pool.gms : Pooling problem

Description

This model presents a number of pooling problems from the
literature in a unified framework. It represents the
pq-formulation as of the pooling problem described in:

M. Tawarmalani and N. V. Sahinidis, in "Convexification
and Global Optimization of the Pooling Problem", May 2002,
Mathematical Programming, submitted.

All 14 problems have known global solutions.

Summary reports across all 14 problems allow quick assessment
of local and global solution methods. Also note the importance
of good starting points for local solvers.

This model and the generic pq-formulation has been provided
by Mohit Tawarmalani, August 2002.


References

  • Haverly, C A, Studies of the Behavior of Recursion for the Pooling Problem. ACM SIGMAP Bull 25 (1978), 19-28.
  • Tawarmalani, M, and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer, Nonconvex Optimization and Its Applications, 2002.
  • Haverly, C A, Behaviour of recursion model - More studies. ACM SIGMAP Bulletin 26 (1979), 22-28.
  • Foulds, L R, Haugland, D, and Jornsten, K, A bilinear approach to the pooling problem. Optimization 24 (1992), 165-180.
  • Ben-Tal, A, Eiger, G, and Gershovitz, V, Global Minimization by Reducing the Duality Gap. Mathematical Programming 63, 1 (1994), 193-212.
  • Audet, C, Brimberg, J, Hansen, P, and Mladenovic, N, Pooling problem: Alternate formulations and solution methods. Tech. rep., Les Cashiers Du GERAD G-2000-23, Montreal, 2000.
  • Adhya, N, Tawarmalani, M, and Sahinidis, N, Global optimization of the pooling problem. Industrial and Engineering Chemistry 38 (1999), 1956–1972.

Large Model of Type : NLP


Category : GAMS Model library


Main file : pool.gms   includes :  poolmod.inc

$title The Pooling Problem (POOL,SEQ=254)

$onText
This model presents a number of pooling problems from the
literature in a unified framework. It represents the
pq-formulation as of the pooling problem described in:

M. Tawarmalani and N. V. Sahinidis, in "Convexification
and Global Optimization of the Pooling Problem", May 2002,
Mathematical Programming, submitted.

All 14 problems have known global solutions.

Summary reports across all 14 problems allow quick assessment
of local and global solution methods. Also note the importance
of good starting points for local solvers.

This model and the generic pq-formulation has been provided
by Mohit Tawarmalani, August 2002.


References:

Tawarmalani, M. and Sahinidis, N., Convexification and Global
Optimization in Continuous and Mixed-Integer Nonlinear
Programming: Theory, Algorithms, Software, and Applications,
Kluwer, 2002.

Adhya, N. and Tawarmalani, M. and Sahinidis, N. V.,
"Global optimization of the pooling problem", Industrial and
Engineering Chemistry, 38, pp. 1956-1972, 1999.

C. Audet and J. Brimberg and P. Hansen and N. Mladenovic,
"Pooling problem: Alternate formulations and solution methods",
Technical Report Les Cashiers Du GERAD G-2000-23, Montreal,
2000.

Ben-Tal, A and Eiger, G and Gershovitz, V, "Global Minimization
by Reducing the Duality Gap", Mathematical Programming, 63,
pp. 193-212, 1994.

Foulds, L. R. and Haugland, D. and Jornsten, K., "A bilinear
approach to the pooling problem", Optimization, 24, pp. 165-180,
1992.

Haverly, C A, Studies of the Behavior of Recursion for the
Pooling Problem, ACM SIGMAP Bull, 25, pp. 19-28, 1978.

Haverly, C. A., "Behaviour of recursion model - More studies",
ACM SIGMAP Bulletin, 26, pp. 22-28, 1979.

