The problems of facility location and the allocation of demand points to facilities are crucial research issues in spatial data analysis and urban planning. It is very important for an organization ...or governments to best locate its resources and facilities and efficiently manage resources to ensure that all demand points are covered and all the needs are met. Most of the recent studies, which focused on solving facility location problems by performing spatial clustering, have used the Euclidean distance between two points as the dissimilarity function. Natural obstacles, such as mountains and rivers, can have drastic impacts on the distance that needs to be traveled between two geographical locations. While calculating the distance between various supply chain entities (including facilities and demand points), it is necessary to take such obstacles into account to obtain better and more realistic results regarding locationallocation. In this article, new models were presented for location of urban facilities while considering geographical obstacles at the same time. In these models, three new distance functions were proposed. The first function was based on the analysis of shortest path in linear network, which was called SPD function. The other two functions, namely PD and P2D, were based on the algorithms that deal with robot geometry and route-based robot navigation in the presence of obstacles. The models were implemented in ArcGIS Desktop 9.2 software using the visual basic programming language. These models were evaluated using synthetic and real data sets. The overall performance was evaluated based on the sum of distance from demand points to their corresponding facilities. Because of the distance between the demand points and facilities becoming more realistic in the proposed functions, results indicated desired quality of the proposed models in terms of quality of allocating points to centers and logistic cost. Obtained results show promising improvements of the allocation, the logistics costs and the response time. It can also be inferred from this study that the P2D-based model and the SPD-based model yield similar results in terms of the facility location and the demand allocation. It is noted that the P2D-based model showed better execution time than the SPD-based model. Considering logistic costs, facility location and response time, the P2D-based model was appropriate choice for urban facility location problem considering the geographical obstacles.
•We study effects of spatial defects or heterogeneities in social systems.•Random distributions of obstacles and opinion leaders considered as lattice defects.•A high enough density of geographic ...obstacles contributes to cultural diversity.•Counterintuitively, if density of leaders increases, they induce multiculturality.•Leaders and obstacles sites favor formation of boundaries between cultural groups.
We employ an agent-based model for cultural dynamics to investigate the effects of spatial heterogeneities on the collective behavior of a social system. We introduce heterogeneity as a random distribution of defects or imperfections in a two-dimensional lattice. Two types of defects are considered separately: obstacles that represent geographic features, and opinion leaders, described as agents exerting unidirectional influence on other agents. In both cases, we characterize two collective phases on the space of parameters of the system, given by the density of defects and a quantity expressing the number of available states: one ordered phase, consisting of a large homogeneous group; and a disordered phase, where many small cultural groups coexist. In the case of leaders, the homogeneous state corresponds to their state. We find that a high enough density of obstacles contributes to cultural diversity in the system. On the other hand, we find a nontrivial effect when opinion leaders are distributed in the system: if their density is greater than some threshold value, leaders are no longer efficient in imposing their state to the population, but they actually promote multiculturality. In this situation, we uncover that leaders, as well as obstacles, serve as locations for the formation of boundaries and segregation between different cultural groups. Moreover, a lower density of leaders than obstacles is needed to induce multiculturality in the system.
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