jointc2.gms : Educational bilevel model

**Description**

This is an example that shows that upper level joint constraints cannot simply be put into lower level model First model ----------- The lower level problem essentially requires y = -x which implies x <= 1 for the upper level problem. Since x has a lower bound of 1 the solution is x = 1, y = -1. Second model ------------ The upper level problem maximizes x s.t. no constraint, hence, x will be at its upper bound, x = 2. That implies y >= 0 for the lower level problem which minimzes y, hence y = 0. Contributor: Michael Ferris, November 2009

**Small Model of Type : ** BP

**Category :** GAMS EMP library

**Main file :** jointc2.gms

```
$title Educational bilevel model (JOINTC2, SEQ=23)
$ontext
This is an example that shows that upper level joint constraints
cannot simply be put into lower level model
First model
-----------
The lower level problem essentially requires y = -x which implies x <= 1
for the upper level problem. Since x has a lower bound of 1 the solution
is x = 1, y = -1.
Second model
------------
The upper level problem maximizes x s.t. no constraint, hence, x will be
at its upper bound, x = 2. That implies y >= 0 for the lower level problem
which minimzes y, hence y = 0.
Contributor: Michael Ferris, November 2009
$offtext
variables x, y;
equations upper, lower;
upper.. y =g= x - 2;
lower.. y =g= -x;
model jc /all/;
x.lo = 1;
x.up = 2;
y.up = 100;
file fhandle /"%emp.info%"/;
*First model
putclose fhandle 'bilevel min y lower';
solve jc using emp max x;
* check that solution is x = 1, y = -1
abort$(jc.solvestat <> %SOLVESTAT.NORMAL COMPLETION%
or ((abs(x.l-1) > 1e-6) or (abs(y.l-(-1)) > 1e-6)) ) 'Wrong solution: 1st model';
*Start from known solution
x.l = 2;
y.l = 0;
*Second model
putclose fhandle 'bilevel min y upper lower';
solve jc using emp max x;
* check that solution is x = 2, y = 0
abort$(jc.solvestat <> %SOLVESTAT.NORMAL COMPLETION%
or ((abs(x.l-2) > 1e-6) or (abs(y.l-0) > 1e-6)) ) 'Wrong solution: 2nd model';
```