Keywords: nonlinear programming, pooling problem, chemical engineering, global
          optimization, nonlinear network flow problem
$offText

$include poolmod.inc
$eolCom //

Set
   comp_ 'components and raw materials' / c1*c32 /
   pro_  'products'                     / p1*p16 /
   qual_ 'qualities'                    / q1*q10 /
   pool_ 'pools'                        / o1*o10 /
   case  'case index'
          / haverly1*haverly3, foulds2*foulds5, bental4*bental5, rt2, adhya1*adhya4 /
   labels / lo 'lower bound', up 'upper bound', price /;

Parameter sol(case) 'global solution' / haverly1         -400
                                        haverly2         -600
                                        haverly3         -750
                                        foulds2         -1100
                                        foulds3*foulds5    -8
                                        bental4          -450
                                        bental5         -3500
                                        rt2             -4391.8258928
                                        adhya1*adhya2    -549.80305
                                        adhya3           -561.044687
                                        adhya4           -877.64574   /;

Table ComponentData(case,comp_,labels)
                lo    up      price
   adhya1.c1     0    75          7
   adhya1.c2     0    75          3
   adhya1.c3     0    75          2
   adhya1.c4     0    75         10
   adhya1.c5     0    75          5
   adhya2.c1     0    75          7
   adhya2.c2     0    75          3
   adhya2.c3     0    75          2
   adhya2.c4     0    75         10
   adhya2.c5     0    75          5
   adhya3.c1     0    75          7
   adhya3.c2     0    75          3
   adhya3.c3     0    75          2
   adhya3.c4     0    75         10
   adhya3.c5     0    75          5
   adhya3.c6     0    75          5
   adhya3.c7     0    75          9
   adhya3.c8     0    75         11
   adhya4.c1     0    85         15
   adhya4.c2     0    85          7
   adhya4.c3     0    85          4
   adhya4.c4     0    85          5
   adhya4.c5     0    85          6
   adhya4.c6     0    85          3
   adhya4.c7     0    85          5
   adhya4.c8     0    85          5
   rt2.c1        0    60.9756    49.2
   rt2.c2        0   161.29      62
   rt2.c3        0     5        300
   bental4.c1    0   300          6
   bental4.c2    0    50         15
   bental4.c3    0   300         16
   bental4.c4    0   300         10
   bental5.c1    0   600          6
   bental5.c2    0   600         16
   bental5.c3    0   600         15
   bental5.c4    0   600         12
   bental5.c5    0   600          6
   bental5.c6    0   600         16
   bental5.c7    0   600         15
   bental5.c8    0   600         12
   bental5.c9    0   600          6
   bental5.c10   0   600         16
   bental5.c11   0   600         15
   bental5.c12   0   600         12
   bental5.c13   0   600         10
   haverly1.c1   0   300          6
   haverly1.c2   0   300         16
   haverly1.c3   0   300         10
   haverly2.c1   0   800          6
   haverly2.c2   0   800         16
   haverly2.c3   0   800         10
   haverly3.c1   0   300          6
   haverly3.c2   0   300         13
   haverly3.c3   0   300         10
   foulds2.c1    0   600          6
   foulds2.c2    0   600         16
   foulds2.c3    0   600         10
   foulds2.c4    0   600          3
   foulds2.c5    0   600         13
   foulds2.c6    0   600          7
   foulds3.c1    0    16         20
   foulds3.c2    0    16         19
   foulds3.c3    0    16         18
   foulds3.c4    0    16         17
   foulds3.c5    0    16         19
   foulds3.c6    0    16         18
   foulds3.c7    0    16         17
   foulds3.c8    0    16         16
   foulds3.c9    0    16         18
   foulds3.c10   0    16         17
   foulds3.c11   0    16         16
   foulds3.c12   0    16         15
   foulds3.c13   0    16         17
   foulds3.c14   0    16         16
   foulds3.c15   0    16         15
   foulds3.c16   0    16         14
   foulds3.c17   0    16         16
   foulds3.c18   0    16         15
   foulds3.c19   0    16         14
   foulds3.c20   0    16         13
   foulds3.c21   0    16         15
   foulds3.c22   0    16         14
   foulds3.c23   0    16         13
   foulds3.c24   0    16         12
   foulds3.c25   0    16         14
   foulds3.c26   0    16         13
   foulds3.c27   0    16         12
   foulds3.c28   0    16         11
   foulds3.c29   0    16         13
   foulds3.c30   0    16         12
   foulds3.c31   0    16         11
   foulds3.c32   0    16         10
   foulds4.c1    0    16         20
   foulds4.c2    0    16         19
   foulds4.c3    0    16         18
   foulds4.c4    0    16         17
   foulds4.c5    0    16         16
   foulds4.c6    0    16         15
   foulds4.c7    0    16         14
   foulds4.c8    0    16         13
   foulds4.c9    0    16         12
   foulds4.c10   0    16         11
   foulds4.c11   0    16         10
   foulds5.c1    0    16         20
   foulds5.c2    0    16         19
   foulds5.c3    0    16         18
   foulds5.c4    0    16         17
   foulds5.c5    0    16         16
   foulds5.c6    0    16         15
   foulds5.c7    0    16         14
   foulds5.c8    0    16         13
   foulds5.c9    0    16         12
   foulds5.c10   0    16         11
   foulds5.c11   0    16         10;

