A Verification of Relationship Between Multiplicatively Weighted Voronoi Diagram and Huff Model: A Case Study on Order Assignment in E-Commerce

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Abstract
This study examines the relationship between a multiplicatively weighted (MW-) Voronoi diagram and the Huff model. A mathematical comparison demonstrates that the models are structurally equivalent when the Huff model is deterministic and the distance decay parameter λ takes a specific value. This theoretical finding was empirically validated using real-world e-commerce order assignment data. The experiments demonstrate the distinct strengths of each model. The Huff model enables the flexible balancing of competing objectives through parameter adjustment, whereas the MW-Voronoi diagram provides geometric clarity in the interpretation of territories. We conclude that the selection of the two models should be guided by the problem objectives, depending on whether probabilistic flexibility or deterministic spatial partitioning is required.

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