75 .50 .25
2.1 4 4 2
2.2 3 3 1
2.3 2 2 .5
3.1 12 6
3.2 5 4
4.1 6
Sets k location of four neighboring blocks / nw, "ne", se, sw /
c(l,i,j) neighboring blocks related to extraction feasibility
d(l,i,j) complete set of block identifiers
Parameters li(k) lead for i / (se,sw) = 1 /
lj(k) lead for j / ("ne",se) = 1 /
cost(l) block extraction cost / 1=3000, 2=6000, 3=8000, 4=10000 /
Scalar value extracted block value if 100 percent metal / 200000 / ;
c(l,i,j) = yes$((ord(l) + ord(i)) le card(l) and (ord(l) + ord(j)) le card(l)); display c;
d(l,i,j) = yes$(ord(l) + ord(i) le card(l) + 1 and ord(l) + ord(j) le card(l) + 1); display d;
Variables x(l,i,j) extraction of blocks
profit
Positive Variable x
Equations pr(k,l,i,j) precedence relationships
def profit definition ;
def.. profit =e= sum((l,i,j)$d(l,i,j), (conc(l,i,j)*value/100 - cost(l))*x(l,i,j)) ;
pr(k,l+1,i,j)$c(l,i,j).. x(l,i+li(k),j+lj(k)) =g= x(l+1,i,j);
x.up(l,i,j) = 1;
Model mine /all/ ;
Solve mine maximizing profit using lp;
Parameter rep(i,j,l) extraction decision table;
rep(i,j,l) = x.l(l,i,j);
Display rep;
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