Table ComponentQuality(case,comp_,qual_)
                   q1     q2    q3     q4     q5    q6
   adhya1.c1        1      6     4    0.5
   adhya1.c2        4      1     3      2
   adhya1.c3        4    5.5     3    0.9
   adhya1.c4        3      3     3      1
   adhya1.c5        1    2.7     4    1.6
   adhya2.c1        1      6     4    0.5      5     9
   adhya2.c2        4      1     3      2      4     4
   adhya2.c3        4    5.5     3    0.9      7    10
   adhya2.c4        3      3     3      1      3     4
   adhya2.c5        1    2.7     4    1.6      3     7
   adhya3.c1        1      6     4    0.5      5     9
   adhya3.c2        4      1     3      2      4     4
   adhya3.c3        4    5.5     3    0.9      7    10
   adhya3.c4        3      3     3      1      3     4
   adhya3.c5        1    2.7     4    1.6      3     7
   adhya3.c6      1.8    2.7     4    3.5    6.1     3
   adhya3.c7        5      1   1.7    2.9    3.5   2.9
   adhya3.c8        3      3     3      1      5     2
   adhya4.c1      0.5    1.9   1.3      1
   adhya4.c2      1.4    1.8   1.7    1.6
   adhya4.c3      1.2    1.9   1.4    1.4
   adhya4.c4      1.5    1.2   1.7    1.3
   adhya4.c5      1.6    1.8   1.6      2
   adhya4.c6      1.2    1.1   1.4      2
   adhya4.c7      1.5    1.5   1.5    1.5
   adhya4.c8      1.4    1.6   1.2    1.6
   rt2.c1         0.82   3     99.2   90.5
   rt2.c2         0.62   0     87.9   83.5
   rt2.c3         0.75   0     114    98.7
   bental4.c1      3
   bental4.c2      1
   bental4.c3      1
   bental4.c4      2
   bental5.c1      3       1
   bental5.c2      1       3
   bental5.c3    1.2       5
   bental5.c4    1.5     2.5
   bental5.c5      3       1
   bental5.c6      1       3
   bental5.c7    1.2       5
   bental5.c8    1.5     2.5
   bental5.c9      3       1
   bental5.c10     1       3
   bental5.c11   1.2       5
   bental5.c12   1.5     2.5
   bental5.c13     2     2.5
   haverly1.c1     3
   haverly1.c2     1
   haverly1.c3     2
   haverly2.c1     3
   haverly2.c2     1
   haverly2.c3     2
   haverly3.c1     3
   haverly3.c2     1
   haverly3.c3     2
   foulds2.c1      3
   foulds2.c2      1
   foulds2.c3      2
   foulds2.c4    3.5
   foulds2.c5    1.5
   foulds2.c6    2.5
   foulds3.c1    1
   foulds3.c2    1.1
   foulds3.c3    1.2
   foulds3.c4    1.3
   foulds3.c5    1.1
   foulds3.c6    1.2
   foulds3.c7    1.3
   foulds3.c8    1.4
   foulds3.c9    1.2
   foulds3.c10   1.3
   foulds3.c11   1.4
   foulds3.c12   1.5
   foulds3.c13   1.3
   foulds3.c14   1.4
   foulds3.c15   1.5
   foulds3.c16   1.6
   foulds3.c17   1.4
   foulds3.c18   1.5
   foulds3.c19   1.6
   foulds3.c20   1.7
   foulds3.c21   1.5
   foulds3.c22   1.6
   foulds3.c23   1.7
   foulds3.c24   1.8
   foulds3.c25   1.6
   foulds3.c26   1.7
   foulds3.c27   1.8
   foulds3.c28   1.9
   foulds3.c29   1.7
   foulds3.c30   1.8
   foulds3.c31   1.9
   foulds3.c32   2
   foulds4.c1    1
   foulds4.c2    1.1
   foulds4.c3    1.2
   foulds4.c4    1.3
   foulds4.c5    1.4
   foulds4.c6    1.5
   foulds4.c7    1.6
   foulds4.c8    1.7
   foulds4.c9    1.8
   foulds4.c10   1.9
   foulds4.c11   2
   foulds5.c1    1
   foulds5.c2    1.1
   foulds5.c3    1.2
   foulds5.c4    1.3
   foulds5.c5    1.4
   foulds5.c6    1.5
   foulds5.c7    1.6
   foulds5.c8    1.7
   foulds5.c9    1.8
   foulds5.c10   1.9
   foulds5.c11   2  ;

