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';
``````