* Cute AMPL model  (translation to GAMS)
*
*
***************************
* SET UP THE INITIAL DATA *
***************************
*   Problem
*   ********
*   The problem arises in the field of computer networks and parallel
*   computation.  It deals with the static load balancing in a tree
*   computer network with two-way traffic.  A set of heterogeneous host
*   computers are interconnected, in which each node processes jobs (the
*   jobs arriving at each node according to a time invariant Poisson process)
*   locally or sends it to a remote node,.  In the latter case, there is a
*   communication delay of forwarding the job and getting a response back.
*   The problem is then to minimize the mean response time of a job.
*   The example considered here features 11 computers arranged as follows
*         1      6      9
*          \     |     /
*           \    |    /
*        2---4---5---8---10
*           /    |    \
*          /     |     \
*         3      7      11
*   Source
*   J. Li and H. Kameda,
*   "Optimal load balancing in tree network with two-way traffic",
*   Computer networks and ISDN systems, vol. 25, pp. 1335-1348, 1993.
*   SIF input  Masha Sosonkina, Virginia Tech., 1995.
*   classification OLR2-MN-31-31
* Parameter eter assignment.
* Problem dimentions
* FI = SUM(arrival rate for a node)
* Objective function
* Constrains
* Comm. constrains
* XIJ --Link flow rate.
$offdigit ;
        Parameter       p1  /   3     /;
        Parameter        n  /   11    /;
        Parameter    nlink  /   20    /;
        Parameter  nlinkm3  /   17    /;
        Parameter  nlinkm4  /   16    /;
        Parameter       fi  /  514.0  /;
        Parameter     cije  / 9999.99 /;
        Parameter ip3 ; ip3  = 3 + (3);
        Parameter ip6 ; ip6  = 6 + (3);
        Parameter ip8 ; ip8  = 8 + (3);
        Parameter ip9 ; ip9  = 9 + (3);
        Parameter i2  ; i2  = 2 * (7);
        Parameter i2p1; i2p1  = 1 + (2 * (7));
        Parameter i2p2; i2p2  = 2 + (2 * (7));

Positive Variable  x4_1 , x1_4 , x4_2 , x2_4 , x4_3 , x3_4 ,
                   x4_5 , x5_4 , x5_6 , x6_5 , x5_7 , x7_5 ,
                   x5_8 , x8_5 , x8_9 , x9_8 , x8_10, x10_8,
                   x8_11, x11_8,   b1 ,   b2 ,   b3 ,   b4 ,
                     b5 ,   b6 ,   b7 ,   b8 ,   b9 ,  b10 ,
                    b11 ;
Variable obj ;

Equation    cnst1  ,  cnst2  , cnst3  , cnst4  , cnst5  , cnst6  , cnst7  , cnst8  , cnst9  , cnst10 ,
            cnst11 ,  cnst12 , cnst13 , cnst14 , cnst15 , cnst16 , cnst17 , cnst18 , cnst19 , cnst20 ,
               n1  ,     n2  ,    n3  ,    n4  ,    n5  ,    n6  ,    n7  ,    n8  ,    n9  ,    n10 ,
               n11 , Def_obj ;
   cnst1..         0 =g= 20.0* x4_1 + 80.0* x1_4 -  999.99 ;
   cnst2..         0 =g= 80.0* x4_1 + 20.0* x1_4 -  999.99 ;
   cnst3..         0 =g= 20.0* x4_2 + 80.0* x2_4 -  999.99 ;
   cnst4..         0 =g= 80.0* x4_2 + 20.0* x2_4 -  999.99 ;
   cnst5..         0 =g= 20.0* x4_3 + 80.0* x3_4 -  999.99 ;
   cnst6..         0 =g= 80.0* x4_3 + 20.0* x3_4 -  999.99 ;
   cnst7..         0 =g= 20.0* x5_6 + 80.0* x6_5 -  999.99 ;
   cnst8..         0 =g= 80.0* x5_6 + 20.0* x6_5 -  999.99 ;
   cnst9..         0 =g= 20.0* x5_7 + 80.0* x7_5 -  999.99 ;
   cnst10..        0 =g= 80.0* x5_7 + 20.0* x7_5 -  999.99 ;
   cnst11..        0 =g= 20.0* x8_9 + 80.0* x9_8 -  999.99 ;
   cnst12..        0 =g= 80.0* x8_9 + 20.0* x9_8 -  999.99 ;
   cnst13..        0 =g= 20.0*x8_10 + 80.0*x10_8 -  999.99 ;
   cnst14..        0 =g= 80.0*x8_10 + 20.0*x10_8 -  999.99 ;
   cnst15..        0 =g= 20.0*x8_11 + 80.0*x11_8 -  999.99 ;
   cnst16..        0 =g= 80.0*x8_11 + 20.0*x11_8 -  999.99 ;
   cnst17..        0 =g= 20.0* x4_5 + 80.0* x5_4 - 9999.99 ;
   cnst18..        0 =g= 80.0* x4_5 + 20.0* x5_4 - 9999.99 ;
   cnst19..        0 =g= 20.0* x5_8 + 80.0* x8_5 - 9999.99 ;
   cnst20..        0 =g= 80.0* x5_8 + 20.0* x8_5 - 9999.99 ;

