Quick start - Gams

The optimization example is as follows
Max
s.
t.
109*
X
X
X
X
corn
corn
corn
corn
+
90*
+ X
_ 4*
X
X
wheat
X
wheat
wheat
wheat
+ 115*
X
+ X
+ 8*
X
X
Cotton
Cotton
Cotton
Cotton
≤100
≤ 500
≥ 0
This is a special case of the general resource allocation problem that can be written as
where
Max
s.
t.
∑
j
∑
j
C
a
X
j
ij
j
X
X
j
j
b
i
0
for all i
for all
j = { corn wheat cotton }
i = { land labor }
xj = { Xcorn Xwheat Xcotton }
cj = { 109 90 115 }
aij = 1 1 1
6 4 8
bi = { 100 500 }’
Such a model can be cast in GAMS as (optalgebra.gms)
SET j /Corn,Wheat,Cotton/
i /Land ,Labor/;
PARAMETER
c(j) / corn 109 ,wheat 90 ,cotton 115/
b(i) /land 100 ,labor 500/;
TABLE a(i,j)
corn wheat cotton
land 1 1 1
labor 6 4 8 ;
POSITIVE VARIABLES x(j);
VARIABLES PROFIT ;
EQUATIONS OBJective ,
constraint(i) ;
OBJective.. PROFIT=E= SUM(J,(c(J))*x(J)) ;
constraint(i).. SUM(J,a(i,J) *x(J)) =L= b(i);
MODEL RESALLOC /ALL/;
SOLVE RESALLOC USING LP MAXIMIZING PROFIT;
I will dissect the GAMS components after presenting the other example.
Revised equilibrium example
≤
≥
j
( land)
( labor)
( nonnegativity)
Courtesy of B.A. McCarl, October 2002 25