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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!

Marco Bonelli
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J_Smith
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  • This is not reproducible, and not a particularly good fit for StackOverflow. Consider instead Operations Research. – Reinderien May 14 '23 at 18:40
  • In general, this leads to a non-convex quadratic model. Sometimes we can exploit some properties of the rest of the model to make things easier. – Erwin Kalvelagen May 15 '23 at 02:49

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