Structural Properties of Voronoi Diagrams in Facility Location Problems with Continuous Demand

Structural Properties of Voronoi Diagrams in Facility Location Problems with Continuous Demand

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Article ID: iaor20164651
Volume: 63
Issue: 2
Start Page Number: 394
End Page Number: 411
Publication Date: Apr 2015
Journal: Operations Research
Authors: , , ,
Keywords: combinatorial optimization, graphs, demand, simulation, heuristics
Abstract:

We consider facility location problems where the demand is continuously and uniformly distributed over a convex polygon with m vertices in the rectilinear plane, n facilities are already present, and the goal is to find an optimal location for an additional facility. Based on an analysis of structural properties of incremental Voronoi diagrams, we develop polynomial exact algorithms for five conditional location problems. The developed methodology is applicable to a variety of other facility location problems with continuous demand. Moreover, we briefly discuss the Euclidean case.

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