A computational method for optimizing the hierarchy and spatial configuration of successively inclusive facilities on a continuous plane

This paper shows a computational method for optimizing a system of successively inclusive hierarchical facilities (a system in which the services provided by a certain rank of facilities include all services provided by lower rank facilities) on a continuous plane. The system is optimized with respect to not only the configuration of ranked facilities, but also its hierarchical structure (i.e. the composition of the number of ranks and the numbers of ranked facilities). The optimization procedure has two steps. The first step optimizes a system of exclusive hierarchical facilities by an analytical method. Using this optimal solution, the second step optimizes a system of successively inclusive hierarchical facilities by a computational search method. Numerical experiments show that the proposed method tends to reach a near optimal solution within a few iterations.