Exploring the Location Set Covering Problem (LSCP)

LSCPs fall within a class of problems known as set covering problems. The set covering problem class is an NP-hard problem within the combinatorial optimization space. These problems typically aim at minimizing the number of sets within a space that cover all the demand within that space. Take, for example, the emergency services problem we mentioned at the start of this chapter, where a given number of emergency service facilities must service the demand of all the residents in a given community. The emergency planning departments within this community may want to know if the demand from the community can be met with the existing infrastructure. If there are too few facilities to triage the community’s needs, then additional facilities may need to be constructed. Conversely, there may be too many facilities in the community than needed. This may present opportunities to consolidate the facilities, resulting in operational savings...