Two lower-bounding algorithms for the p-center problem in an area

Abstract

The p-center location problem in an area is an important yet very difficult problem in location science. The objective is to determine the location of p hubs within a service area so that the distance from any point in the area to its nearest hub is as small as possible. While effective heuristic methods exist for finding good feasible solutions, research work that probes the lower bound of the problem’s objective value is still limited. This paper presents an iterative solution framework along with two optimization-based heuristics for computing and improving the lower bound, which is at the core of the problem’s difficulty. One method obtains the lower bound via solving the discrete version of the Euclidean p-center problem, and the other via solving a relatively easier clustering problem. Both methods have been validated in various test cases, and their performances can serve as a benchmark for future methodological improvements.