Weighted furthest point voronoi diagrams
There's something on the multiplicatively weighted farthest neighbor query problem (but not on the associated Voronoi diagram) in my paper

Approximate weighted farthest neighbors and minimum dilation stars.
J. Augustine, D. Eppstein, and K. Wortman.
arXiv:cs.CG/0602029.
Proc. 16th Annual International Computing and Combinatorics Conference (COCOON 2010), Nha Trang, Vietnam.
Lecture Notes in Comp. Sci. 6196, Springer-Verlag, 2010, pp. 90-99.
Discrete Mathematics, Algorithms and Applications 2(4): 553-656, 2010.