The Hierarchical Service Location Problem

Abstract

A location problem with a hierarchy of facilities and services is proposed and solved. The formulation defines a demand point to be covered for a given level of service if some member of the facility hierarchy eligible to provide that service is present within an appropriate distance. Furthermore, the absence of coverage at any one service level for a demand point is taken to imply lack of coverage in the grand measure of coverage. The problem's objective is the maximum coverage of population given specific limits on either the number of each type of facility or on the total investment that can be made in all facility types. Relaxed linear programming, supplemented by branch and bound where necessary, is used to solve the resulting integer programming problem. An application is described that uses distance and population data developed for a region of Honduras. Honduran nationals are currently being trained in the use of this and related location methodologies under a contract with the Agency for International Development. This effort is in support of work being undertaken by the Honduran National Planning Council to develop a nationwide data set of populated places in Honduras to which location methodologies will be applied.

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