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From a stock of various computer accessories of different brands, the optimization problem requires deciding to keep or discard products. The decision should be made maintaining the following if-then condition: If one product of a certain brand is eliminated than all the products of that brand should be eliminated. So, for example, if the stock has different models of HP branded monitor, printer, mouse and keyboard, and decision is made to discard one model of HP mouse, then all other HP products need to be discarded as well.

As the number of items under each brand varies, how do I formulate this?

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  • $\begingroup$ Just use material implication. You want to specify that formula X => Y must be true, for instance "If one product of a certain brand is eliminated than all the products of that brand should be eliminated" is translated to X = any product of a brand is eliminated, Y = product is eliminated (for each product in that brand). Material implication can be translated to conjunction and disjunction, both of them can be represented as blog.adamfurmanek.pl/2015/08/22/ilp-part-1 $\endgroup$ Nov 1, 2020 at 14:03
  • $\begingroup$ cs.stackexchange.com/q/12102/755 $\endgroup$
    – D.W.
    Nov 1, 2020 at 19:00

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