I’m trying to solve a problem with Multiple Integer Linear Programming (MILP) that includes binary variables. The situation is as follows;
I have a set of 35 people, which must be even distributed into 5 groups – every person must belong into a group. For each person, there is a corresponding binary variable indicating if they are in a group (Xij = 1) or not in the group (Xij = 2), where i is the person # from 1 to 35, and j is the group number from 1 to 5.
Person 3 for example, would be referenced in X31, X32, X33, X34 and X35 and only one of which would be set to 1.
My issue is as follows, 17 of these individuals are female and if a female is included in the group, at least 3 females must be in the group.
How would I go about structuring a Big-M constraint to model this issue?
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