Table ProductData(case,pro_,labels)
                lo    up   price
   adhya1.p1     0    10    16
   adhya1.p2     0    25    25
   adhya1.p3     0    30    15
   adhya1.p4     0    10    10
   adhya2.p1     0    10    16
   adhya2.p2     0    25    25
   adhya2.p3     0    30    15
   adhya2.p4     0    10    10
   adhya3.p1     0    10    16
   adhya3.p2     0    25    25
   adhya3.p3     0    30    15
   adhya3.p4     0    10    10
   adhya4.p1     0    15    10
   adhya4.p2     0    25    25
   adhya4.p3     0    10    30
   adhya4.p4     0    20     6
   adhya4.p5     0    15    10
   rt2.p1        5   300   190
   rt2.p2        5   300   230
   rt2.p3        5   300   150
   bental4.p1    0   100     9
   bental4.p2    0   200    15
   bental5.p1    0   100    18
   bental5.p2    0   200    15
   bental5.p3    0   100    19
   bental5.p4    0   100    16
   bental5.p5    0   100    14
   haverly1.p1   0   100     9
   haverly1.p2   0   200    15
   haverly2.p1   0   600     9
   haverly2.p2   0   200    15
   haverly3.p1   0   100     9
   haverly3.p2   0   200    15
   foulds2.p1    0   100     9
   foulds2.p2    0   200    15
   foulds2.p3    0   100     6
   foulds2.p4    0   200    12
   foulds3.p1    0     1    20
   foulds3.p2    0     1    19.5
   foulds3.p3    0     1    19
   foulds3.p4    0     1    18.5
   foulds3.p5    0     1    18
   foulds3.p6    0     1    17.5
   foulds3.p7    0     1    17
   foulds3.p8    0     1    16.5
   foulds3.p9    0     1    16
   foulds3.p10   0     1    15.5
   foulds3.p11   0     1    15
   foulds3.p12   0     1    14.5
   foulds3.p13   0     1    14
   foulds3.p14   0     1    13.5
   foulds3.p15   0     1    13
   foulds3.p16   0     1    12.5
   foulds4.p1    0     1    20
   foulds4.p2    0     1    19.5
   foulds4.p3    0     1    19
   foulds4.p4    0     1    18.5
   foulds4.p5    0     1    18
   foulds4.p6    0     1    17.5
   foulds4.p7    0     1    17
   foulds4.p8    0     1    16.5
   foulds4.p9    0     1    16
   foulds4.p10   0     1    15.5
   foulds4.p11   0     1    15
   foulds4.p12   0     1    14.5
   foulds4.p13   0     1    14
   foulds4.p14   0     1    13.5
   foulds4.p15   0     1    13
   foulds4.p16   0     1    12.5
   foulds5.p1    0     1    20
   foulds5.p2    0     1    19.5
   foulds5.p3    0     1    19
   foulds5.p4    0     1    18.5
   foulds5.p5    0     1    18
   foulds5.p6    0     1    17.5
   foulds5.p7    0     1    17
   foulds5.p8    0     1    16.5
   foulds5.p9    0     1    16
   foulds5.p10   0     1    15.5
   foulds5.p11   0     1    15
   foulds5.p12   0     1    14.5
   foulds5.p13   0     1    14
   foulds5.p14   0     1    13.5
   foulds5.p15   0     1    13
   foulds5.p16   0     1    12.5;

Table ProductQualityLower(case,pro_,qual_)
              q1  q2  q3   q4  q5  q6
   rt2.p1   0.74   0  95   85
   rt2.p2   0.74   0  96   88
   rt2.p3   0.74   0  91 83.5        ;

