Optimal Location of k-centrum Problems in a Planar Space

Abstract

This paper considers k -centrum criterion location model in a planar space. This criterion to be minimized is the sum of the k largest traveling costs. So that it generalizes the mini-sum criterion, which minimizes the sum of the all traveling costs, and the mini-max criterion, which minimizes the largest traveling costs, so it contains explicitly the tradeoff between both criteria. We characterize the optimal solution and the contour lines associated with the model. Then we exhibit its geometrical solution procedure based on higher-order Voronoi diagrams, taking account of the convexity of its objective function. Finally, we apply this location model to two prefectures in the north part of Kanto Region, in which the migration is serious.