A comparison of formulations and solution methods for the Minimum-Envy   Location Problem. Additional results
  We consider a discrete facility location problem with a new form of equity criterion. The model discussed in the paper analyzes the case where demand points only have strict preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the total envy felt by the entire set of demand points. We define this new total envy criterion and provide several integer linear programming formulations that reflect and model this approach. Extensive computational tests are reported, showing the potentials and limits of each formulation on several types of instances. 
Inmaculada Espejo, Alfredo Marin, Justo Puerto, Antonio Rodriguez-Chia