Table ProductQualityUpper(case,pro_,qual_)
                   q1     q2      q3      q4   q5    q6
   adhya1.p1        3      3    3.25    0.75
   adhya1.p2        4    2.5    3.5     1.5
   adhya1.p3      1.5    5.5    3.9     0.8
   adhya1.p4        3      4      4     1.8
   adhya2.p1        3      3    3.25    0.75    6     5
   adhya2.p2        4    2.5    3.5     1.5     7     6
   adhya2.p3      1.5    5.5    3.9     0.8     7     6
   adhya2.p4        3      4      4     1.8     8     6
   adhya3.p1        3      3    3.25    0.75    6     5
   adhya3.p2        4    2.5    3.5     1.5     7     6
   adhya3.p3      1.5    5.5    3.9     0.8     7     6
   adhya3.p4        3      4      4     1.8     8     6
   adhya4.p1      1.2    1.7    1.4     1.7
   adhya4.p2      1.4    1.3    1.8     1.4
   adhya4.p3      1.3    1.3    1.9     1.9
   adhya4.p4      1.2    1.1    1.7     1.6
   adhya4.p5      1.6    1.9      2     2.5
   rt2.p1        0.79    3      114    98.7
   rt2.p2        0.79    0.9    114    98.7
   rt2.p3        0.79    3      114    98.7
   bental4.p1     2.5
   bental4.p2     1.5
   bental5.p1     2.5    2
   bental5.p2     1.5    2.5
   bental5.p3       2    2.6
   bental5.p4       2    2
   bental5.p5       2    2
   haverly1.p1    2.5
   haverly1.p2    1.5
   haverly2.p1    2.5
   haverly2.p2    1.5
   haverly3.p1    2.5
   haverly3.p2    1.5
   foulds2.p1     2.5
   foulds2.p2     1.5
   foulds2.p3     3
   foulds2.p4     2
   foulds3.p1     1.05
   foulds3.p2     1.1
   foulds3.p3     1.15
   foulds3.p4     1.2
   foulds3.p5     1.25
   foulds3.p6     1.3
   foulds3.p7     1.35
   foulds3.p8     1.4
   foulds3.p9     1.45
   foulds3.p10    1.5
   foulds3.p11    1.55
   foulds3.p12    1.6
   foulds3.p13    1.65
   foulds3.p14    1.7
   foulds3.p15    1.75
   foulds3.p16    1.8
   foulds4.p1     1.05
   foulds4.p2     1.1
   foulds4.p3     1.15
   foulds4.p4     1.2
   foulds4.p5     1.25
   foulds4.p6     1.3
   foulds4.p7     1.35
   foulds4.p8     1.4
   foulds4.p9     1.45
   foulds4.p10    1.5
   foulds4.p11    1.55
   foulds4.p12    1.6
   foulds4.p13    1.65
   foulds4.p14    1.7
   foulds4.p15    1.75
   foulds4.p16    1.8
   foulds5.p1     1.05
   foulds5.p2     1.1
   foulds5.p3     1.15
   foulds5.p4     1.2
   foulds5.p5     1.25
   foulds5.p6     1.3
   foulds5.p7     1.35
   foulds5.p8     1.4
   foulds5.p9     1.45
   foulds5.p10    1.5
   foulds5.p11    1.55
   foulds5.p12    1.6
   foulds5.p13    1.65
   foulds5.p14    1.7
   foulds5.p15    1.75
   foulds5.p16    1.8 ;

Table Poolsize(case,pool_)
                o1     o2    o3   o4   o5   o6   o7   o8
   adhya1       75     75
   adhya2       75     75
   adhya3       75     75    75
   adhya4       85     85
   rt2        12.5   17.5
   bental4     300
   bental5     600    600   600
   haverly1    300
   haverly2    800
   haverly3    300
   foulds2     600    600
   foulds3      16     16    16   16   16   16   16   16
   foulds4      16     16    16   16   16   16   16   16
   foulds5      16     16    16   16   16   16   16   16;

