Anti-cover

The anti-covering location problem (ACLP) is a well-recognized coverage-based dispersion model. Admittedly, reaching this conclusion requires a little work, but in fact this problem is related to the node packing, vertex packing, stable/independent set and r-separation problems, with considerable attention being devoted to each of these related problems (see Padberg 1973; Erkut 1990; Nemhauser and Sigismondi 1992; Murray 1995; Erkut et al. 1996; Murray and Kim 2008; Niblett 2014; Niblett and Church 2015). The name anti-cover can be attributed to Moon and Chaudhry (1984) who attempted to distinguish it from other well-known coverage problems. The name, therefore, reflects a sort of opposing goal compared to the set covering problem. The anti-covering location problem seeks to maximize the total weighted benefit of facilities sited in a region, doing so in a manner that ensures at least a minimum pre-specified distance or travel time between facilities and demand is maintained. If the benefit is the same for each potential facility location, then this is equivalent to maximizing the number of facilities that can be sited while maintaining minimum separation restrictions between all facilities and demand or between a sited facility and all other sited facilities. Of course, the goal of the location set covering problem detailed in Chap. 2 is to minimize the number of facilities needed for complete coverage of all demand, assuming the costs for selecting facilities is the same for every potential site. In this sense, then, the two problems have contrasting intents.