blend.gms : Blending Problem I
A company wishes to produce a lead-zinc-tin alloy at minimal cost.
The problem is to blend a new alloy from other purchased alloys.
Reference:
- Dantzig, G B, Chapter 3.4. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963.
Small Model of Type: LP
<![CDATA[
$Title Blending Problem I (BLEND,SEQ=2)
$Ontext
A company wishes to produce a lead-zinc-tin alloy at minimal cost.
The problem is to blend a new alloy from other purchased alloys.
Dantzig, G B, Chapter 3.4. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.
$Offtext
Sets alloy products on the market / a, b, c, d, e, f, g, h, i /
elem required elements / lead, zinc, tin /
Table compdat(*,alloy) composition data (pct and price)
a b c d e f g h i
lead 10 10 40 60 30 30 30 50 20
zinc 10 30 50 30 30 40 20 40 30
tin 80 60 10 10 40 30 50 10 50
price 4.1 4.3 5.8 6.0 7.6 7.5 7.3 6.9 7.3
Parameters rb(elem) required blend / lead = 30, zinc = 30, tin = 40 /
ce(alloy) composition error (pct-100);
ce(alloy) = sum(elem, compdat(elem,alloy)) - 100; display ce;
Variables v(alloy) purchase of alloy (pounds)
phi total cost
Positive Variable v
Equations pc(elem) purchase constraint
mb material balance
ac accounting: total cost;
pc(elem).. sum(alloy, compdat(elem,alloy)*v(alloy)) =e= rb(elem);
mb.. sum(alloy, v(alloy)) =e= 1;
ac.. phi =e= sum(alloy, compdat("price",alloy)*v(alloy));
Models b1 problem without mb / pc, ac /
b2 problem with mb / pc,mb,ac /
Parameter report(alloy,*) comparison of model 1 and 2;
Solve b1 minimizing phi using lp; report(alloy,"blend-1") = v.l(alloy);
Solve b2 minimizing phi using lp; report(alloy,"blend-2") = v.l(alloy);
Display report;
]]></plaintext></body></div>