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-

Mathematical optimization models for reallocating and sharing health equipment in pandemic situations

In this paper we provide a mathematical programming based decision tool to optimally reallocate and share equipment between different units to efficiently equip hospitals in pandemic emergency situations under lack of resources. The approach is motivated by the COVID-19 pandemic in which many Heath National Systems were not able to satisfy the demand of ventilators, sanitary individual protection equipment or different human resources. Our tool is based in two main principles: (1) Part of the stock of equipment at a unit that is not needed (in near future) could be shared to other units; and (2) extra stock to be shared among the units in a region can be efficiently distributed taking into account the demand of the units. The decisions are taken with the aim of minimizing certain measures of the non-covered demand in a region where units are structured in a given network. The mathematical programming models that we provide are stochastic and multiperiod with different robust objective functions. Since the proposed models are computationally hard to solve, we provide a divide-et-conquer math-heuristic approach. We report the results of applying our approach to the COVID-19 case in different regions of Spain, highlighting some interesting conclusions of our analysis, such as the great increase of treated patients if the proposed redistribution tool is applied.Spanish Ministerio de Ciencia e Innovacion, Agencia Estatal de Investigacion/FEDER PID2020-114594GB-C21Junta de Andalucia SEJ-584 FQM-331 P18-FR-1422 US-1256951 P18-FR-2369Spanish Government PEJ2018-002962-ADoctoral Program in Mathematics at the Universidad of GranadaProyect NetMeetData (Fundacion BBVA - Big Data)IMAG-Maria de Maeztu grant CEX2020-001105-M/AEICenter for Forestry Research & Experimentation (CIEF)European Commission CIGE/2021/16

Multitype Maximal Covering Location Problems: Hybridizing discrete and continuous problems

Acknowledgements This research has been partially supported by Spanish Ministerio de Ciencia e Innovación, AEI/FEDER grant number PID2020-114594GBC21, Junta de Andalucía projects P18-FR- 1422/2369 and projects FEDERUS-1256951, B-FQM-322-UGR20, CEI-3-FQM331 and Netmeet- Data (Fundación BBVA 2019). The first author was also partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033. The second author was partially supported by Spanish Ministry of Education and Science grant number PEJ2018- 002962-A, the PhD Program in Mathematics at the Universidad de Granada and Becas de Movilidad entre Universidades Andaluzas e Iberoamericanas (AUIP). The third author was partially funded by grant UIDB/04561/2020 from National Funding from FCT|Fundaçao para a Ciencia e Tecnologia, Portugal.This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different metric spaces are simultaneously decided to maximize the demand generated by a set of points. From the need of intertwining location decisions in discrete and in continuous sets, a general hybridized problem is considered in which some types of facilities are to be located in finite sets and the others in continuous metric spaces. A natural non-linear model is proposed for which an integer linear programming reformulation is derived. A branch-and-cut algorithm is developed for better tackling the problem. The study proceeds considering the particular case in which the continuous facilities are to be located in the Euclidean plane. In this case, taking advantage from some geometrical properties it is possible to propose an alternative integer linear programming model. The results of an extensive battery of computational experiments performed to assess the methodological contribution of this work is reported on. The data consists of up to 920 demand nodes using real geographical and demographic data.Spanish Ministerio de Ciencia e Innovación, AEI/FEDER grant number PID2020-114594GBC21Junta de Andalucía projects P18-FR- 1422/2369FEDERUS-1256951B-FQM-322-UGR20CEI-3-FQM331Netmeet- Data (Fundación BBVA 2019)MAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033Spanish Ministry of Education and Science grant number PEJ2018- 002962-Agrant UIDB/04561/2020 from National Funding from FCT|Fundaçao para a Ciencia e Tecnologia, Portuga

The Cooperative Maximum Capture Facility Location Problem

In the Maximum Capture Facility Location (MCFL) problem with a binary choice rule, a company intends to locate a series of facilities to maximize the captured demand, and customers patronize the facility that maximizes their utility. In this work, we generalize the MCFL problem assuming that the facilities of the decision maker act cooperatively to increase the customers' utility over the company. We propose a utility maximization rule between the captured utility of the decision maker and the opt-out utility of a competitor already installed in the market. Furthermore, we model the captured utility by means of an Ordered Median function (OMf) of the partial utilities of newly open facilities. We name this problem "the Cooperative Maximum Capture Facility Location problem" (CMCFL). The OMf serves as a means to compute the utility of each customer towards the company as an aggregation of ordered partial utilities, and constitutes a unifying framework for CMCFL models. We introduce a multiperiod non-linear bilevel formulation for the CMCFL with an embedded assignment problem characterizing the captured utilities. For this model, two exact resolution approaches are presented: a MILP reformulation with valid inequalities and an effective approach based on Benders' decomposition. Extensive computational experiments are provided to test our results with randomly generated data and an application to the location of charging stations for electric vehicles in the city of Trois-Rivi\`eres, Qu\`ebec, is addressed.Comment: 32 pages, 8 tables, 2 algorithms, 8 figure

