* Test problem 9.2.7 in the Test Collection Book
* Test problem 9.1.6 in the web page
* Test Problem from Anandalingam and White 1990
* They took from Bialas and Karwan 1982

SET i /1*6/;

PARAMETER bigu;

bigu = 400;

VARIABLES

z;

POSITIVE VARIABLES

x, y, s(i), lb(i);

BINARY VARIABLES

yb(i);

EQUATIONS

ob, c1, c2, c3, c4, c5, c6, kt1, cs1(i), cs2(i);

* Outer Objective function

ob.. -x -3*y =e= z;

* Inner Problem Constraints

c1..  - x - 2*y + s('1') =e= -10;

c2..    x - 2*y + s('2') =e= 6;

c3..  2*x -   y + s('3') =e= 21;

c4..    x + 2*y + s('4') =e= 38;

c5..   -x + 2*y + s('5') =e= 18;

c6..        - y + s('6') =e= 0;

* KKT conditions for the inner problem optimum

kt1..  3 - 2*lb('1') - 2*lb('2') - lb('3') 
         + 2* lb('4') + 2*lb('5') - lb('6') =e= 0;

* Complementarity Constraints

cs1(i).. lb(i) - bigu*yb(i) =l= 0;
cs2(i)..  s(i) - bigu*(1 - yb(i)) =l= 0;

s.up(i)  = 200;
lb.up(i) = 200;


MODEL ANWH90/ALL/;

SOLVE ANWH90 USING MIP MINIMIZING z;