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farmersPH3s.gms
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farmersPH3s.gms
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* David Prentiss
* Farmer's problem with progressive hedging
sets
crop crops we can plant / wheat, corn, beets /
need crops we may need to buy / wheat, corn /
surplus crops we can sell / wheat, corn, beets, excessBeets /
scenarios yields for loop / 1*3 /
parameters
plantingCost(crop) / wheat 150
corn 230
beets 260 /
purchasePrice(need) / wheat 283
corn 210 /
salePrice(surplus) / wheat 170
corn 150
beets 36
excessBeets 10 /
minimum(need) / wheat 200
corn 240 /
maxLand / 500 /
beetQuota / 6000 /
yield(crop)
prob
Eplant(crop)
EplantNew(crop)
g
ws(scenarios, crop)
w(crop)
k
*** probabilities for each scenario
scenarioProb(scenarios) / 1 0.3333333333333333
2 0.3333333333333333
3 0.3333333333333333 /
*** all yields by scenario
table yields(scenarios, crop)
wheat corn beets
1 2.0 2.4 16
2 2.5 3.0 20
3 3.0 3.6 24
scalar
rho / 2 /
threshold / 0.000001 /
positive variables
plant(crop)
purchase(need)
sell(surplus)
variables
z current objective value
equations
obj0 minimize negative profit
objk minimize negative profit
land must not exceed maximum land area
quotaWheat wheat quota must be met
quotaCorn corn quota must be met
quotaBeets beets must not exceed quota
quotaExcessBeets excessBeets exceed quota
;
obj0..
z
=E=
sum(crop, plantingCost(crop) * plant(crop))
- sum(surplus, sell(surplus) * salePrice(surplus))
+ sum(need, purchase(need) * purchasePrice(need));
objk..
z
=E=
sum(crop, plantingCost(crop) * plant(crop))
- sum(surplus, sell(surplus) * salePrice(surplus))
+ sum(need, purchase(need) * purchasePrice(need))
+ sum(crop, w(crop) * plant(crop))
+ rho/2 * sqrt(sum(crop, power((plant(crop) - EPlant(crop)), 2)))**2;
land..
sum(crop, plant(crop))
=L= maxLand;
quotaWheat..
yield("wheat") * plant("wheat") + purchase("wheat") - sell("wheat")
=G= minimum("wheat");
quotaCorn..
yield("corn") * plant("corn") + purchase("corn") - sell("corn")
=G= minimum("corn");
quotaBeets..
sell("beets")
=L= beetQuota;
quotaExcessBeets..
sell("beets") + sell("excessBeets")
=L= yield("beets") * plant("beets");
model firstIter / obj0, land, quotaWheat, quotaCorn, quotaBeets, quotaExcessBeets /;
model kthIter / objk, land, quotaWheat, quotaCorn, quotaBeets, quotaExcessBeets /;
option solprint = off;
*** init output
file out / farmersPH.put /;
put out;
*** solve each scenario without penalties
loop(crop, Eplant(crop) = 0;);
loop(scenarios,
prob = scenarioProb(scenarios);
loop(crop, yield(crop) = yields(scenarios, crop););
solve firstIter using lp minimizing z;
loop(crop,
Eplant(crop) = Eplant(crop) + prob * plant.l(crop);
ws(scenarios, crop) = plant.l(crop);
);
);
loop((scenarios, crop),
ws(scenarios, crop) = rho * (ws(scenarios, crop) - EPlant(crop));
);
g = sum(scenarios, scenarioProb(scenarios)
* sqrt(sum(crop, power(plant.l(crop) - Eplant(crop),2))));
k = 0;
put k:>5:0, loop(crop, put EPlant(crop):>10:3); put g:>10:4 /;
*** solve penalized version until converged
while(g gt threshold,
loop(crop, EPlantNew(crop) = 0;);
loop(scenarios,
prob = scenarioProb(scenarios);
loop(crop,
w(crop) = ws(scenarios, crop);
yield(crop) = yields(scenarios, crop);
);
solve kthIter using nlp minimizing z;
loop(crop,
EPlantNew(crop) = EPlantNew(crop) + prob * plant.l(crop);
ws(scenarios, crop) = ws(scenarios, crop) + rho * plant.l(crop);
);
);
loop(crop, Eplant(crop) = EplantNew(crop););
loop((scenarios, crop),
ws(scenarios, crop) = ws(scenarios, crop) - rho * EPlant(crop);
);
g = sum(scenarios, scenarioProb(scenarios)
* sqrt(sum(crop, power(plant.l(crop) - Eplant(crop),2))));
k = k + 1;
put k:>5:0, loop(crop, put EPlant(crop):>10:3); put g:>10:4 /;
);
*** close output
putclose out;