chance.gms : Chance Constrained Feed Mix Problem

**Description**

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

**Category :** GAMS Model library

**Main file :** chance.gms

$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;