Originally posted by: Treee

Hello,

i am trying to find the optimal solution of my minimizing problem.

I have a distance matrix which gives the distances to the "places"(in a storage yard) in the matrix. My goal is to put for example 4 containers to the storage yard at minimum distance costs. The positions should be shown in the matrix "placed" and set to 1.

my .dat so far ; 

AmountOfContainers = 4;
Rows = 4;
Columns = 5; 
Distance = [ 
       [ 1, 7, 13, 19, 25 ], 
       [ 3, 9, 15, 21, 27 ],
       [ 5, 11, 17, 23, 29 ],
       [  7, 13, 19, 29, 35 ]];

and my .mod:

int AmountOfContainers=...;

range Container = 1..AmountOfContainers;
int Rows = ...;
range Row = 1..Rows;
int Columns = ...;
range Column = 1..Columns;
int Distance [Row][Column] = ...;
dvar boolean placed[Row][Column];

minimize
  sum(r in Row, c in Column)
   Distance[r][c]*placedt[r][c]
    ;
    
 subject to {
 }

execute DISPLAY_RESULTS {
};

how i have to change my program to place the 4 containers at the lowest distance costs and display the summed distance costs?

the "placed" matrix should be like :

Placed= [ 
       [ 1, 1, 0, 0, 0 ], 
       [ 1, 1, 0, 0, 0 ],
       [ 0, 0, 0, 0, 0 ],
       [  0,0, 0, 0, 0 ]];

thanks and kind regards

Hi,

you could try

int AmountOfContainers=...;

range Container = 1..AmountOfContainers;
int Rows = ...;
range Row = 1..Rows;
int Columns = ...;
range Column = 1..Columns;
int Distance [Row][Column] = ...;
dvar boolean placed[Row][Column];

minimize
  sum(r in Row, c in Column)
   Distance[r][c]*placed[r][c]
    ;
    
 subject to {
 sum(r in Row, c in Column) placed[r][c]==AmountOfContainers;
 
 }

execute DISPLAY_RESULTS {
writeln(placed);

};

regards

Originally posted by: Treee

thank you again!

Sorry for the late answer, but i had some internet issues and holidays.

Your suggestion worked fine, thanks!

Now i want to split the containers into two types. "Type One" and "Type Two".

"Type One" containers should just be stores in the first 2 columns, the "type two" containers in the other columns.

I would suggest to make an array of the different types : 

AmountOfContainers = [5,2];      // 5 containers of "type one" and 2 containers of "type 2"

But how do I limit the "Type One" Containers to the first 2 columns?

And how do I show, that a certain position is occupied by a container?

Should there be a constraint, that a container can not be placed at a position which value is 1?

Many thanks and kind regards

Hi,

then you could write:

.mod

int

 

nbTypesOfContainers=...;

 

range

 

containerTypes=1..nbTypesOfContainers;

 

　

 

int AmountOfContainers[containerTypes]=...;

 

 

 

int Rows = ...;

 

range Row = 1..Rows;

 

int Columns = ...;

 

range Column = 1..Columns;

 

int Distance [Row][Column] = ...;

 

 

dvar boolean placed[containerTypes][Row][Column];

 

 

minimize

 

sum(r in Row, c in Column, t in containerTypes)

 

Distance[r][c]*placed[t][r][c]

;

 

 

subject to {

 

forall(t in containerTypes)

 

sum(r in Row, c in Column) placed[t][r][c]==AmountOfContainers[t];

 

 

// Max one container at a location

 

forall(r in Row, c in Column) sum(t in containerTypes) placed[t][r][c]<=1;

 

}

 

 

execute DISPLAY_RESULTS {

 

writeln(placed);

 

};

.dat

nbTypesOfContainers

 

=2;

AmountOfContainers

 

=[5,2];

Rows

 

= 4;

Columns

 

= 5;

Distance

 

= [

[ 1, 7, 13, 19, 25 ],

[ 3, 9, 15, 21, 27 ],

[ 5, 11, 17, 23, 29 ],

[ 7, 13, 19, 29, 35 ]];

regards

NB:

to get a nice display you could get ideas at

https://www.ibm.com/developerworks/community/forums/html/topic?id=84ac39db-dcaf-4661-aebd-eeeb89cb4b62&ps=25

and get a 2D display with different colors according to the kind of container

PS:

So in the .mod if at the end you add

tuple sequence_like {
   int start;
   int end;
   string label;
   int type;
 };  
 
int placedDisplay[i in Row][j in Column]=maxl(0,max(t in containerTypes:placed[t][i][j]!=0) t);
 

 

{sequence_like} array2[i in Row] = {<j-1,j," ",2*placedDisplay[i][j]> | j in Column: placedDisplay[i][j]!=0};

 
  execute noname {
    
   array2;
}
   

and then click array2 you will see in the gantt the positions of the containers