Table ComponentPoolFraction(case,comp_,pool_) 'upper bound on q'
                o1   o2   o3   o4   o5   o6   o7   o8
   adhya1.c1     1
   adhya1.c2     1
   adhya1.c3          1
   adhya1.c4          1
   adhya1.c5          1
   adhya2.c1     1
   adhya2.c2     1
   adhya2.c3          1
   adhya2.c4          1
   adhya2.c5          1
   adhya3.c1     1
   adhya3.c2     1
   adhya3.c3          1
   adhya3.c4          1
   adhya3.c5          1
   adhya3.c6               1
   adhya3.c7               1
   adhya3.c8               1
   adhya4.c1     1
   adhya4.c2     1
   adhya4.c3     1
   adhya4.c4     1
   adhya4.c5          1
   adhya4.c6          1
   adhya4.c7          1
   adhya4.c8          1
   rt2.c1        1    1
   rt2.c2        1    1
   rt2.c3        1    1
   bental4.c1    1
   bental4.c2    1
   bental4.c3    1
   bental4.c4
   bental5.c1    1
   bental5.c2    1
   bental5.c3    1
   bental5.c4    1
   bental5.c5         1
   bental5.c6         1
   bental5.c7         1
   bental5.c8         1
   bental5.c9              1
   bental5.c10             1
   bental5.c11             1
   bental5.c12             1
   bental5.c13
   haverly1.c1   1
   haverly1.c2   1
   haverly1.c3
   haverly2.c1   1
   haverly2.c2   1
   haverly2.c3   0
   haverly3.c1   1
   haverly3.c2   1
   haverly3.c3
   foulds2.c1    1
   foulds2.c2    1
   foulds2.c3
   foulds2.c4         1
   foulds2.c5         1
   foulds2.c6

*               o1   o2   o3   o4   o5   o6   o7   o8
   foulds3.c1    1
   foulds3.c2    1
   foulds3.c3    1
   foulds3.c4    1
   foulds3.c5         1
   foulds3.c6         1
   foulds3.c7         1
   foulds3.c8         1
   foulds3.c9              1
   foulds3.c10             1
   foulds3.c11             1
   foulds3.c12             1
   foulds3.c13                  1
   foulds3.c14                  1
   foulds3.c15                  1
   foulds3.c16                  1
   foulds3.c17                       1
   foulds3.c18                       1
   foulds3.c19                       1
   foulds3.c20                       1
   foulds3.c21                            1
   foulds3.c22                            1
   foulds3.c23                            1
   foulds3.c24                            1
   foulds3.c25                                 1
   foulds3.c26                                 1
   foulds3.c27                                 1
   foulds3.c28                                 1
   foulds3.c29                                      1
   foulds3.c30                                      1
   foulds3.c31                                      1
   foulds3.c32                                      1

*               o1   o2   o3   o4   o5   o6   o7   o8
   foulds4.c1    1
   foulds4.c2         1    1
   foulds4.c3              1    1    1
   foulds4.c4    1              1         1    1
   foulds4.c5         1    1         1              1
   foulds4.c6              1    1    1    1
   foulds4.c7    1              1         1    1
   foulds4.c8         1              1         1    1
   foulds4.c9                             1    1    1
   foulds4.c10   1                                  1
   foulds4.c11        1

*               o1   o2   o3   o4   o5   o6   o7   o8
   foulds5.c1    1                             1
   foulds5.c2    1         1                   1
   foulds5.c3    1         1                   1
   foulds5.c4    1         1         1         1
   foulds5.c5              1         1              1
   foulds5.c6                        1              1
   foulds5.c7                   1    1              1
   foulds5.c8         1         1         1         1
   foulds5.c9         1         1         1
   foulds5.c10        1         1         1
   foulds5.c11        1                   1          ;

Table PoolProductBound(case,pool_,pro_) 'upper bound on y'
                     p1     p2     p3    p4    p5  p6*p16
   adhya1.o1         10     25     30    10
   adhya1.o2         30     10     10    25
   adhya2.o1         10     25     30    10
   adhya2.o2         30     10     10    25
   adhya3.o1         10     25     30    10
   adhya3.o2         10     10     25    30
   adhya3.o3         30     10     10    25
   adhya4.o1         15     25     10    20    15
   adhya4.o2         10     20     15    15    25
   rt2.o1          12.5   12.5   12.5
   rt2.o2          17.5   17.5   17.5
   bental4.o1       100    200
   bental5.o1       100    200    100   100   100
   bental5.o2       100    100    100   200   100
   bental5.o3       200    100    100   100   100
   haverly1.o1      100    200
   haverly2.o1      600    200
   haverly3.o1      100    200
   foulds2.o1*o2    100    200    100   200
   foulds3.o1*o8     16     16     16    16    16      16
   foulds4.o1*o8     16     16     16    16    16      16
   foulds5.o1*o8     16     16     16    16    16      16;

