I am trying to come up with the set of equations that will help solve the following problem, but am stuck without a starting point - I can't classify the question to look up more info.
The problem:
Divide a set of products among a set of categories such that a product does not belong to more than one category and the total products within each category satisfies a minimum number.
Example:
I have 6 products that can belong to 3 categories with the required minimums for each category in the final row. For each row, the allowed categories for that product are marked with an X - eg. Product A can only be categorized in CatX, Product B can only be categorized in CatX or CatY. $ \begin{matrix} Product & CatX & CatY & CatZ \\ A & X & & \\ B & X & X & \\ C & X & & \\ D & X & X & X \\ E & & & X\\ F & & X & \\ Min Required& 3 & 1 & 2\\ \end{matrix} $ The solution - where * marks how the product was categorized: $ \begin{matrix} Product & CatX & CatY & CatZ \\ A & * & & \\ B & * & & \\ C & * & & \\ D & & & * \\ E & & & *\\ F & & * & \\ Total & 3 & 1 & 2\\ \end{matrix} $