[Help-glpk] Invert a set-of-sets with mutually exclusive elements

[Meketon, Marc]

I have a simple set of sets that has mutually exclusive elements that I would like to invert into a param that, for each element, gives me the ID of the set it belongs to.

 

Below is an example of the set of sets with mutually exclusive elements:

 

set POOLS := {"Pool201", "Pool203", "Pool204", "Pool205"};

set x_IN_POOLS{POOLS};

 

check {pool1 in POOLS, pool2 in POOLS : pool1 != pool2} card(x_IN_POOL[pool1] inter x_IN_POOL[pool2])==0;

 

data;

set x_IN_POOLS ["Pool201"] := 234, 345, 456, 567, 678, 012, 543;

set x_IN_POOLS ["Pool203"] := 789, 890;

set x_IN_POOLS ["Pool204"] := 123, 901;

set x_IN_POOLS ["Pool205"] := 987, 876, 765, 654;

 

end;

 

I would like to calculate a param PoolID that, for a given “x”, gives the “Pool” it belongs to.  This is equivalent to the following, but I want to use GMPL to calculate the following and not code this into the data:

 

set All_x := setof{pool in POOLS, x in x_IN_POOL[pool]} x;

param PoolID{All_x}, symbolic;

 

data;

param PoolID :=

  123 Pool204

  234 Pool201

  345 Pool201

  456 Pool201

  567 Pool201

  678 Pool201

 789 Pool203

  890 Pool203

  901 Pool204

  012 Pool201

 987 Pool205

  876 Pool205

  765 Pool205

  654 Pool205

  543 Pool201

;

 

I have not yet figured out a clever way to do the above with calculations and no “data” section.

 

BTW, I do know that I could begin with the definition of All_x and PoolID, and derive the set POOLS and the set-of-sets x_IN_POOLS:

set POOLS := setof{x in All_x} PoolID[x];

set x_IN_POOL{pool in POOLS} := setof{x in All_x : pool = PoolID[x]} x;

display x_IN_POOL;

 

But I didn’t want to model my data that way.

 

-Marc

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