New spatial clustering-based models for optimal urban facility location considering geographical obstacles

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 location-allocation. 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.