   n1..          x4_1 -  x1_4 -   b1 + 95.0 =e= 0;
   n2..          x4_2 -  x2_4 -   b2 + 95.0 =e= 0;
   n3..          x4_3 -  x3_4 -   b3 + 19.0 =e= 0;
   n4..         -x4_1 +  x1_4 - x4_2 + x2_4 - x4_3 + x3_4 - x4_5 + x5_4 - b4 + 70.0 =e= 0;
   n5..          x4_5 -  x5_4 - x5_6 + x6_5 - x5_7 + x7_5 - x5_8 + x8_5 - b5 + 70.0 =e= 0;
   n6..          x5_6 -  x6_5 -   b6 + 19.0 =e= 0;
   n7..          x5_7 -  x7_5 -   b7 + 19.0 =e= 0;
   n8..          x5_8 -  x8_5 - x8_9 + x9_8 - x8_10 + x10_8 - x8_11 + x11_8 - b8 + 70.0 =e= 0;
   n9..          x8_9 -  x9_8 -   b9 + 19.0 =e= 0;
   n10..        x8_10 - x10_8 -  b10 + 19.0 =e= 0;
   n11..        x8_11 - x11_8 -  b11 + 19.0 =e= 0;

Def_obj.. obj =e=
  ((b1  / ((100.0) -  b1 ) )/102.80000000000001) +
  ((b2  / ((100.0) -  b2 ) )/102.80000000000001) +
  ((b3  / (( 20.0) -  b3 ) )/102.80000000000001) +
  ((b4  / ((100.0) -  b4 ) )/102.80000000000001) +
  ((b5  / ((100.0) -  b5 ) )/102.80000000000001) +
  ((b6  / (( 20.0) -  b6 ) )/102.80000000000001) +
  ((b7  / (( 20.0) -  b7 ) )/102.80000000000001) +
  ((b8  / ((100.0) -  b8 ) )/102.80000000000001) +
  ((b9  / (( 20.0) -  b9 ) )/102.80000000000001) +
  ((b10 / (( 20.0) - b10 ) )/102.80000000000001) +
  ((b11 / (( 20.0) - b11 ) )/102.80000000000001) +
 (( x4_1 /(( 1000.0) - ((80.0) * x4_1 + (20.0) * x1_4 )))/ 6.425000000000001) +
 (( x4_1 /(( 1000.0) - ((20.0) * x4_1 + (80.0) * x1_4 )))/25.700000000000003) +
 (( x4_2 /(( 1000.0) - ((80.0) * x4_2 + (20.0) * x2_4 )))/ 6.425000000000001) +
 (( x4_2 /(( 1000.0) - ((20.0) * x4_2 + (80.0) * x2_4 )))/25.700000000000003) +
 (( x4_3 /(( 1000.0) - ((80.0) * x4_3 + (20.0) * x3_4 )))/ 6.425000000000001) +
 (( x4_3 /(( 1000.0) - ((20.0) * x4_3 + (80.0) * x3_4 )))/25.700000000000003) +
 (( x1_4 /(( 1000.0) - ((80.0) * x1_4 + (20.0) * x4_1 )))/ 6.425000000000001) +
 (( x1_4 /(( 1000.0) - ((20.0) * x1_4 + (80.0) * x4_1 )))/25.700000000000003) +
 (( x2_4 /(( 1000.0) - ((80.0) * x2_4 + (20.0) * x4_2 )))/ 6.425000000000001) +
 (( x2_4 /(( 1000.0) - ((20.0) * x2_4 + (80.0) * x4_2 )))/25.700000000000003) +
 (( x3_4 /(( 1000.0) - ((80.0) * x3_4 + (20.0) * x4_3 )))/ 6.425000000000001) +
 (( x3_4 /(( 1000.0) - ((20.0) * x3_4 + (80.0) * x4_3 )))/25.700000000000003) +
 (( x8_9 /(( 1000.0) - ((80.0) * x8_9 + (20.0) * x9_8 )))/ 6.425000000000001) +
 (( x8_9 /(( 1000.0) - ((20.0) * x8_9 + (80.0) * x9_8 )))/25.700000000000003) +
 ((x8_10 /(( 1000.0) - ((80.0) *x8_10 + (20.0) *x10_8 )))/ 6.425000000000001) +
 ((x8_10 /(( 1000.0) - ((20.0) *x8_10 + (80.0) *x10_8 )))/25.700000000000003) +
 ((x8_11 /(( 1000.0) - ((80.0) *x8_11 + (20.0) *x11_8 )))/ 6.425000000000001) +
 ((x8_11 /(( 1000.0) - ((20.0) *x8_11 + (80.0) *x11_8 )))/25.700000000000003) +
 (( x9_8 /(( 1000.0) - ((80.0) * x9_8 + (20.0) * x8_9 )))/ 6.425000000000001) +
 (( x9_8 /(( 1000.0) - ((20.0) * x9_8 + (80.0) * x8_9 )))/25.700000000000003) +
 ((x10_8 /(( 1000.0) - ((80.0) *x10_8 + (20.0) *x8_10 )))/ 6.425000000000001) +
 ((x10_8 /(( 1000.0) - ((20.0) *x10_8 + (80.0) *x8_10 )))/25.700000000000003) +
 ((x11_8 /(( 1000.0) - ((80.0) *x11_8 + (20.0) *x8_11 )))/ 6.425000000000001) +
 ((x11_8 /(( 1000.0) - ((20.0) *x11_8 + (80.0) *x8_11 )))/25.700000000000003) +
 (( x5_6 /(( 1000.0) - ((80.0) * x5_6 + (20.0) * x6_5 )))/ 6.425000000000001) +
 (( x5_6 /(( 1000.0) - ((20.0) * x5_6 + (80.0) * x6_5 )))/25.700000000000003) +
 (( x6_5 /(( 1000.0) - ((80.0) * x6_5 + (20.0) * x5_6 )))/ 6.425000000000001) +
 (( x6_5 /(( 1000.0) - ((20.0) * x6_5 + (80.0) * x5_6 )))/25.700000000000003) +
 (( x5_7 /(( 1000.0) - ((80.0) * x5_7 + (20.0) * x7_5 )))/ 6.425000000000001) +
 (( x5_7 /(( 1000.0) - ((20.0) * x5_7 + (80.0) * x7_5 )))/25.700000000000003) +
 (( x7_5 /(( 1000.0) - ((80.0) * x7_5 + (20.0) * x5_7 )))/ 6.425000000000001) +
 (( x7_5 /(( 1000.0) - ((20.0) * x7_5 + (80.0) * x5_7 )))/25.700000000000003) +
 (( x5_4 /((10000.0) - ((80.0) * x5_4 + (20.0) * x4_5 )))/ 6.425000000000001) +
 (( x5_4 /((10000.0) - ((20.0) * x5_4 + (80.0) * x4_5 )))/25.700000000000003) +
 (( x4_5 /((10000.0) - ((80.0) * x4_5 + (20.0) * x5_4 )))/ 6.425000000000001) +
 (( x4_5 /((10000.0) - ((20.0) * x4_5 + (80.0) * x5_4 )))/25.700000000000003) +
 (( x5_8 /((10000.0) - ((80.0) * x5_8 + (20.0) * x8_5 )))/ 6.425000000000001) +
 (( x5_8 /((10000.0) - ((20.0) * x5_8 + (80.0) * x8_5 )))/25.700000000000003) +
 (( x8_5 /((10000.0) - ((80.0) * x8_5 + (20.0) * x5_8 )))/ 6.425000000000001) +
 (( x8_5 /((10000.0) - ((20.0) * x8_5 + (80.0) * x5_8 )))/25.700000000000003)  ;

