Directional approach to gradual cover: the continuous case

The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed "directional gradual cover". Contrary to all gradual cover models, the joint cover depends on the facilities' directions. In order to calculate the joint cover, existing models apply the partial cover by each facility disregarding their direction. We develop a genetic algorithm to solve the facilities location problem and also solve the problem for facilities that can be located anywhere in the plane. The proposed modifications were extensively tested on a case study of covering Orange County, California

Fairness in maximal covering location problems

Acknowledgments The authors thank the anonymous reviewers and the guest editors of this issue for their detailed comments on this paper, which provided significant insights for improving the previous versions of this manuscript. This research has been partially supported by Spanish Ministerio de Ciencia e Innovación, AEI/FEDER grant number PID2020-114594GB C21, AEI grant number RED2022-134149-T (Thematic Network: Location Science and Related Problems), Junta de Andalucía projects P18- FR-1422/2369 and projects FEDERUS-1256951, B-FQM-322-UGR20, CEI-3-FQM331 and NetmeetData (Fundación BBVA 2019). The first author was also partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033 and UENextGenerationEU (ayudas de movilidad para la recualificación del profesorado universitario. The second author was also partially supported by the Research Program for Young Talented Researchers of the University of Málaga under Project B1-2022_37, Spanish Ministry of Education and Science grant number PEJ2018-002962-A, and the PhD Program in Mathematics at the Universidad de Granada.This paper provides a mathematical optimization framework to incorporate fairness measures from the facilities’ perspective to discrete and continuous maximal covering location problems. The main ingredients to construct a function measuring fairness in this problem are the use of (1) ordered weighted averaging operators, a popular family of aggregation criteria for solving multiobjective combinatorial optimization problems; and (2) -fairness operators which allow generalizing most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are first formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained from an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.Spanish Ministerio de Ciencia e InnovaciónAEI/FEDER grant number PID2020-114594GB C21AEI grant number RED2022-134149-T (Thematic Network: Location Science and Related Problems)Junta de Andalucía projects P18- FR-1422/2369FEDERUS-1256951B-FQM-322-UGR20CEI-3-FQM331NetmeetData (Fundación BBVA 2019)IMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033UE NextGenerationEUResearch Program for Young Talented Researchers of the University of Málaga under Project B1-2022_37Spanish Ministry of Education and Science grant number PEJ2018-002962-