The p-Median Problem

The p-median problem is central to much of discrete location modeling and theory. While the p-median problem is NP-hard on a general graph, it can be solved in polynomial time on a tree. A linear time algorithm for the 1-median problem on a tree is described. We also present a classical formulation of the problem. Basic construction and improvement algorithms are outlined. Results from the literature using various metaheuristics including tabu search, heuristic concentration, genetic algorithms, and simulated annealing are summarized. A Lagrangian relaxation approach is presented and used for computational results on 40 classical test instances as well as a 500-node instance derived from the most populous counties in the contiguous United States. We conclude with a discussion of multi-objective extensions of the p-median problem.