[Clp] 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 CLP.



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
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