Weighted Voronoi Diagrams for Optimal Location of Goods and Services in Planar Maps

Abstract

Location of industries or services is a classical problem with an overlapping of techniques involving a geographic support, a quantitative evaluation of supply and demand components, and communication networks. Traditional Cost-Benefit Analysis are focused towards maximization of economic and social benefits in terms of distance maps, minimization transport costs and desirability of goods and services. Economic, population and infrastructures models are variable along time, and consequently, sites used for their representation must be adequately weighted according to different criteria. The aggregation of different criteria in a unique objective function (depending on adjustable parameters) allows to identify a unique solution for the problem in terms of weighted distance maps linked to the objective function. Thus, Weighted Voronoi Diagrams (WVD) provide the most adequate framework for computing and representing the optimal localization linked to a unique global function. This paper considers the interaction between Weighted Voronoi Diagrams and Multicriteria Analysis in Facility Location Problem. First, we introduce a weighted Voronoi diagram based on the places to avoid filter the points of the scenario from infinite to a finite number. Then, Multicriteria Analysis chooses one point of the resulting set from a function that accumulates a list of given criteria. As a result of the process we get the ideal position of the new facility we want to locate in. The solution can afford both private and public facilities, desirable or undesirable as well with three levels of application relative to urban, metropolitan and regional areas.