Table ComponentProductBound(case,comp_,pro_) 'upper bound on z'
                     p1    p2       p3    p4    p5
   rt2.c1             0   7.5        0
   rt2.c2        161.29     0   161.29
   rt2.c3           7.5     0        0
   bental4.c4       100   200
   bental5.c13      100   200      100   100   100
   haverly1.c3      100   200
   haverly2.c3      600   200
   haverly3.c3      100   200
   foulds2.c3       100   200      100   200
   foulds2.c6       100   200      100   200      ;

Parameter
   rep1(case,*) 'problem characteristics'
   rep2(case,*) 'solution summary';

option optCr = 0.0, optCa = 1e-6;

loop(case,
   // extract domains for current problem
   comp(comp_) = ComponentData(case,comp_,'up');
   qual(qual_) = sum(comp_$ComponentQuality(case,comp_,qual_), 1);
   pool(pool_) = PoolSize(case,pool_);
   pro (pro_ ) = ProductData(case,pro_,'up');

   // extract data
   cl(comp)         = ComponentData(case,comp,'lo');
   cu(comp)         = ComponentData(case,comp,'up');
   cprice(comp)     = ComponentData(case,comp,'price');
   cqual(comp,qual) = ComponentQuality(case,comp,qual);
   prl(pro)         = ProductData(case,pro,'lo');
   pru(pro)         = ProductData(case,pro,'up');
   pprice(pro)      = ProductData(case,pro,'price');
   pqlbd(pro,qual)  = ProductQualityLower(case,pro,qual);
   pqubd(pro,qual)  = ProductQualityUpper(case,pro,qual);
   psize(pool)      = PoolSize(case,pool);

   // find domain restrictions
   y_dom(pool,pro)       = PoolProductBound(case,pool,pro);
   z_dom(comp,pro)       = ComponentProductBound(case,comp,pro);
   q_dom(comp,pool)      = ComponentPoolFraction(case,comp,pool);
   qy_dom(comp,pool,pro) = q_dom(comp,pool)*y_dom(pool,pro);

   option clear = q,          clear = y,       clear = z  // start from same default point
          clear = obj,        clear = clower,  clear = cupper
          clear = pszrlt,     clear = plower,  clear = pupper
          clear = pqlower,    clear = pqupper, clear = fraction
          clear = extensions;

   // set variable bounds
   q.up(comp,pool) = ComponentPoolFraction(case,comp,pool);
   y.up(pool,pro)  = PoolProductBound(case,pool,pro);
   z.up(comp,pro)  = ComponentProductBound(case,comp,pro);

   // loacl solvers need a better starting point than 0*0
   // anything better than 0 will do, without this starting
   // point, most local solvers will give very poor results or
   // get stuck at a local stationary point
   q.l(comp,pool) = 0.1;
   y.l(pool,pro)  = 0.1;
   z.l(comp,pro)  = 0.1;

   solve poolprob minimizing cost using nlp;

   rep1(case, 'RawMat')    = card(comp);
   rep1(case, 'Products')  = card(pro);
   rep1(case, 'Qualities') = card(qual);
   rep1(case, 'Pools')     = card(pool);
   rep1(case, 'Equs')      = poolprob.numEqu;
   rep1(case, 'Vars')      = poolprob.numVar;
   rep1(case, 'NZ')        = poolprob.numNZ;
   rep2(case, 'Solstat')   = poolprob.solveStat;
   rep2(case, 'Modstat')   = poolprob.modelStat;
   rep2(case, 'Obj')       = poolprob.objVal;
   rep2(case, 'CPU')       = poolprob.resUsd;
);
rep2(case,'GlobalObj') = sol(case);
rep2(case,'optcr')$(abs(sol(case)) > 1e-6)= round(abs((rep2(case,'Obj') - sol(case))/sol(case)),6);
rep2(case,'optca')$(abs(sol(case)) > 1e-6)= round(abs(rep2(case,'Obj')  - sol(case)),6);

display rep1, rep2;