Zone design of specific sizes using adaptive additively weighted voronoi diagrams

Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of seeds. This type of partitioning has not been sufficiently researched; therefore, there are no known approaches for automated zone delimitation. This study proposes a new method based on a discrete version of the adaptive additively weighted Voronoi diagram that makes it possible to partition a two-dimensional space into zones of specific sizes, taking both the position and the weight of each seed into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that each seed?s weight is updated at every iteration. The zones are geographically connected using a metric based on the shortest path. Tests conducted on the extensive farming system of three municipalities in Castile-La Mancha (Spain) have established that the proposed heuristic procedure is valid for solving this type of partitioning problem. Nevertheless, these tests confirmed that the given seed position determines the spatial configuration the method must solve and this may have a great impact on the resulting partition

CLUSTERING OF TERRITORIAL AREAS: A MULTI-CRITERIA DISTRICTING PROBLEM

Endogenous resources, economic profile and socio-economic issues are the criteria that define the development level and the identity features of a territorial unit. The territorial units that organize the country, in political and administrative terms – parishes and counties –, have a hierarquical structure, which initially reflected the organization of productive activities as well as the tradition State organization. The success of development policies addressed to territorial agglomerates depends on its homogeneity and of their territorial units. Facing to this the clustering of territorial areas can be stated as a districting multi-criteria problem. Thus, this paper aims to propose a framework for obtaining homogenous territorial clusters based on a Pareto frontier that includes multicriteria related to the territorial endogenous resources, economic profile and sociocultural features. This framework is developed in two phases. First, the criteria correlated with the development at the territory unit level are determined through statistical and econometric methods. Then, a multi-criteria approach is developed to allocate each territory unit to an agglomerate of territory according to the Pareto frontier established. The framework is applied to the context of a set of parishes and counties of the Alentejo Central region, southern Portugal. Results are presented and discussed in the scope of a regional strategy of development

A GRASP-Tabu Heuristic Approach to Territory Design for Pickup and Delivery Operations for Large-Scale Instances

Weaddressalogisticsdistrictingproblemfacedbyaparcelcompanywhoseoperationsconsistofpickingupanddeliveringpackages overaserviceregion.Thedistrictingprocessaimstofindapartitionoftheserviceregionintodeliveryandcollectionzonesthat may be served by a single vehicle that departs from a central depot. Criteria to be optimized are to balance workload content among the districts and to create districts of compact shape. A solution approach based on a hybrid procedure that combines elements of GRASP and Tabu Search (TS) is proposed to solve large-scale instances. Numerical experimentation is performed consideringdifferentinstancesizesandtypes.Resultsshowthattheproposedsolutionapproachisabletosolvelarge-scaleinstances inreasonablecomputationaltimeswithgoodqualityofthesolutionsobtained.Todeterminethequalityofthesolutions,resultsare comparedwithCPLEXsolutionsandwiththecurrentrealsolutiontohighlightthebenefitsoftheproposedapproach.Conclusions andrecommendationsforfurtherresearchareprovided

A novel methodology for pipe grouping and rehabilitation interventions scheduling in water distribution networks

The establishment of effective medium and long-term rehabilitation strategies is essential to counter the continuous process of deterioration of the water distribution networks. A novel methodology to support pipe rehabilitation planning, including the establishment and scheduling of interventions in the medium and long-term using the graph theory, is developed, and demonstrated using a real case study. This methodology is divided into two main phases: the first is the definition of rehabilitation pipe groups according to the available budget and pipes connectivity and the second is the scheduling of these groups over time according to relevant criteria. This approach allows a clearer correspondence between the financial amounts to be annually invested in rehabilitation and a grouping of single pipes to be rehabilitated. Results demonstrate that the methodology allows a better and advanced planning of interventions when compared with the current traditional approaches applied by water utilities.info:eu-repo/semantics/publishedVersio

