$ontext max flow network example Data from example in Mitsuo Gen, Runwei Cheng, Lin Lin Network Models and Optimization: Multiobjective Genetic Algorithm Approach Springer, 2008 Erwin Kalvelagen, Amsterdam Optimization, May 2008 $offtext sets i 'nodes' /node1*node11/ source(i) /node1/ sink(i) /node11/ ; alias(i,j); parameter capacity(i,j) / node1.node2 60 node1.node3 60 node1.node4 60 node2.node3 30 node2.node5 40 node2.node6 30 node3.node4 30 node3.node6 50 node3.node7 30 node4.node7 40 node5.node8 60 node6.node5 20 node6.node8 30 node6.node9 40 node6.node10 30 node7.node6 20 node7.node10 40 node8.node9 30 node8.node11 60 node9.node10 30 node9.node11 50 node10.node11 50 /; set arcs(i,j); arcs(i,j)$capacity(i,j) = yes; display arcs; parameter rhs(i); rhs(source) = -1; rhs(sink) = 1; variables x(i,j) 'flow along arcs' f 'total flow' ; positive variables x; x.up(i,j) = capacity(i,j); equations flowbal(i) 'flow balance' ; flowbal(i).. sum(arcs(j,i), x(j,i)) - sum(arcs(i,j), x(i,j)) =e= f*rhs(i); model m/flowbal/; solve m maximizing f using lp;