* Pooling problem (Ben-Tal et al., 1994)

VARIABLES
	 q11  fraction of flow to pool 1 coming from feed 1
	 q21  fraction of flow to pool 1 coming from feed 2
	 q41  fraction of flow to pool 1 coming from feed 4
	 y11  flow from pool 1 to product 1
	 y12  flow from pool 1 to product 2
	 z31  flow from feed 3 to product 1
	 z32  flow from feed 3 to product 2
     objval    objective function variable;

FREE VARIABLES    objval;


EQUATIONS
	 f Objective function
	 g1  
	 g2  
	 g3  
	 g4  
	 g5  
	 g6  ;

f  .. objval =e= (9 - 6*q11 - 16*q21 - 15*q41)*y11 + (15 - 6*q11 - 16*q21 - 15*q41)*y12 - z31 + 5*z32; 
g1  .. q41*y11 + q41*y12 =l= 50;
g2  .. y11 + z31 =l= 100;
g3  .. y12 + z32 =l= 200;
g4  .. (3*q11 + q21 + q41 -2.5)*y11 - 0.5*z31 =l= 0;
g5  .. (3*q11 + q21 + q41 -1.5)*y12 + 0.5*z32 =l= 0;
g6  .. q11 + q21 + q41 =e= 1;

* Bounds
q11.LO = 0; q11.UP = 1;
q21.LO = 0; q21.UP = 1;
q41.LO = 0; q41.UP = 1;
y12.LO = 0; y12.UP = 200;
y11.LO = 0; y11.UP = 100;
z31.LO = 0; z31.UP = 100;
z32.LO = 0; z32.UP = 200;

* Starting point (global solution)
* q11.L =  0; q21.L =  0.5; q41.L =  0.5;
* y11.L =  0; y12.L =  100;
* z31.L =  0; z32.L =  100;

MODEL test /ALL/;
SOLVE test USING NLP MAXIMIZING objval;