A game theoretic approach to the maximal covering prevention location problem

The objective of many location problems, such as the Maximal Covering Problem (MCLP), is to maximize the demand that is covered by the located set of facilities. For these problems it is assumed that all users of the located facilities have equal access to the facility and that all demand covered by a facility can be served by it. The coverage pattern in these types of problems tends to have a high level of single coverage, meaning that demand nodes may only be covered by a single facility. This is due to the goal of these problems; to cover as much demand as possible, not ensure that facilities are covered by multiple facilities. If a scenario were presented that removed any number of facilities after they were located using the MCLP the remaining coverage would be greatly impacted because when a facility is removed much of its demand is no longer covered. ^ The location and coverage of the facilities has become an important topic in location research, especially after the events of September, 11 2001. If facilities are located in such a pattern that the removal of a few impacts the services of many, alternative facility patterns need to be evaluated. This study proposes a model to limit the demand lost after an interdiction event. The objective of the Maximal Covering Prevention Location Problem (MCPLP) is to cover as much demand as possible before interdiction but also to position facilities in such a manner that if an interdiction event does occur, the remaining coverage will be as great as possible. A single player, zero sum game will be used to model the problem. The MCPLP will be formulated as a linear program and a heuristic. To evaluate the validity of the results, the MCPLP will be compared to the results of several other problems including the MCLP for a number of different facility combinations. The demand covered before and after interdiction as well as the spatial arrangement of facilities of the MCPLP is calculated and mapped.