Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Two dimensional spline interpolation algorithms
Two dimensional spline interpolation algorithms
Computers and Operations Research
An Optimization Based Heuristic for Political Districting
Management Science
A continuous approach to the design of physical distribution systems
Computers and Operations Research
Discrete Optimization Algorithms with Pascal Programs
Discrete Optimization Algorithms with Pascal Programs
A simulated annealing approach to police district design
Computers and Operations Research - Location analysis
Computers and Industrial Engineering - Supply chain management
Solving continuous location-districting problems with Voronoi diagrams
Computers and Operations Research
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The objective of districting in logistics distribution problems is to find a near optimal partition of the served region into delivery zones or districts. This kind of problem has been treated in the literature with geometric-shaped districts and continuous approximations. Usually it is assumed an underlying road network equivalent to a Euclidean, rectangular, or ring-radial metric. In most real problems, however, the road network is a coarse combination of metrics. In this context, it is unclear what is the optimal shape of the districts and how one should orientate them. A possibility is to treat the problem with a Voronoi diagram approach. Departing from a previously determined ring-radial districting pattern and relaxing the initial district boundaries, we apply the multiplicatively-weighted Voronoi diagram formulation in order to smooth district contours. The computing process is iterated until the convergence is attained. The model has been applied to solve a parcel delivery problem in the city of São Paulo, Brazil, whose results are presented and discussed in the paper.