THE MAXIMAL COVERING LOCATION PROBLEM

The belief that mathematical location modeling can identify "optimal" location patterns rests on the basis that some realistic objective can be identified and by some measure quantified. For example, in the area of private facilities location analysis, a reasonably accurate statement of the objective of locating warehouses is to minimize the costs of manufacturing and distribution. Since most cost elements included in the objectives of private facility location can be reasonably estimated, the models can picture with some degree of accuracy the real location problem they are designed to solve. Unlike private facility location analysis, the objectives of public facility location analysis are more difficult to embrace and to quantify. The difficulty in defining direct measures of public objectives has resulted in a search for some surrogate measure with which the decision maker may be comfortable. Two different surrogate measures which have received attention in location models are: (1) total weighted distance or time for travel to the facilities, and (2) the distance or time that the user most distant from a facility would have to travel to reach that facility, that is, the maximal service distance.* The use of a maximal service distance as a measure of the value of a given locational configuration has been discussed at length by Toregas and ReVelle 1 who show that it is an important surrogate measurement for the value of a given locational configuration. For a given location solution, the maximum distance which any user would have to travel to reach a facility would reflect the worst possible performance of the system. In the regional location of emergency facilities such as fire stations or ambulance dispatching stations, the concept of the maximal service distance is well established. ~,3 The maximal service distance concept appears in the Location Set Covering