Tag: Programação matemática

Port in a storm

Here’s follow the solution (aimms) to the challenge Port in a Storm (puzzleor).

We need to create the sets docks and groups.

The distances, given in the spreadsheet:

Tip: in the definition, we can fill the matrix with the values.

Another tip: it is easy to exchange indexes. Make sure it does not happen.

The variable has range integer in dimensions (g,d)

Contraints: max docks and the minimum we have to distribute from the groups

Next, the mathematical programming.

We’re minimizing.

FO is the sum of variables times distances.

In the main execution, we write solve port (name of the mathematical programming);

Type F6 to run:

Result is FO = 31, the same as in the excel.

Note that the assignment is different from excel – in this case there’s more than one solution.

The zip file here contains the formulation. And here, the Excel solver version.

Below transcribed the full formulation.

MAIN MODEL Main_Port_in_a_storm

DECLARATION SECTION

SET:

   identifier   :  Docks

   subset of    :  Integers

   index        :  d

   definition   :  {1..3} ;



SET:

   identifier   :  Groups

   subset of    :  Integers

   index        :  g

   definition   :  {1..3} ;



PARAMETER:

   identifier   :  distances

   index domain :  (g,d)

   definition   :  data { ( 1, 1 ) : 1,  ( 1, 2 ) : 3,  ( 1, 3 ) : 2,  ( 2, 1 ) : 2,  ( 2, 2 ) : 2,  ( 2, 3 ) : 1,  ( 3, 1 ) : 3,  ( 3, 2 ) : 2,  ( 3, 3 ) : 1 } ;



PARAMETER:

   identifier   :  max_docks

   index domain :  d

   definition   :  data { 1 : 4,  2 : 7,  3 : 9 } ;



PARAMETER:

   identifier   :  min_groups

   index domain :  (g)

   definition   :  data { 1 : 8,  2 : 5,  3 : 7 } ;



VARIABLE:

   identifier   :  aloc

   index domain :  (g,d)

   range        :  integer ;



VARIABLE:

   identifier   :  fo

   range        :  free

   definition   :  sum((g,d),aloc(g, d)*distances(g, d)) ;



CONSTRAINT:

   identifier   :  c_docks

   index domain :  d

   definition   :  sum(g, aloc(g,d))<=max_docks(d) ;



CONSTRAINT:

   identifier   :  c_groups

   index domain :  (g)

   definition   :  sum(d, aloc(g,d))>=min_groups(g) ;



MATHEMATICAL PROGRAM:

   identifier   :  Port

   objective    :  fo

   direction    :  minimize

   constraints  :  AllConstraints

   variables    :  AllVariables

   type         :  Automatic ;

ENDSECTION ;

PROCEDURE

identifier :  MainInitialization

ENDPROCEDURE ;

PROCEDURE

identifier :  MainExecution

body       : 

  solve port;

ENDPROCEDURE ;

PROCEDURE

identifier :  MainTermination

body       : 

  return DataManagementExit();

ENDPROCEDURE ;

ENDMODEL Main_Port_in_a_storm ;

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