Good Morning guys, I really need your help, I'm trying to figure out a problem in my implementation of a min cost flow problem in AMPL. I have to create the code for the problem in the image:
I tried this code, but I'm not able to solve the problem of unsplittable flow and I don't know how to put constraints on origin and destination nodes.
set nodes;
param commodity1{nodes};
set arcs within {nodes cross nodes};
param cap{arcs} >= 0;
param cost{arcs} >= 0;
var flow{arcs} >= 0;
minimize z:
sum{(i,j) in arcs} cost[i,j]*flow[i,j];
subject to c1{ (i,j) in arcs}:
flow[i,j] <= cap[i,j];
subject to c2{i in nodes}:
-sum{ (j,i) in arcs} flow[j,i] + sum{(i,j) in arcs} flow[i,j] = commodity1[i];
data;
set nodes := 1 2 3 4 5 6 ;
param: arcs: cap cost :=
1,2 15 3
2,3 1 6
3,4 6 3
4,1 6 8
2,4 10 4
2,5 10 4
5,6 10 4
5,3 4 12
3,6 7 8
4,6 8 10;
param commodity1 :=
3 6,
4 0,
1 4,
2 0,
6 -4,
5 -6
;
I hope someone can help me. Thank you !