Network density and the p-median solution

The p-medianmodel is commonly used to find optimal locations of facilities for geographically distributed demands. So far, there are few studies that have considered the importance of the road network in the model. However, Han, Håkansson, and Rebreyend (2013) examined the solutions of the p-median model with densities of the road network varying from 500 to 70,000 nodes. They found as the density went beyond some 10,000 nodes, solutions have no further improvements but gradually worsen. The aim of this study is to check their findings by using an alternative heuristic being vertex substitution, as a complement to their using simulated annealing. We reject the findings in Han et al (2013). The solutions do not further improve as the nodes exceed 10,000, but neither do the solutions deteriorate.

Does road network density matter in optimally locating facilities?

Optimal location on the transport infrastructure is the preferable requirement for many decision making processes. Most studies have focused on evaluating performances of optimally locate p facilities by minimizing their distances to a geographically distributed demand (n) when p and n vary. The optimal locations are also sensitive to geographical context such as road network, especially when they are asymmetrically distributed in the plane. The influence of alternating road network density is however not a very well-studied problem especially when it is applied in a real world context. This paper aims to investigate how the density level of the road network affects finding optimal location by solving the specific case of p-median location problem. A denser network is found needed when a higher number of facilities are to locate. The best solution will not always be obtained in the most detailed network but in a middle density level. The solutions do not further improve or improve insignificantly as the density exceeds 12,000 nodes, some solutions even deteriorate. The hierarchy of the different densities of network can be used according to location and transportation purposes and increase the efficiency of heuristic methods. The method in this study can be applied to other location-allocation problem in transportation analysis where the road network density can be differentiated.