In optimization models, we often use an aggregate measure in the objective function, such as total profit, the sum of tardiness of jobs, and countrywide GDP. This can lead to particularly bad results for some individuals or groups.
Here is an example I have used on several occasions.
Problem Statement
We have \(P\) persons. They must be assigned to \(M\) groups or teams. For simplicity, we can assume \(n\) is a multiple of \(m\), and the group size is \[\frac{N}{M}\] Each person \(p_1\) specifies some preferences to be placed in the same group as a person \(p_2\). A negative preference can be used to indicate that I prefer to be in a different group. Find an optimal assignment taking into account these preferences.