farm.gms : The Farmer's Problem formulated for DECIS
This model helps a farmer to decide how to allocate
his or her land. The yields are uncertain.
Reference:
- Birge, J R, and Louveaux, F V, Introduction to Stochastic Programming. Springer, 1997.
Small Model of Types: DECIS lp
<![CDATA[
$title The Farmer's Problem formulated for GAMS/DECIS (FARM,SEQ=199)
$ontext
This model helps a farmer to decide how to allocate
his or her land. The yields are uncertain.
Birge, R, and Louveaux, F V, Introduction to Stochastic Programming.
Springer, 1997.
$offtext
$if not set decisalg $set decisalg decism
set crop / wheat, corn, sugarbeets /;
set cropr(crop) crops required for feeding cattle /wheat, corn/;
set cropx /wheat,
corn,
beets1 up to 6000 ton,
beets2 in excess of 6000 ton/;
parameter yield(crop) tons per acre /
wheat 2.5
corn 3
sugarbeets 20
/;
parameter plantcost(crop) dollars per acre /
wheat 150
corn 230
sugarbeets 260
/;
parameter sellprice(cropx) dollars per ton /
wheat 170
corn 150
beets1 36
beets2 10
/;
parameter purchprice(cropr) dollars per ton /
wheat 238
corn 210
/;
parameter minreq(cropr) minimum requirements in ton /
wheat 200
corn 240
/;
scalar land available land /500/;
scalar maxbeets1 max allowed /6000/;
*--------------------------------------------------------------------------
* First a non-stochastic version
*--------------------------------------------------------------------------
variables
x(crop) acres of land
w(cropx) crops sold
y(cropr) crops purchased
yld(crop) yield
profit objective variable
;
positive variables x,w,y;
equations
profitdef objective function
landuse capacity
req(cropr) crop requirements for cattle feed
ylddef calc yields
beets total beet production
;
$ontext
The YLD variable and YLDDEF equation isolate the stochastic
YIELD parameter into one equation, making the DECIS setup
somewhat easier than if we would substitute YLD out of
the model.
$offtext
profitdef.. profit =e= -sum(crop, plantcost(crop)*x(crop)) - sum(cropr, purchprice(cropr)*y(cropr))
+ sum(cropx, sellprice(cropx)*w(cropx));
landuse.. sum(crop, x(crop)) =l= land;
ylddef(crop).. yld(crop) =e= yield(crop)*x(crop);
req(cropr).. yld(cropr) + y(cropr) - sum(sameas(cropx,cropr),w(cropx)) =g= minreq(cropr);
beets.. w('beets1')+w('beets2') =l= yld('sugarbeets');
w.up('beets1') = maxbeets1;
model simple /profitdef,landuse,req,beets,ylddef/;
solve simple using lp maximizing profit;
*--------------------------------------------------------------------------
* Extensive form stochastic model
* This is a standard LP.
*--------------------------------------------------------------------------
set s scenarios / above, avg, below /;
variables
ws(cropx, s) crops sold under scenario s
ys(cropr, s) crops purchased under scenario s;
positive variable ws, ys;
parameter p(s) probability;
p(s) = 1/3;
abort$(abs( sum(s,p(s)) - 1.0 ) > 0.001) "probabilities don't add up";
parameter syield(crop,s);
syield(crop,'below') = 0.8*yield(crop);
syield(crop,'avg') = yield(crop);
syield(crop,'above') = 1.2*yield(crop);
equations
sprofitdef objective function extensive form stochastic model
sreq(cropr,s)
sbeets(s)
;
sprofitdef.. profit =e= -sum(crop, plantcost(crop)*x(crop))
+sum(s, p(s)*(
-sum(cropr, purchprice(cropr)*ys(cropr,s))
+sum(cropx, sellprice(cropx)*ws(cropx,s))
));
sreq(cropr,s).. syield(cropr,s)*x(cropr) + ys(cropr,s) - sum(sameas(cropx,cropr),ws(cropx,s)) =g= minreq(cropr);
sbeets(s).. ws('beets1',s)+ws('beets2',s) =l= syield('sugarbeets',s)*x('sugarbeets');
ws.up('beets1',s) = maxbeets1;
model extform /sprofitdef,landuse,sreq,sbeets/;
solve extform using lp maximizing profit;
* collect results for x for different runs
set runs / extform extensive form
decisapprox default decis
decisexact stochastic universe option
/;
parameter px(runs,crop) results for stage 1 variables;
* store stage 1 results
px('extform',crop) = x.l(crop);
*--------------------------------------------------------------------------
* Default DECIS setup
* Based upon the non-stochastic (core) model.
*--------------------------------------------------------------------------
* output the stochastic file
file stg / MODEL.STG /;
put stg;
put 'BLOCKS DISCRETE'/;
loop(s,
put 'BL BLOCK1 PERIOD2 ',p(s)/;
loop(crop,
put 'x ',crop.tl,' ylddef ',crop.tl,' ',(-syield(crop,s))/;
);
);
putclose;
$ontext
Notice the (-yield) expression in for the coefficient for x in
equation ylddef. The row listing for YLDDEF shows that the expression
yield(crop)*x(crop) is moved by GAMS to the left-hand side causing a
minus sign. The parentheses are needed as the PUT syntax does
not allow expressions there.
$offtext
*output a MINOS option file
file mopt / MINOS.SPC /;
put mopt;
put "begin"/;
put "rows 250"/;
put "columns 250"/;
put "elements 10000"/;
put "end"/;
putclose;
* assign stages
x.stage(cropr) = 1;
y.stage(cropr) = 2;
w.stage(cropx) = 2;
yld.stage(crop) = 2;
landuse.stage = 1;
ylddef.stage(crop) = 2;
req.stage(cropr)=2;
beets.stage=2;
option lp=%decisalg%;
solve simple using lp maximizing profit;
* store stage 1 results
px('decisapprox',crop) = x.l(crop);
*--------------------------------------------------------------------------
* Let DECIS solve the model exactly
* Stochastic Universe option: 4 "ISTRAT"
*--------------------------------------------------------------------------
file decopt / %decisalg%.opt /;
put decopt;
put '4 "ISTRAT"'/;
putclose;
simple.optfile=1;
solve simple using lp maximizing profit;
* store stage 1 results
px('decisexact',crop) = x.l(crop);
display px;
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