* MOLPg.mod
* Original AMPL coding by Sven Leyffer, Argonne National Laboratory
*
* A generic MOLP (matrices are upper case; note transpose!)
*
*       minimize   C^T x
*       subj. to   A^T x <= b
*
* for data files, see ...
*
* filename              reference
* ------------------------------------------------------------
* MOLPg-001.dat                [Steu:86] p. 411, Exercise 13-4C
* MOLPg-002.dat                [Steu:86] p. 415, Exercise 13-14C
* MOLPg-003.dat                [Steu:86] p. 416, Exercise 13-15C
*                       ... there are many more MOLPs in there!
* ------------------------------------------------------------
* References:
* ~~~~~~~~~~
* [Steu:86]     R.E. Steuer, Multiple Criteria Optimization:
*               Theory, Computation and Applications, John
*               Wiley, 1986, New York.
* ------------------------------------------------------------


* ... problem dimensions & index sets

* ... number of variables
$Set nn 12
* ... number of constraints
$Set mm 16
* ... number of objectives
$Set pp 3

set N / n1*n%nn% / ;
set M / m1*m%mm% / ;
set P / p1*p%pp% / ;

* ... problem data

* ... objective gradients
Table C[P,N]
            n1 n2 n3 n4  n5  n6 n7  n8  n9 n10  n11  n12
        p1   3  0  2  2   3   1 -1   2   3  -1    1    4
        p2  -1  4  0  0   2   0 -1   4  -1   0   -1    0
        p3   0  3  2  2  -1   2  4   1   0   0   -1    3  ;


* ... constraint Jacobian
Table A[M,N]
       n1   n2   n3   n4   n5   n6   n7   n8   n9  n10   n11   n12
 m1     0    2   -1    0    0    0    0    4    2    0     0     0
 m2     0    0    0    0    0    3    0    0    0    0     0     3
 m3    -1    4    4    0    0    3    0    0    0    0    -1     0
 m4     0    4    0    3    0    0    0    0    2    0     0     4
 m5     0    0    0    0   -1    0    4    2    0    5     0     0
 m6     0    0    2    3    0    0    0    0    0    0     0     5
 m7     2    0    1    0    0    0    0    2    2   -1     2     4
 m8     0    0    0    0    0    0    0    0    2    0     3     0
 m9     0    0    0   -1    0    0    2    1    4    0     0     0
 m10    4   -1    0    0    0    0    0    0    0    4     0     0
 m11    0    0    0   -1    0    0    0    0    2    5     0     0
 m12    0    0    0    0    0    0    0    0    0    0     2     0
 m13   -1   -1    0    0    0    0    0    0    0    0     0     0
 m14    2    0    0    3    0    5    0    0    0    0     0     0
 m15    0    2    1    0    3    5    0    0    0    0     0     0
 m16    0    2    5    0    4    0    3    0    0    0     0     0 ;



* ... upper bounds on A^T x
Parameter b[M];
        b['m1']  =    10;
        b['m2']  =    10;
        b['m3']  =    10;
        b['m4']  =    7 ;
        b['m5']  =    10;
        b['m6']  =    5 ;
        b['m7']  =    5 ;
        b['m8']  =    6 ;
        b['m9']  =    5 ;
        b['m10'] =    7 ;
        b['m11'] =    6 ;
        b['m12'] =    7 ;
        b['m13'] =    9 ;
        b['m14'] =    5 ;
        b['m15'] =    9 ;
        b['m16'] =    5 ;


Positive Variable x[N] ;

Variable f ;

Equation lin(M)  ,
         Def_Obj ;

* ... linear constraints
lin(M)..
    Sum{N, A[M,N]*x[N] } =l= b[M] ;

* ... objective functions
Def_Obj..
    f =e= -Sum{(N,P)$(ord(P) eq 1), C[P,N]*x[N]} ;

Model MOLPg / all / ;

Solve MOLPg using NLP minimazing f ;

Display f.l ;