$ondollar title Building Evacuation (NF) Example 10.4 of Rardin (1998)

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

option lp = bdmlp;

set i  "nodes" /1*10/;
alias (i,j);
alias (i,k);

set arc(i,j) "arc set of the digraph"
/1.2, 1.4, 1.6, 1.8,
2.3, 3.2, 3.4, 4.3, 4.5, 5.4, 5.6, 6.5, 6.7,
7.6, 7.8, 8.7, 8.9, 9.8, 9.2, 2.9,
2.10, 3.10, 5.10, 7.10, 9.10, 10.1/;

parameter u(i,j) "arc capacities"
/1.2 600, 1.4 600, 1.6 600, 1.8 600,
2.3 350, 3.2 350, 3.4 350, 4.3 350, 4.5 350, 5.4 350, 5.6 350, 6.5 350, 6.7 350,
7.6 350, 7.8 350, 8.7 350, 8.9 350, 9.8 350, 9.2 350, 2.9 350,
2.10 800, 3.10 400, 5.10 400, 7.10 400, 9.10 400, 10.1 10000/;

free variable maxf "maximum flow";

positive variables
x(i,j) "flow on arc (i,j)";

equations
obj      "maximize flow",
bal(k)   "balance of flow at node k",
cap(i,j) "arc capacities";

obj..
maxf =e= x('10','1');

bal(k)..
sum(i$arc(i,k), x(i,k)) - sum(j$arc(k,j), x(k,j)) =e= 0;

cap(i,j)$arc(i,j)..
x(i,j) =l= u(i,j);

model bldgevac /all/;

solve bldgevac using lp maximizing maxf;