$*************************************************************
$ A. Aggarwal and C.A. Floudas, "Synthesis of General
$   Distillation Sequences: Nonsharp Separation", Comput.
$   Chem. Eng., 1990, 14 (6), 631--653.
$
$ Example 2
$
$ Optimal Solution:  0.625967
$*************************************************************

OPTIONS{{
  FTOL = 1e-6;
  OTOL = 1e-6;
  RFIX; BALLR = "1.0"; BALLS = "1.0"; RFIXBOTH; BALLT = "1e+10";
}}

VARIABLES{{
  INDEX {i,j};
  SET I = |0:2|;
  SET J = |0:19|;
  SET K = |0:1|;

  PARA feed(I) = {100,100,100};
  PARA comp(I) = <i E I| feed(i)/300>;
  PARA prod0(I) = {80,30,20};
  PARA prod1(I) = {20,70,80};
  PARA tot0     = <<i E I| prod0(i)>>;
  PARA tot1     = <<i E I| prod1(i)>>;

  XVAR {x4(I), x5(I), x8(I), x12(I), x13(I), x17(I), rlk(K), rhk(K)};
  YVAR {y(K), f(J), ff4(I), ff12(I)};
  POSI {x4(I), x5(I), x8(I), x12(I), x13(I), x17(I),
        rlk(K), rhk(K), f(J), ff4(I), ff12(I)};
  BINA {y(K)};

  UBDS f(J)   = <j E J| 300>;
  UBDS ff4(I)  = {100, 100, 100};
  UBDS ff12(I) = {100, 100, 100};
  LBDS rhk(K)  = {0.85, 0.85};
  UBDS rhk(K)  = {1, 1};
  LBDS rlk(K)  = {0.85, 0.85};
  UBDS rlk(K)  = {1, 1};

  UBDS x4(I)  = <i E I| 1>;
  UBDS x5(I)  = <i E I| 1>;
  UBDS x8(I)  = <i E I| 1>;
  UBDS x12(I) = <i E I| 1>;
  UBDS x13(I) = <i E I| 1>;
  UBDS x17(I) = <i E I| 1>;

  STP y(K)  = {1, 1};

#Columns 1 and 2 in series
#  STP f(J) = {300,  0,0,0,300,100,80,20,200,200, 0, 0,200,100,  0,30,70,100,20,80};
#  STP ff4(I)  = {100,100,100};
#  STP ff12(I) = {100,100,  0};

#Columns 2 and 1 in series
  STP f(J) = {  0,300,0,0,200,100,80,20,100,  0,30,70,300,200,200, 0, 0,100,20,80};
  STP ff4(I)  = {100,100,  0};
  STP ff12(I) = {100,100,100};
}}

CONSTRAINTS{{
  MIN: 0.23947*y(0) + -0.0139904*f(4) + 0.0093514*rlk(0)*f(4)
       + 0.0077308*rhk(0)*f(4) - 0.0005719*x4(0)*f(4)
       + 0.0042656*x4(1)*f(4) + 0*x4(2)*f(4) + 0.75835*y(1)
       + -0.0661588*f(12) + 0.0338147*rlk(1)*f(12)
       + 0.0373349*rhk(1)*f(12) + 0.0016371*x12(0)*f(12)
       + 0.0288996*x12(1)*f(12) + 0*x12(2)*f(12);
  l1: f(0) + f(1) + f(2) + f(3) =e= 300;
  l2: f(5)  =e= f(6)  + f(7);
  l3: f(8)  =e= f(9)  + f(10) + f(11);
  l4: f(13) =e= f(14) + f(15) + f(16);
  l5: f(17) =e= f(18) + f(19);
  ln1: f(5) *x5(0)  =e= rlk(0)*ff4(0);
  ln3: f(8) *x8(1)  =e= rhk(0)*ff4(1);
  ln2: f(13)*x13(1) =e= rlk(1)*ff12(1);
  ln4: f(17)*x17(2) =e= rhk(1)*ff12(2);
  ln5(i E I): ff4(i)  =e= f(4) *x4(i);
  ln6(i E I): ff12(i) =e= f(12)*x12(i);
  l6:  <<i E I|ff4(i)>>  =e= f(4);
  l7:  <<i E I|ff12(i)>> =e= f(12);
  ln7(i E I): ff4(i)  =e= f(5) *x5(i)  + f(8) *x8(i);
  ln8(i E I): ff12(i) =e= f(13)*x13(i) + f(17)*x17(i);
  l8:  f(4)  =e= f(5)  + f(8);
  l9:  f(12) =e= f(13) + f(17);
  ln9(i E I):  comp(i)*f(0) + f(14)*x13(i) =e= ff4(i);
  ln10(i E I): comp(i)*f(1) + f(9)*x8(i)   =e= ff12(i);
  ln11(i E I): comp(i)*f(2) + f(6)*x5(i) + f(10)*x8(i)
           + f(15)*x13(i) + f(18)*x17(i) =e= prod0(i);
  ln12(i E I): comp(i)*f(3) + f(7)*x5(i) + f(11)*x8(i)
           + f(16)*x13(i) + f(19)*x17(i) =e= prod1(i);
  l10: f(2) + f(6) + f(10) + f(15) + f(18) =e= tot0;
  l11: f(3) + f(7) + f(11) + f(16) + f(19) =e= tot1;
  l12: x5(2) =E= 0;
  l13: x17(0) =E= 0;
  l14: <<i E I| x4(i)  >> =e= 1;
  l15: <<i E I| x5(i)  >> =e= 1;
  l16: <<i E I| x8(i)  >> =e= 1;
  l17: <<i E I| x12(i) >> =e= 1;
  l18: <<i E I| x13(i) >> =e= 1;
  l19: <<i E I| x17(i) >> =e= 1;
  l20: f(4)  =l= 300*y(0);
  l21: f(12) =l= 300*y(1);
}}