Estado del arte en procesos de zonificacion

Los procesos de partición espacial implican la división de un espacio geográfico en diferentes unidades o zonas según un conjunto específico de criterios. En ámbitos relacionados con las ciencias geoespaciales, la delimitación de estas zonas se realiza por agrupación de otras unidades básicas de área existentes en el espacio de trabajo. En este artículo se ofrece una revisión de los métodos de solución diseñados para este tipo de problemas, comenzando por una introducción a las técnicas heurísticas y modelos matemáticos más utilizados desde los años 60, para finalizar describiendo los recientes algoritmos aplicados a diagramas de Voronoi. También se revisan las aplicaciones en las que se han implementado algunos de estos modelos, quedando patente que son herramientas diseñadas para el tratamiento de problemas específicos, dada la dificultad de diseñar modelos genéricos y versátiles para este tipo de particiones espaciales o zonificacione

Multi-objective sustainable location-districting for the collection of municipal solid waste : two case studies

This paper presents a multi-objective location-districting optimization model for sustainable collection of municipal solid waste, motivated by strategic waste management decisions in Iran. The model aims to design an efficient system for providing municipal services by integrating the decisions regarding urban area districting and the location of waste collection centers. Three objectives are minimized, given as 1) the cost of establishing collection centers and collecting waste, 2) a measure of destructive environmental consequences, and 3) a measure of social dissatisfaction. Constraints are formulated to enforce an exclusive assignment of urban areas to districts and that the created districts are contiguous. In addition, constraints make sure that districts are compact and that they are balanced in terms of the amount of waste collected. A multi-objective local search heuristic using the farthest-candidate method is implemented to solve medium and large-scale numerical instances, while small instances can be solved directly by commercial software. A set of randomly generated test instances is used to test the effectiveness of the heuristic. The model and the heuristic are then applied to two case studies from Iran. The obtained results indicate that waste collection costs can be reduced by an estimated 20-30 %, while significantly improving the performance with respect to environmental and social criteria. Thus, the provided approach can provide important decision support for making strategic choices in municipal solid waste management. Keywords: multi-objective optimization, local search, best-worst methodpublishedVersio

Heurística recursiva de expansión mínima para el rediseño de territorios de venta

La globalización económica ha generado cambios profundos en las relaciones comerciales y disminuido el ciclo de vida de los productos y servicios. Esta situación incrementa los niveles de oferta y obliga a las empresas a establecer estrategias que les permitan asumir la aceleración del cambio, mediante la adquisición y retención de clientes en el largo plazo, a un costo aceptable. Un elemento importante en este proceso es la fuerza de ventas, constituida por un conjunto de vendedores que representan un enlace directo entre la empresa y sus clientes. Idealmente, cada vendedor debe estar asociado a un conjunto de clientes, ubicados dentro de un área geográfica bien delimitada. El rediseño de territorios de venta es una actividad estratégica para lograrlo. En este artículo se presenta y describe una heurística recursiva de expansión mínima para el rediseño de territorios de venta biobjetivo. El problema se inspira en una empresa real que distribuye sus productos en México. La administración de la empresa busca una configuración territorial compacta, que minimice la variación de las nuevas carteras de venta con respecto a las actuales y la distancia total recorrida por los vendedores. Para observar el comportamiento de la heurística, se resuelven dos instancias extremas obtenidas a partir de la configuración regional actual y la instancia integral que no ha podido ser resuelta mediante métodos exactos. Los resultados muestran que es posible obtener territorios contiguos, detectar mercados potenciales y fuerzas de ventas excesivas o insuficientes.Economic globalization has been produced heavy changes into trade, thus lifecycle for products and services has been reduced.  This is increasing supply levels and force to companies to establishing strategies for facing change acceleration by acquiring and retaining customers in long term. All this must have an acceptable cost. Sales force is an important element for do this. Sales force consists of a set of salespeople. They represent a direct link between company and customers. Ideally, each salesman must be associated with a set of customers. Customers may be located within a well-defined geographical area. Thus, redesigning sales territories is a strategic activity that contributing to achieve that one territory will be exclusively assigned to one salesman. This paper introduces and describes a recursive minimum spanning heuristic for bi-objective redesigning sales territories. The problem was inspired for a real company which distributes its products into Mexico. The management of the company seeks for a territorial compact configuration that minimizing the difference between current and new turnover variances, and the total distance traveled by salespeople. For analyze the behavior from the proposed heuristic, two extreme instances corresponding to current regions and the integral instance were solved. Until now, has been impossible solved the integral instance by exact methods. Results showed that contiguous territories are possible, and these can contribute to identify potential markets, and detect excessive or insufficient sales force

