The \(p\) maximal cover -- \(p\) partial center problem on networks (Q1317171)

The \(p\) maximal cover problem is to locate \(p\) facilities on a network so as to maximize the number of customers that are at most \(T\) units away from a closest facility. A limitation of this problem is put in evidence with a simple example. Then, in order to overcome this limitation, the author introduces a new problem, called the \(p\) partial center problem, where the objective is to minimize the maximum distance between a closest facility and the covered demands. Next, when \(p=1\), the maximal cover problem is considered on a tree and an algorithm is presented for finding all Pareto locations with respect to the two objectives: maximum cover and minimax distance. Then, an algorithm is given for solving the 1- maximal cover problem on a general network. Finally, the author presents an efficient heuristic to solve the problem with \(p\) facilities. A branch-and-bound algorithm is also proposed.