\$title Educational bilevel model (JOINTC1, SEQ=22) \$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 >= x for the upper level problem. Since has a lower bound 1 this model is infeasible. Second model ------------ The lower level problem essentially requires y = |x|. Since x and y are minimized and x has a lower bound of 1 the solution is x = 1 = y. Contributor: Michael Ferris, November 2009 \$offtext variables x, y; equations upper, lower; upper.. y =g= x; lower.. y =g= -x; model jc /all/; x.lo = 1; file fhandle /"%emp.info%"/; *First model putclose fhandle 'bilevel min y lower'; solve jc using emp min x; * check that it is indeed infeasible abort\$(jc.solvestat <> %SOLVESTAT.NORMAL COMPLETION% or ((jc.modelstat <> %MODELSTAT.INFEASIBLE%) and (jc.modelstat <> %MODELSTAT.LOCALLY INFEASIBLE%)) ) 'Wrong solution: 1st model'; *Reset initial values x.l = 2; y.l = 0; *Second model putclose fhandle 'bilevel min y upper lower'; solve jc using emp min x; * check that solution is x = y = 1 abort\$(jc.solvestat <> %SOLVESTAT.NORMAL COMPLETION% or ((abs(x.l-1) > 1e-6) or (abs(y.l-1) > 1e-6)) ) 'Wrong solution: 2nd model';