We consider facility location problems with a new form of equity criterion. Demand points have preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the envy felt by the demand points with respect to the rest of the demand points allocated to the same plant. After defining this new envy criterion and the general framework based on it, we provide formulations that model this approach in both the discrete and the continuous framework. The problems are illustrated with examples and the computational tests reported show the potential and limits of each formulation on several types of instances. Although this article is mainly focused on the introduction, modeling and formulation of this new concept of envy, some improvements for all the formulations presented are developed, obtaining in some cases better solution times.Project TED2021-130875B-I00, supported by MCIN/AEI/ 10.13039/
501100011033 and the European Union ‘‘NextGenerationEU/PRTR’’Research project PID2022-
137818OB-I00 (Ministerio de Ciencia e Innovación, Spain)Agencia
Estatal de Investigación (AEI), Spain: PID2020-114594GB-C2; Regional
Government of Andalusia, Spain P18-FR-1422 and B-FQM-322-UGR20
(ERDFIMAG-Maria
de Maeztu, Spain grant CEX2020-001105-M/AEI/10.13039/
501100011033Funding for open access charge: Universidad de
Granada / CBU
