Sum-of-squares clustering on networks

Finding p prototypes by minimizing the sum of the squared distances from a set of points to its closest prototype is a well-studied problem in clustering, data analysis and continuous location. In this note, this very same problem is addressed assuming, for the first time, that the space of possible prototype locations is a network. We develop some interesting properties of such clustering problem. We also show that optimal cluster prototypes are not necessary located at vertices of the network.Ministerio de Ciencia e InnovaciónJunta de AndalucíaEuropean Regional Development FundSerbian Ministry of Science

Algunas aportaciones de la investigación operativa a los problemas de localización

La toma de decisiones sobre localizaciones atrae, por su impacto social y económico, creciente interés de geógrafos, economistas y matemáticos. En las páginas que siguen describimos algunas aportaciones que se están realizando desde las Matemáticas (más concretamente, desde la Investigación Operativa), tanto en el modelado, como en la resolución de los problemas de Análisis de Localizaciones

A generalized model of equality measures in network location problems

In this paper, the concept of the ordered weighted averaging operator is applied to define a model which unifies and generalizes several inequality measures. For a location x, the value of the new objective function is the ordered weighted average of the absolute deviations from the average distance from the facilities to the location x. Several kinds of networks are studied: cyclic, tree and path networks and, for each of them, the properties of the objective function are analyzed in order to identify a finite dominating set for optimal locations. Polynomial-time algorithms are proposed for these problems, and the corresponding complexity is discussed.Future and Emerging Technologies Unit (European Commission)Ministerio de Educación y Cienci

Balancing the arrival times of users in a two-stage location problem

There has been a number of facility location problems dealing with the introduction of the equity issue in the travel distances distribution. In this paper we analyze a new aspect of equity concerning the distribution of the arrival times of customers. Given a depot and a set of demand points generating flow which also represent potential locations, we consider a discrete two-stage location problem whose aim is to locate a given number of facilities and to allocate the demand points to a facility. We assume as objective the maximization of the minimum difference between two consecutive arrival times of flows to the depot through the patronized facility. This particular equity measure is introduced in order to reduce risks of congestion in the dynamic of flow arrivals at the common destination. The problem is described through two Integer Programming formulations. Computational results for solution methods based on both formulations are then shown and analyzed

IMPROVING QUALITY OF SERVICE IN EMS SYSTEMS BY REDUCING DISPARITIES BETWEEN SERVICE ZONES

Emergency medical service (EMS) systems respond to emergency or urgent calls so as to provide immediate care, such as pre-hospital care and/or transportation, to hospitals. Care must be provided in a timely manner; in fact quality of service is usually directly associated with response time. To reduce the response time, the number and location of vehicles within the service area are important variables. However with limited capacity, increasing the number of vehicles is often an infeasible alternative. Therefore, a critical design goal is to decide at which facilities stations should be located in order to serve as much demand as possible in a reasonable time, and at the same time maintain equitable service between customers. This study aims to focus on locating ambulances which respond to 911 calls in EMS systems. The goals are to find the optimal base station location for vehicles so that the number of calls or customers served is maximized while disparity between those customers is minimized, to consider the survival rate of patients directly in the model, and develop appropriate meta-heuristics for solving problems which cannot be solved optimally

Localización simple de servicios deseados y no deseados en redes con múltiples criterios

Análisis y desarrollo de varios modelos de localización de servicios deseados y no deseados en redes con múltiples criterios. Asimismo, se han propuesto algunas mejoras en modelos de localización de servicios no deseados en redes con un solo criterio. Por consiguiente, con respecto a la localización de servicios deseados sobre redes, se propone un algoritmo polinomial para solucionar el problema del cent-dian biobjetivo. También se ha estudiado la localización de un servicio en una red con múltiples objetivos tipo mediana. Asimismo, se ha desarrollado un algoritmo polinomial para solucionar el problema cent-dian multicriterio en redes con múltiples pesos por nodo y múltiples longitudes por arista. Con respecto a los problemas de localización de servicios no deseados, primero tratamos el problema de localización del 1-centro no deseado en redes. Demostramos que las cotas superiores ya propuestas en trabajos anteriores pueden ser ajustadas. Por medio de una formulación más adecuada del problema, se ha desarrollado un nuevo algoritmo polinomial el cual es más sencillo y computacionalmente más rápido que los ya divulgados en la literatura. También se ha analizado el problema de localizar una mediana no deseada en una red, obteniendo una nueva y mejor cota superior. Se presenta un nuevo algoritmo para solucionar este problema. Por otra parte, siguiendo la resolución del problema maxian, también se ha propuesto un nuevo algoritmo para solucionar el problema del anti-cent-dian en redes. Finalmente, se han estudiado los problemas del centro no deseado y de la mediana no deseada en redes multicriterio, estableciendo nuevas propiedades y reglas para eliminar aristas ineficientes. También se presenta el modelo anti-cent-dian como combinación convexa de los dos últimos problemas. Se propone una regla eficaz para quitar aristas que contienen puntos ineficientes, así como un algoritmo polinomial. Además, este modelo se puede modificar ligeramente para generalizar otros modelos presentados en la literatura

Proceedings /5th International Symposium on Industrial Engineering – SIE2012, June 14-15, 2012., Belgrade

editors Dragan D. Milanović, Vesna Spasojević-Brkić, Mirjana Misit