Healthcare Districting Optimization Using Gray Wolf Optimizer and Ant Lion Optimizer Algorithms (case study: South Khorasan Healthcare System in Iran)

In this paper, the problem of population districting in the health system of South Khorasan province has been investigated in the form of an optimization problem. Now that the districting problem is considered as a strategic matter, it is vital to obtain efficient solutions in order to implement in the system. Therefore in this study two meta-heuristic algorithms, Ant Lion Optimizer (ALO) and Grey Wolf Optimizer (GWO), have been applied to solve the problem in the dimensions of the real world. The objective function of the problem is to maximize the population balance in each district. Problem constraints include unique assignment as well as non-existent allocation of abnormalities. Abnormal allocation means compactness, lack of contiguous, and absence of holes in the districts. According to the obtained results, GWO has a higher level of performance than the ALO. The results of this problem can be applied as a useful scientific tool for districting in other organizations and fields of application

Rediseño territorial biobjetivo usando estadística multivariante

Redesign of sales territories is a strategic activity which enables companies adapt to changes in the market and helps it to identify opportunity areas for its own expansion. This paper proposes a methodology to solve bi-objective redesign sales territories problem through an approximate Pareto front obtained by use of multivariate statistics. The redesign looks for minimization of the total distance traveled by salespeople and the turnover variation between new and current portfolios. The first objective is achieved through of a cluster analysis application based on distances of the residence population from salespeople to customer’s populations. The second objective required a customer’s classification according to some points of interest to the company. Pareto front results are obtained through structured combination of groups obtained by cluster analysis. The proposed methodology is applied to a real case and the results show that is possible to obtain an approximate Pareto front. El rediseño de territorios de venta es una actividad estratégica que permite a las empresas adaptase a los constantes cambios en el mercado y que contribuye a la identificación de áreas de oportunidad para la expansión. En este artículo se propone una metodología orientada a resolver un problema de rediseño de territorios de venta biobjetivo para obtener un frente de Pareto aproximado a partir de la utilización de estadística multivariante. Los objetivos del rediseño son la minimización de la distancia total recorrida por los vendedores y la variación de los portafolios de venta nuevos con respecto a los actuales. El primer objetivo se alcanzó a través de la aplicación de un análisis de clúster basado en las distancias de las poblaciones de residencia de los vendedores a las de los clientes. El segundo objetivo requirió la clasificación de clientes en función de algunos puntos de interés para la empresa. Los resultados múltiples se obtienen a través de la combinación estructurada de los grupos resultantes del análisis de clúster. La metodología propuesta se aplica a un caso real y los resultados muestran que es posible obtener un frente de Pareto aproximado mediante estadística multivariante.&nbsp

How to Know it is "the One"? Selecting the Most Suitable Solution from the Pareto Optimal Set. Application to Sectorization

Multi-objective optimization (MOO) considers several objectives to find a feasible set of solutions. Selecting a solution from Pareto frontier (PF) solutions requires further effort. This work proposes a new classification procedure that fits into the analytic hierarchy Process (AHP) to pick the best solution. The method classifies PF solutions using pairwise comparison matrices for each objective. Sectorization is the problem of splitting a region into smaller sectors based on multiple objectives. The efficacy of the proposed method is tested in such problems using our instances and real data from a Portuguese delivery company. A non-dominated sorting genetic algorithm (NSGA-II) is used to obtain PF solutions based on three objectives. The proposed method rapidly selects an appropriate solution. The method was assessed by comparing it with a method based on a weighted composite single-objective function. (original abstract