[Help-glpk] Formulate a large scale linear programing model by reducing the number of similar constraints and keeping them all satisfied

[usa usa]

Hi,

 

I need to build a large scale LP model and solve it by GLPK.

 

In the model, there is a kind of constraint like:

    

Max: sum of (constantValueP_i  * decVarX_i) from i=1 to  N

s.t.

      decVarT + sum of (decVarK_i ) from i=1 to I = N  <=  [sum of (constantValueP_i  * decVarX_i)  from i=1 to  N ] * constantQ

      [sum of (constantValueE_i  * decVarX_i)  from i=1 to  N ] <= [sum of (constantValueE_i )  from i=1 to  N ] * constantD

      decVarK_1 >= sum of (constantValue_1_i  * decVarX_i) from i=1 to  N - decVarT

      decVarK_2 >= sum of (constantValue_2_i  * decVarX_i) from i=1 to  N - decVarT

      …

      decVarK_L >= sum of (constantValue_j_i  * decVarX_i) from i=1 to  N - decVarT

 

Decision variables:

decVarT , 0 <= decVarX_i <= 1, decVarK_i >= 0

 

The problem is that the number of constraints of   decVarK_i for i=1 to L and L can be very large, e.g. 100,0000.

 

It means that it will have 100,000 constraints in the LP, which I want to avoid.

 

How to combine them so that I can reduce the size of the LP model meanwhile keeping all constraints satisfied ?

 

thanks