A branch-and-price approach for the continuous multifacility monotone ordered median problem

Acknowledgements The authors of this research acknowledge financial support by the Spanish Ministerio de Ciencia y Tecnología, Agencia Estatal de Investigación and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020-114594GB-C21. The authors also acknowledge partial support from project B-FQM-322-UGR20. The first, third and fourth authors also acknowledge partial support from projects FEDER-US-1256951, Junta de Andaluca P18-FR-1422, CEI-3-FQM331, FQM-331, and NetmeetData: Ayudas Fundacin BBVA a equipos de investigacin científica 2019. The first and second authors were par- tially supported by research group SEJ-584 (Junta de Andalucía). The first author was also partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M/AEI/10.13039/50110 0 011033. The second author was supported by Spanish Ministry of Education and Science grant number PEJ2018-002962-A and the Doctoral Program in Mathematics at the Universidad of Granada. The third author also acknowledges the grant Contratación de Personal Investigador Doctor (Convocatoria 2019) 43 Contratos Capital Humano Línea 2 Paidi 2020, supported by the European Social Fund and Junta de Andalucía.In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. The goal of this problem is to locate facilities in minimizing a monotone ordered weighted median function of the distances between given demand points and its closest facility. We propose a new branch-and-price procedure for this problem, and three families of matheuristics based on: solving heuristically the pricer problem, aggregating the demand points, and discretizing the decision space. We give detailed discussions of the validity of the exact formulations and also specify the implementation details of all the solution procedures. Besides, we assess their performances in an extensive computational experience that shows the superiority of the branch-and-price approach over the compact formulation in medium-sized instances. To handle larger instances it is advisable to resort to the matheuristics that also report rather good results.Spanish Ministerio de Ciencia y Tecnología, Agencia Estatal de Investigación and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020-114594GB-C21Partial support from project B-FQM-322-UGR20Partial support from projects FEDER-US-1256951, Junta de Andaluca P18-FR-1422, CEI-3-FQM331, FQM-331, and NetmeetData: Ayudas Fundación BBVA a equipos de investigacin científica 2019Research group SEJ-584 (Junta de Andalucía)Partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M/AEI/10.13039/50110 0 011033Spanish Ministry of Education and Science grant number PEJ2018-002962-AEuropean Social Fund and Junta de Andalucí

Validez y utilidad diagnóstica de la escala EAT-26 para la evaluación del riesgo de trastornos de la conducta alimentaria en población femenina de Medellín, Colombia

ResumenObjetivoEvaluar la validez y la utilidad diagnóstica de la escala EAT-26 para la evaluación del riesgo de trastornos de conducta alimentaria (TCA) en población femenina.DiseñoEstudio observacional de validación de pruebas.EmplazamientoRealizado en la ciudad de Medellín en nivel de atención comunitaria de consulta psiquiátrica mixta (pública y privada).ParticipantesVeinticinco mujeres con edades entre 15 y 25años que cumplieran criterios DSM-IV-TR para anorexia y bulimia nerviosa y 111controles sin TCA.Mediciones principalesLa muestra de casos fue por conveniencia y en controles, aleatoria simple. Se comparó el «criterio de oro» (entrevista estructurada por psiquiatra para determinar el cumplimiento o no de criterios de inclusión de caso de TCA) con el EAT-26, y al instrumento se le hizo validación cultural y semántica, validación factorial, evaluación de confiabilidad, así como determinación del mejor punto de corte por medio de la curva ROC.ResultadosEn EAT-26 subyacen 4dominios: bulimia, dieta, preocupación por la comida y control oral. El alfa de Cronbach fue de 92,1%, y el mejor valor de corte, el de 11 y más puntos (sensibilidad del 100% y especificidad del 85,6%).ConclusiónEl EAT-26 modificado y abreviado es un instrumento multidimensional, con excelentes valores de confiabilidad y sensibilidad, y con un adecuado valor de especificidad, apropiado para el cribado de posible TCA en población de riesgo y útil en atención primaria para su detección temprana en mujeres jóvenes.AbstractObjectiveTo establish diagnostic validity and usefulness of EAT-26 for the risk assessment of Eating Disorder (ED) in a female population.DescriptionObservational validation study questionnaire.SettingPerformed in a Medellin city community care level of mixed (public and private) psychiatric consultation.SubjectsTwenty five subjects aged 15 to 25 with DSM-IV-TR diagnostic criteria for anorexia and bulimia nervosa and 111 controls without ED.Main outcomes measuresThe case sample was for convenience and in controls an aleatory simple one. Gold standard (structured psychiatrist interview confirming the fulfillment of ED case inclusion criteria) was compared with EAT-26 questionnaire; reliability was assessed, cultural, semantics and factorial validation was made and the best cut-off score was established with the ROC curve.ResultsFour domains remain in the instrument: bulimia, dieting, food preoccupation and oral control. The Cronbach's alpha was 92.1% and a score of 11 and over is the best cut-off (sensitivity 100%, and specificity 85.6%).ConclusionsThis modified and abbreviated EAT-26 questionnaire is an ideal multidimensional instrument for ED screening in risk population, with excellent reliability and sensitivity values and satisfactory specificity. EAT-26 is a useful measure to be considered when strategies for ED early detection are implemented in young women

Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsacker term and an (N-1)-electron kinetic correlation term. We further show that the Weizsacker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsacker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases.Comment: 10 pages, 1 figure. To appear in Theor Chem Ac

Crystal engineering and ferroelectricity at the nanoscale in epitaxial 1D manganese oxide on silicon

Ferroelectric oxides have attracted much attention due to their wide range of applications, particularly in electronic devices such as nonvolatile memories and tunnel junctions. As a result, the monolithic integration of these materials into silicon technology and their nanostructuration to develop alternative cost-effective processes are among the central points in the current technology. In this work, we used a chemical route to obtain nanowire thin films of a novel Sr1+δMn8O16 (SMO) hollandite-type manganese oxide on silicon. Scanning transmission electron microscopy combined with crystallographic computing reveals a crystal structure comprising hollandite and pyrolusite units sharing the edges of their MnO6 octahedra, resulting in three types of tunnels arranged along the c axis, where the ordering of the Sr atoms produces natural symmetry breaking. The novel structure gives rise to ferroelectricity and piezoelectricity, as revealed by local direct piezoelectric force microscopy measurements, which confirmed the ferroelectric nature of the SMO nanowire thin films at room temperature and showed a piezoelectric coefficient d33 value of 22 ± 6 pC N−1. Moreover, we proved that flexible vertical SMO nanowires can be harvested providing an electrical output energy through the piezoelectric effect, showing excellent deformability and high interface recombination. This work indicates the possibility of engineering the integration of 1D manganese oxides on silicon, a step which precedes the production of microelectronic devices.A. C.-G., C. J., R. G.-B. and J. M. V.-F. acknowledge the financial support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (No. 803004) and the French Agence Nationale de la Recherche (ANR), project Q-NOSS ANR ANR-16-CE09-0006-01. This project has received funding from the EU-H2020 research and innovation program under grant agreement no 654360 having benefitted from the access provided by ICMAB-CSIC in Barcelona within the framework of the NFFA-Europe Transnational Access Activity. This project has received funding from the European's Union Horizon 2020 research and innovation programme under Grant No. 823717-ESTEEM3, the Spanish Ministry of Economy and Competitivity through Project MAT2017-82970-C2-2-R, and the Aragon Regional Government through Project No. E13_20R (with European Social Fund). We acknowledge SOLEIL for provision of synchrotron radiation facilities, and we would like to thank Pierre Fertey for assistance in using beamline Cristal. J. G. also acknowledges the Ramon y Cajal program (RYC-2012-11709). The authors thank D. Montero for providing the FEGSEM images. N. M. acknowledges the Spanish Ministry of Science, Innovation and Universities through Severo Ochoa FUNFUTURE (CEX2019-000917-S) and SUMATE (RTI2018-095853-B-C21) projects, co-financed by the European Regional Development Fund. The FEGSEM instrumentation was facilitated by the Institut des Matériaux de Paris Centre (IMPC FR2482). The authors thank Frederic Pichot for his expertise and advice during the nanowire lithographic process. The STEM microscopy work was conducted in the Laboratorio de Microscopias Avanzadas (LMA) at Instituto de Nanociencia de Aragon (INA) at the University of Zaragoza.Peer reviewe