I have a Linear programming problem I am trying to formulate. I need to define a variable which is the fraction of one particular variable divided by the sum of this variable over the entire set it is defined on. Let me explain this further:
sets: t = time g = generator
Variables: Gen(g,t) = Generation/production by generator g at time t PF(g,t) = Power factor, defined for each generator g at each timeblock t
Now, the equation I want is as follows:
PF(g,t) = Gen(g,t)/Sum((g,t),Gen(g,t))
This is clearly a non-linear equation. I need this to be transformed/approximated into a linear equation. Just one more issue I have is that the problem size is HUGE and I won't be able to make a mixed integer programming formulation work, unfortunately.
Any leads on this, or any reference materials to this would be highly appreciated!