$title Large Random Min Cost Flow example 

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

set 
    nodes /1*5000/
    sources(nodes)
    sinks(nodes);

alias (nodes,i,j,k);

set arcs(i,j);
parameter cost(i,j), supply(nodes), randomVector(nodes);

variables f(i,j), totalcost;
positive variable f;

scalar counter;

* first define a random set of arcs of a given density.
* (If density is too low, the problem may not have a solution - 
* there may not be a path from sources to sinks.)
option seed=25671;
arcs(i,j) = yes$(uniform(0,1) < .025);
* no self-directed arcs
arcs(i,i) = no;

* now define costs on these arcs
cost(i,j) = uniform(0,50) $ arcs(i,j);

* determine eligible source nodes (those with outflowing arcs) 
* and sinks (those with inflowing arcs);
sources(nodes) = no; sinks(nodes) = no;
loop(arcs(i,j),
	sources(i) = yes;
	sinks(j) = yes;
);

supply(nodes) = 0;
* pick two sources to have positive supplies
counter = 0;
loop(nodes$(sources(nodes) and counter<2),
  supply(nodes) = 10;
  counter = counter+1;
);
* and five sinks to have balancing negative supplies
counter = 0;
loop(nodes$(sinks(nodes) and counter<5 and supply(nodes)=0),
  supply(nodes) = -4;
  counter = counter+1;
);

* display sources, sinks, supply;

equations balance(i), objective;

balance(i)..
	sum(arcs(i,k), f(arcs)) - sum(arcs(j,i), f(arcs)) =e= supply(i);
objective..
	totalcost =e= sum(arcs, cost(arcs)*f(arcs));

model mcf/balance, objective/;

solve mcf using lp minimizing totalcost;

option f:0:0:2; display f.l;