Solving the continuous space p-centre problem: planning application issues

The Voronoi diagram heuristic has been proposed for solving the p-centre problem in continuous space. However, important assumptions underlie this heuristic and may be problematic for practical applications. These simplifying assumptions include uniformly distributed demand, representing a region as a rectangle; analysis of a simple Voronoi polygon in solving associated one-centre problems and no restrictions on potential facility locations. In this paper, we explore the complexity of solving the continuous space p-centre problem in location planning. Considering the issue of solution space feasibility, we present a spatially restricted version of this problem and propose methods for solving it heuristically. Theoretical and empirical results are provided.