chance.gms : Chance Constrained Feed Mix Problem
Cattle feed problem with chance constraints. Two problems are
formulated, a deterministic model and the chance constraint
version deterministic equivalent.
Reference:
- Bracken, J, and McCormick, G P, Chapter 9. In Selected Applications of Nonlinear Programming. John Wiley and Sons, New York, 1968, pp. 94-100.
Small Model of Types: NLP lp
<![CDATA[
$title Chance Constraint Feed Mix Problem (CHANCE,SEQ=26)
$Ontext
Cattle feed problem with chance constraints. Two problems are
formulated, a deterministic model and the chance constraint
version deterministic equivalent.
Bracken, J, and McCormick, G P, Chapter 9. In Selected Applications of
Nonlinear Programming. John Wiley and Sons, New York, 1968, pp. 94-100.
$Offtext
sets f feeds / barley, oats, sesame, grnd-meal /
n nutrients / protein, fats /
parameters price(f) feed prices (fgld per ton) / barley 24.55
oats 26.75
sesame 39.00
grnd-meal 40.50 /
req(n) requirements (pct) / protein = 21, fats = 5 /
table char(*,n,f) feed characteristics (pct)
barley oats sesame grnd-meal
mean.protein 12.0 11.9 41.8 52.1
mean.fats 2.3 5.6 11.1 1.3
variance.protein .28 .19 20.5 .62
variables cost total cost per ton
x(f) feed mix (pct)
positive variable x;
equations cdef cost definition
mc mix constraint
nbal(n) nutrient balance
cc(n) chance constraint ;
cdef.. cost =e= sum(f, price(f)*x(f));
mc.. sum(f, x(f)) =e= 1;
nbal(n).. sum(f, char("mean",n,f)*x(f)) =g= req(n);
cc(n).. sum(f, char("mean",n,f)*x(f)) - 1.645*sqrt(sum(f, char("variance",n,f)*sqr(x(f)))) =g= req(n);
models det deterministic model / cdef, mc, nbal /
chance chance model / cdef, mc, cc /
parameter mix Mixing report;
solve det minimizing cost using lp; mix(f,'det ') = x.l(f);
solve chance minimizing cost using nlp; mix(f,'chance') = x.l(f);
display mix;
]]></plaintext></body></div>