GNU MathProg

Nota: Esta página es la traducción (en curso) al español de http://lpsolve.sourceforge.net/5.5/MathProg.htm

GNU MathProg es un lenguaje de modelización para la descripción de modelos de programación matemática lineal. Un modelo escrito el lenguaje GNU MathProg consiste en un conjunto de instrucciones y bloques de datos construidos por el usuario.

Véase http://gnuwin32.sourceforge.net/downlinks/glpk-doc-zip.php para una descripción completa de este lenguaje de modelado.

GNU MathProg is part of the GLPK solver. See http://www.gnu.org/software/glpk/glpk.html and http://gnuwin32.sourceforge.net/packages/glpk.htm for the homepage of it. Note that MathProg is a subset of the AMPL modeling language. See Using lpsolve from AMPL. The XLI used by lp_solve to read these models is derived from this code.

lp_solve can read/write and solve these MathProg models directly via the xli_MathProg XLI driver (see External Language Interfaces). It reads such a model in above format and can solve it then.

For example:

lp_solve -rxli xli_MathProg Diet1.mod

This gives as result:

Value of objective function: 88.2

Actual values of the variables: Buy[BEEF] 0 Buy[CHK] 0 Buy[FISH] 0 Buy[HAM] 0 Buy[MCH] 46.6667 Buy[MTL] 0 Buy[SPG] 0 Buy[TUR] 0

MathProg has also the possibility to have the model and data in two separate files. lp_solve can handle this also. For example:

lp_solve -rxli xli_MathProg diet.mod -rxlidata diet.dat

This gives as result:

Value of objective function: 88.2

Actual values of the variables: Buy[BEEF] 0 Buy[CHK] 0 Buy[FISH] 0 Buy[HAM] 0 Buy[MCH] 46.6667 Buy[MTL] 0 Buy[SPG] 0 Buy[TUR] 0

Generating MathProg models

The XLI can also create a MathProg model, however it doesn't use the strength of the language. Constraints are written out line per line. But it can be a starter. For example:

lp_solve model.lp -wxli xli_MathProg model.mod

This gives as model.mod:

/* Variable definitions */ var x >= 0; var y >= 0;

/* Objective function */ maximize obj: +143*x +60*y;

/* Constraints */ R1: +120*x +210*y ⇐ 15000; R2: +110*x +30*y ⇐ 4000; R3: +x +y ⇐ 75;

API

Use the lpsolve API call read_XLI to read a model and write_XLI to write a model. See also External Language Interfaces. IDE

Also from within the IDE, this XLI can be used. However, some entries must be added in LpSolveIDE.ini (in the folder where the IDE is installed).

In the [XLI] section the following must be added:

lib1=xli_MathProg

And a new section for the MathProg XLI must also be added:

[xli_MathProg] extension=.mod language=MATHPROG

Then make sure that the xli_MathProg.dll is available for the IDE. This must be done by placing this dll in the IDE folder or in the Windows system32 folder. Example models/data Diet1.mod

set NUTR; set FOOD;

param cost {FOOD} > 0; param f_min {FOOD} >= 0; param f_max {j in FOOD} >= f_min[j];

param n_min {NUTR} >= 0; param n_max {i in NUTR} >= n_min[i];

param amt {NUTR,FOOD} >= 0;

var Buy {j in FOOD} >= f_min[j], ⇐ f_max[j];

minimize total_cost: sum {j in FOOD} cost[j] * Buy[j];

subject to diet {i in NUTR}:

 n_min[i] <= sum {j in FOOD} amt[i,j] * Buy[j] <= n_max[i];

data;

set NUTR := A B1 B2 C ; set FOOD := BEEF CHK FISH HAM MCH MTL SPG TUR ;

param: cost f_min f_max :=

BEEF   3.19    0     100
CHK    2.59    0     100
FISH   2.29    0     100
HAM    2.89    0     100
MCH    1.89    0     100
MTL    1.99    0     100
SPG    1.99    0     100
TUR    2.49    0     100 ;

param: n_min n_max :=

 A      700   10000
 C      700   10000
 B1     700   10000
 B2     700   10000 ;

param amt (tr):

         A    C   B1   B2 :=
 BEEF   60   20   10   15
 CHK     8    0   20   20
 FISH    8   10   15   10
 HAM    40   40   35   10
 MCH    15   35   15   15
 MTL    70   30   15   15
 SPG    25   50   25   15
 TUR    60   20   15   10 ;

end;

diet.mod

set NUTR; set FOOD;

param cost {FOOD} > 0; param f_min {FOOD} >= 0; param f_max {j in FOOD} >= f_min[j];

param n_min {NUTR} >= 0; param n_max {i in NUTR} >= n_min[i];

param amt {NUTR,FOOD} >= 0;

var Buy {j in FOOD} >= f_min[j], ⇐ f_max[j];

minimize total_cost: sum {j in FOOD} cost[j] * Buy[j];

subject to diet {i in NUTR}:

 n_min[i] <= sum {j in FOOD} amt[i,j] * Buy[j] <= n_max[i];

diet.dat

set NUTR := A B1 B2 C ; set FOOD := BEEF CHK FISH HAM MCH MTL SPG TUR ;

param: cost f_min f_max :=

BEEF   3.19    0     100
CHK    2.59    0     100
FISH   2.29    0     100
HAM    2.89    0     100
MCH    1.89    0     100
MTL    1.99    0     100
SPG    1.99    0     100
TUR    2.49    0     100 ;

param: n_min n_max :=

 A      700   10000
 C      700   10000
 B1     700   10000
 B2     700   10000 ;

param amt (tr):

         A    C   B1   B2 :=
 BEEF   60   20   10   15
 CHK     8    0   20   20
 FISH    8   10   15   10
 HAM    40   40   35   10
 MCH    15   35   15   15
 MTL    70   30   15   15
 SPG    25   50   25   15
 TUR    60   20   15   10 ;

model.lp

/* model.lp */

max: 143 x + 60 y;

120 x + 210 y ⇐ 15000; 110 x + 30 y ⇐ 4000; x + y ⇐ 75;