Sets
i Origin plants / columbus, marshall, cedar_rapids /
j Destination plants / blair, clinton, decatur /
k Transport modes / truck, rail /;
Alias (ii, i), (jj, j);
Parameters
c(i,j,k) Unit transport cost ($/ton)
s(i) Supply at each origin (tons)
d(j) Demand (capacity) at each destination (tons);
Table c(i,j,k)
truck rail
columbus.blair 11 0
columbus.clinton 34.19 34.5
columbus.decatur 49.32 41.87
marshall.blair 22.5 0
marshall.clinton 40.05 43.69
marshall.decatur 56.25 57.35
cedar_rapids.blair 23.67 0
cedar_rapids.clinton 11 18.2
cedar_rapids.decatur 26 25.37;
* Replace 0 with a very high cost (or use equations to restrict routes)
* c(i,j,'rail')$((j='blair')) = 1e6;
s(i) = / columbus 360, marshall 288, cedar_rapids 656 /;
d(j) = / blair 280, clinton 1600, decatur 1500 /;
Variables
x(i,j,k) Shipment from i to j via k (tons)
z Total transportation cost;
Positive Variable x;
Equations
obj Objective function
supply(i) Supply constraint at each origin
demand(j) Demand constraint at each destination
blair_min Min limit to Blair (optional)
blair_max Max limit to Blair;
* Objective Function
obj.. z =e= sum((i,j,k), c(i,j,k) * x(i,j,k));
* Supply constraints
supply(i).. sum((j,k), x(i,j,k)) =e= s(i);
* Demand constraints
demand(j).. sum((i,k), x(i,j,k)) =l= d(j);
* Optional Cargill Blair constraint range
blair_min.. sum((i,k)$(j='blair'), x(i,'blair',k)) =g= 250;
blair_max.. sum((i,k)$(j='blair'), x(i,'blair',k)) =l= 280;
Model CornLogisticsLP / all /;
Solve CornLogisticsLP using lp minimizing z;
There were some simple syntax errors. This tutorial may be useful as it walks you through the fundamentals of GAMS based on a simple problem.
I fixed the syntax errors. Please make sure you understand the changes.
I hope this helps!
Sets
i Origin plants / columbus, marshall, cedar_rapids /
j Destination plants / blair, clinton, decatur /
k Transport modes / truck, rail /;
Alias (ii, i), (jj, j);
Parameters
c(i,j,k) 'Unit transport cost ($/ton)'
s(i) 'Supply at each origin (tons)' / columbus 360, marshall 288, cedar_rapids 656 /
d(j) 'Demand (capacity) at each destination (tons)' / blair 280, clinton 1600, decatur 1500 /;
Table c(i,j,k)
truck rail
columbus.blair 11 0
columbus.clinton 34.19 34.5
columbus.decatur 49.32 41.87
marshall.blair 22.5 0
marshall.clinton 40.05 43.69
marshall.decatur 56.25 57.35
cedar_rapids.blair 23.67 0
cedar_rapids.clinton 11 18.2
cedar_rapids.decatur 26 25.37;
* Replace 0 with a very high cost (or use equations to restrict routes)
* c(i,j,'rail')$((j='blair')) = 1e6;
Variables
x(i,j,k) Shipment from i to j via k (tons)
z Total transportation cost;
Positive Variable x;
Equations
obj Objective function
supply(i) Supply constraint at each origin
demand(j) Demand constraint at each destination
blair_min Min limit to Blair (optional)
blair_max Max limit to Blair;
* Objective Function
obj.. z =e= sum((i,j,k), c(i,j,k) * x(i,j,k));
* Supply constraints
supply(i).. sum((j,k), x(i,j,k)) =e= s(i);
* Demand constraints
demand(j).. sum((i,k), x(i,j,k)) =l= d(j);
* Optional Cargill Blair constraint range
blair_min.. sum((i,k), x(i,'blair',k)) =g= 250;
blair_max.. sum((i,k), x(i,'blair',k)) =l= 280;
Model CornLogisticsLP / all /;
Solve CornLogisticsLP using lp minimizing z;
1 Like
Thank you for helping. I am trying to simplify the code in a standard Transportation model by following the examples on your website, but I am still getting errors.
Sets
i supply nodes /Blair, Clinton, Decatour/
j demand nodes /Columbus, Marshall, Cedar_rapids/;
Parameters
a(i) supply capacities
/Blair 280
Clinton 1600
Decatour 1500 /
b(j) demands
/Columbus 360
Marshall 288
Cedar_rapids 656
Dummy 2076 /;
Table c1(i,j) transport costs for Rails
Columbus Marshall Cedar_rapids Dummy
Blair 0 34.50 41.87 0
Clinton 0 43.69 57.35 0
Decatour 0 18.20 25.37 0 ;
Table c2(i,j) transport costs for Truck
Columbus Marshall Cedar_rapids Dummy
Blair 11 34.19 49.32 0
Clinton 22 40.05 56.25 0
Decatour 23.67 11 26 0 ;
Positive Variables
x(i,j) flow between supply node i and demand node j;
Variables
y(i,j) whether a ship is bought for the trasfer from i to j
z total cost;
Binary Variables y;
Equations
cost objective function
supply(i) supply constraint
demand(j) demand constraint;
cost.. Z =e= sum ((i,j), c1(i,j) * x(i,j) + c2(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 TransportaionCorn /all/;
Solve TransportaionCorn using lp minimizing Z;
Display x.l, x.m ;