On the set covering polytope: I. all the facets with coefficients in {0, 1, 2}
Mathematical Programming: Series A and B
Simpson points in planar problems with locational constraints: the polyhedral-gauge case
Mathematics of Operations Research
On finding an envy-free Pareto-optimal division
Mathematical Programming: Series A and B
Minimizing the sum of the k largest functions in linear time
Information Processing Letters
Improved algorithms for several network location problems with equality measures
Discrete Applied Mathematics
A comparison of formulations and solution methods for the minimum-envy location problem
Computers and Operations Research
A strengthened formulation for the simple plant location problem with order
Operations Research Letters
A comparison of formulations and solution methods for the minimum-envy location problem
Computers and Operations Research
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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. The formulations are illustrated by examples. Extensive computational tests are reported, showing the potentials and limits of each formulation on several types of instances. Finally, some improvements for all the formulations previously presented are developed, obtaining in some cases much better resolution times.