farmsp.gms : The Farmer's Problem - Stochastic

**Description**

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.

**Small Model of Type : ** SP

**Category :** GAMS EMP library

**Main file :** farmsp.gms

```
$title The Farmer's Problem - Stochastic (FARMSP,SEQ=73)
$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
Set crop / wheat, corn, sugarbeets /
ch header for data table /
yield yield in tons per acre
cost plantcost on dollars per acre
pprice crop seed purchase price in dollars per ton
minreq minimum requirements of crop in ton to feed cattle /
alias (c,crop);
Table cd(crop,ch) crop data
yield cost pprice minreq
wheat 2.5 150 238 200
corn 3 230 210 240
sugarbeets 20 260
;
Parameter
yf yield factor / 1 /
land available land in acres /500/;
$ontext
* Not clear what to do, that's why we do EMP!!!
Stochastic Parameter/Random Variable
yf yield factor / 1 /;
Set r realizations / below, avg, above /;
Table yfdistrib(r,*)
value prob
below 0.8 [1/4]
avg 1 [1/2]
above 1.2 [1/4];
option yf%yfdistrib;
yf.stage = 2;
yf.stage(t) = ord(t)+1;
$offtext
Set seq price curve segments / s1*s2 /;
Table pricecurve(crop,seq,*) dollars per ton
price ub
wheat.s1 170 inf
corn.s1 150 inf
sugarbeets.s1 36 6000
sugarbeets.s2 10 inf
;
set pcs(crop,seq) relevant segments; option pcs<pricecurve;
set errorPC(crop) price curve is not concave;
errorPC(c) = smin(pcs(c,seq), pricecurve(c,seq,'price')-pricecurve(c,seq+1,'price'))<0;
abort$card(errorPC) errorPC;
Variables
x(c) crop planted in acres of land
w(c,seq) crops sold in segment of cost curve in tons
y(c) crops purchased in tons
profit objective variable in dollars;
Positive variables x,w,y;
Equations
profitdef objective function
landuse capacity
bal(c) crop balance;
profitdef.. profit =e= sum(pcs, w(pcs)*pricecurve(pcs,'price'))
- sum(c, cd(c,'cost')*x(c) + cd(c,'pprice')*y(c));
landuse.. sum(c, x(c)) =l= land;
bal(c).. yf*cd(c,'yield')*x(c) + y(c) - sum(pcs(c,seq), w(pcs)) =g= cd(c,'minreq');
* No purchase of crops that don't have a purchase price
y.fx(c)$(cd(c,'pprice')=0) = 0;
w.up(pcs) = pricecurve(pcs,'ub');
model farm_emp /all/;
file emp / '%emp.info%' /; put emp '* problem %gams.i%'/;
$onput
randvar yf discrete 0.25 0.8
0.50 1.0
0.25 1.2
stage 2 yf y w bal profit
$offput
putclose emp;
Set s scenarios / s1*s3 /;
Parameter
srep(s,*) scenario attributes / #s.prob 0 /
s_yf(s) yield factor realization by scenario
s_profit(s) profit by scenario
s_w(s,c,seq) crops sold in segment of cost curve in tons by scenario
s_y(s,c) crops purchased in tons by scenario;
Set dict / s .scenario.''
'' .opt. srep
yf .randvar. s_yf
profit.level. s_profit
w .level. s_w
y .level. s_y /;
solve farm_emp using emp maximizing profit scenario dict;
display srep;
```