         b1.l    = 95.0 ;
         b2.l    = 95.0 ;
         b3.l    = 19.0 ;
         b4.l    = 70.0 ;
         b5.l    = 70.0 ;
         b6.l    = 19.0 ;
         b7.l    = 19.0 ;
         b8.l    = 70.0 ;
         b9.l    = 19.0 ;
        b10.l    = 19.0 ;
        b11.l    = 19.0 ;


         b1.up  = 99.99 ;
         b2.up  = 99.99 ;
         b3.up  = 19.99 ;
         b4.up  = 99.99 ;
         b5.up  = 99.99 ;
         b6.up  = 19.99 ;
         b7.up  = 19.99 ;
         b8.up  = 99.99 ;
         b9.up  = 19.99 ;
        b10.up  = 19.99 ;
        b11.up  = 19.99 ;


Model loadbal /all/;

Solve loadbal using nlp minimize obj;

        display x4_1.l;
        display x1_4.l;
        display x4_2.l;
        display x2_4.l;
        display x4_3.l;
        display x3_4.l;
        display x4_5.l;
        display x5_4.l;
        display x5_6.l;
        display x6_5.l;
        display x5_7.l;
        display x7_5.l;
        display x5_8.l;
        display x8_5.l;
        display x8_9.l;
        display x9_8.l;
        display x8_10.l;
        display x10_8.l;
        display x8_11.l;
        display x11_8.l;
        display b1.l;
        display b2.l;
        display b3.l;
        display b4.l;
        display b5.l;
        display b6.l;
        display b7.l;
        display b8.l;
        display b9.l;
        display b10.l;
        display b11.l;
        display obj.l;