$ondollar title Optimal Ovens Inc. (NF) Example 10.1 of Rardin (1998)

$offsymxref offsymlist offuelxref offuellist offupper
option limrow = 0, limcol = 0;

set i  "nodes" /1*8/;
alias (i,j);
alias (i,k);

set arc(i,j) "arc set of the digraph"
/1.3, 1.4, 1.8, 2.3, 2.4, 2.8, 3.4, 3.5, 3.6, 3.7, 4.3, 4.5, 4.6, 4.7/;

parameter c(i,j) "unit costs of flow"
/1.3 7, 1.4 8, 2.3 4, 2.4 7, 3.5 25, 3.6 5, 3.7 17, 4.5 29, 4.6 8, 4.7 5/;

parameter b(k) "net demand at node k"
/1 -1000, 2 -1000, 3 0, 4 0, 5 450, 6 500, 7 610, 8 440/;

free variable cost "total shipping cost";

positive variables
x(i,j)   "flow on arc (i,j)";
x.up('3','4') = 25;
x.up('4','3') = 25;

equations
obj    "minimize total cost",
bal(k) "balance of flow at node k";

obj..
cost =e= sum((i,j)$arc(i,j), c(i,j)*x(i,j));

bal(k)..
sum(i$arc(i,k), x(i,k)) - sum(j$arc(k,j), x(k,j)) =e= b(k);

model optoven /all/;

solve optoven using lp minimizing cost;