Connected infrastructure location design under additive service utilities

An infrastructure system usually contains a number of inter-connected infrastructure links that connect users to services or products. Where to locate these infrastructure links is a challenging problem that largely determines the efficiency and quality of the network. This paper studies a new location design problem that aims to maximize the total weighted benefits between users and multiple services that are measured by the amount of connectivity between users and links in the network. This problem is investigated from both analytical and computational points of view. First, analytical properties of special cases of the problem are described. Next, two integer programming model formulations are presented for the general problem. We also test intuitive heuristics including greedy and interchange algorithms, and find that the interchange algorithm efficiently yields near-optimum solutions. Finally, a set of numerical examples demonstrate the proposed models and reveal interesting managerial insights. In particular, we found that a more distance-dependent utility measure and a higher concentration of users help achieve a better total utility. As the population becomes increasingly concentrated, the optimal link design evolves from a linear path to a cluster of links around the population center. As the budget level increases, the installed links gradually sprawl from the population center towards the periphery, and in the case of multiple population centers, they grow and eventually merge into one connected component.