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Let's say I have sourced 10 different suppliers to send products via 6 different routes to the same distribution center. Depending on costs some suppliers won't send any products, but those that do are constrained by a min and max amount.

How can I model this constraint using solver? I can't use an if function, because that would make it non-linear.

But if I set a min constraint for all suppliers then solver won't account for suppliers who shouldn't ship any products due to a high cost.

thx

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A variable x that can assume values zero or between L and U (i.e. x ∈ 0 ∪ [L,U]) is called a semi-continuous variable. Many MIP solvers support this type of variable. If not then semi-continuous behavior can be simulated with an additional binary variable:

 L⋅δ ≤ x ≤ U⋅δ
 δ ∈ {0,1}  (i.e. δ is a binary variable)

This can be handled by any MIP solver. You may have to split the sandwich constraint into two constraints.

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