reset;
model vcolor.mod;
data italia.dat;

for {i in V} let a[i,i] := 1;

problem Master: L, colors, cover_all;
problem Pricing: x, reduced_cost, independence; 
#display a;
repeat {
	problem Master;
	#expand Master;
	option solver gurobi;
	option relax_integrality 1;
	solve;
	
	#display L;
	#display cover_all.dual; # the dual value for each constraint
	
	
	for {i in V} let pi[i]:= cover_all.dual[i];
	
	problem Pricing;
	#display pi;
	
	option solver gurobi;
	option relax_integrality 0;
	solve;
	
	if (reduced_cost > -1e-16) then
		break; 
	
	let p := p+1;
	let {i in V} a[i,p] := x[i];
	
} until 0;
	problem Master;
	option solver gurobi;
	option relax_integrality 1;
	solve;
	display L;
	
	problem Master;
	option solver gurobi;
	option relax_integrality 0;
	solve;
	
	for {j in P: L[j]=1} {
		for {i in V: a[i,j]=1} 
			printf"%d ", i;
		printf" are in set %d\n" , j;
	}