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I'm not an expert in OR but I would like to determine what is the maximum manufacturing capacity of a plant (or how much a plant can produce of mix products).

Each person in the plant has a known set of competences and is available a certain amount of hours per week.

Each product (+1000 SKUs) uses in each section of the plant a set of competences for a determined amount of time (which is also known).

When the problem stays like this it's not that hard I'm able to determine the max mix-product by using Google's linear solver (OR-tools).

But if I say that I also have to consider the fact that each product needs in each section a defined number of people (while keeping true the competences constraints described earlier) I have a hard time figuring out how my equations are going to look like.

I'm even wondering if this stays a linear problem since I have to ask the question : Are enough people available at a certain time for this section ? If yes then do this, If no then do that.

I'm looking for some inspiration here, so here are my questions :

  • How would you solve this ?
  • Do you know any literature about capacity determination in a high mix environnement ?
  • What other problem this remind you of ?

Thank you for your help,

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