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I am currently writing my thesis and am developing an MILP optimization model. I have a lot of constraints that should only be created if certain conditions regarding the respective parameters of the underlying sets are true.

I have attached an example of a constraint to illustrate, how I currently wrote them: example of a contraint.

I did this based on this post: Representing IF ... THEN ... ELSE ... in math notation. This equation basically states that the end of a process equals the starting time plus its duration. But this equation must only be created for a certain subset of processes J, otherwise the model is infeasible. The two conditions regarding m and lvl are connected by a logical AND.

  • et: end time, variable
  • st: start time, variable
  • d: duration, parameter
  • m,lvl: properties of the individual processes in set J, parameters

Even though this notation feels natural (to me at least), I cannot find this notation in the literature on the topic.

Is it possible to write constraints like this? Are their major issues with this type of notation?

Thanks a lot in advance.

ahi
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  • I often use implications for this, using $\Rightarrow$ and $\Leftrightarrow$. – Erwin Kalvelagen Jan 13 '18 at 10:32
  • @ErwinKalvelagen Thanks for the comment. Here are two examples. Is this how you meant it? I think the second (eq. 41) would be more appropriate in my case, because if and only if the conditions hold the constraint must be created. – ahi Mar 11 '18 at 15:46

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