$Title A Transportation Problem (TRNSPORT,SEQ=1)
$Ontext
This program is a modified version of trnsport.gms and
illustrates use of reading data from a GDX file during
execution time
$Offtext
Sets
i canning plants
j markets;
$gdxin Trnsport.gdx
$load i j
Parameters
a(i) capacity of plant i in cases
b(j) demand at market j in cases
d(i,j) distance in thousands of miles ;
Scalar f freight in dollars per case per thousand miles;
execute_load 'Trnsport.gdx' a,b,d,f;
Parameter c(i,j) transport cost in thousands of dollars per case ;
c(i,j) = f * d(i,j) / 1000 ;
Variables
x(i,j) shipment quantities in cases
z total transportation costs in thousands of dollars ;
Positive Variable x ;
Equations
cost define objective function
supply(i) observe supply limit at plant i
demand(j) satisfy demand at market j ;
cost .. z =e= sum((i,j), c(i,j)*x(i,j)) ;
supply(i) .. sum(j, x(i,j)) =l= a(i) ;
demand(j) .. sum(i, x(i,j)) =g= b(j) ;
Model transport /all/ ;
Solve transport using lp minimizing z ;
Display x.l, x.m ;