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Location-Allocation Modeling
Some time ago, a real estate professional stated that there were three important issues in selecting a site for a business: location, location, and location. Although there are other important issues in business site selection, location is definitely one of the most important. Location modeling involves the development of a formal model and solution approach to identify the best place for an activity or a set of places for a set of related activities. Allocation is the related task of allocating services or activities provided by the facilities in order to meet geographically distributed demand. Locationallocation models optimize both location and allocation simultaneously.
There are many fundamental areas in which geographic information science (GISci) has advanced the field of location modeling and site selection. To discuss the role of GISci in location-allocation modeling, it is important to first define the difference between problems of location and problems of location-allocation. Then, we present a broad class of location-allocation modeling constructs that represent many different application areas. Finally, we describe how geographic information systems (GIS) are becoming an integral component in location modeling and how GISci is now joining operations research to provide some underlying scientific elements to the modeling process.
Example of Location Modeling
We may wish to locate positions across a city from which to dispatch ambulances in order to minimize the average time it takes to respond to an emergency call for service. To calculate the level of service provided by an ambulance location plan, it is necessary to depict how demand for emergency medical services (EMS) varies across a city as well as how long it might take an EMS vehicle to travel from any one point in the city to some other point. Using such data, it is possible to build a location model, comprising mathematical equations and location decision variables, which can identify optimal or near-optimal patterns for deploying a given number of ambulances.
To depict this problem within a geographical construct, one needs to define the form of representation (or abstraction) for demand locations, potential dispatch sites, and modeling response time. For example, demand can be represented by points, polygons, or on a raster, while response time can be modeled by calculating distances or travel times along a route.
Types of Location Problems
There are two principal types of location problems: (1) location and (2) location-allocation. To describe the differences between these two types of problems, consider the problem of locating several dry-cleaning shops, Shop A and Shop B, in an urban area. Assume for the moment that these two shops will be owned by the same firm. Thus, it would be important to locate Shop A and B in such a manner that the market area of Shop A does not overlap much with the market area of Shop B; for, if they overlapped much, then the two stores A and B would compete for the same customers and the potential total revenues for the two stores would be less than what might be possible by locating the two stores farther apart.
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