GAMS is a programming language created in 1988.
#1792on PLDB | 36Years Old |
Sets
i canning plants / Seattle, San-Diego /
j markets / New-York, Chicago, Topeka / ;
Parameters
a(i) capacity of plant i in cases
/ Seattle 350
San-Diego 600 /
b(j) demand at market j in cases
/ New-York 325
Chicago 300
Topeka 275 / ;
Table d(i,j) distance in thousands of miles
New-York Chicago Topeka
Seattle 2.5 1.7 1.8
San-Diego 2.5 1.8 1.4 ;
Scalar f freight in dollars per case per thousand miles /90/ ;
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 variables 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 ;