Location analysis: A synthesis and survey

Beginning with Hodgson (Geogr.Anal.22(1990) 270), several researchers have been developing a new kind of location-allocation model for “flow capturing.” Instead of locating central facilities to serve demand at fixed points in space, their models aim to serve demand consisting of origin-destination flows along their shortest paths. This paper extends flow-capturing models to optimal location of refueling facilities for alternative-fuel (alt-fuel) vehicles, such as hydrogen fuel cells or natural gas. Existing flow-capturing models assume that if a flow passes just one facility along its path, it is covered. This assumption does not carry over to vehicle refueling because of the limited range of vehicles. For refueling, it may be necessary to stop at more than one facility in order to successfully refuel the entire path, depending on the vehicle range, the path length, and the node spacing. The Flow Refueling Location Model (FRLM) optimally locates p refueling stations on a network so as to maximize the total flow volume refueled. This paper presents a mixed-integer programming formulation for the nodes-only version of the problem, as well as an algorithm for determining all combinations of nodes that can refuel a given path. A greedy-adding approach is demonstrated to be suboptimal, and the tradeoff curve between number of facilities and flow volume refueled is shown to be nonconvex.

The flow-refueling location problem for alternative-fuel vehicles

Survey: Covering problems in facility location: A review

We present a survey of over 50 representative problems in location research. Our goal is not to review all variants of different location models or to describe solution results, but rather to provide a broad overview of major location problems that have been studied, indicating briefly how they are formulated and how they relate to one another. We review standard problems such as median, center, and warehouse location problems, as well as less traditional location problems which have emerged in recent years. Our primary focus is on problems for which operations research-type models have been developed. Most of the problems we review have been formulated as optimization problems.

An overview of representative problems in location research

A bibliography for some fundamental problem categories in discrete location science

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.

The Hierarchical Service Location Problem

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The Hierarchical Service Location Problem