Networked facilities expansion problem

This paper considers how best to sequence the acquisition of new locations (e.g. office park buildings, multi-tenant units, etc.) to expand the coverage area or fill in the geographic footprint of a network service provider or other business-service activities. Consider several locations, candidates for acquisition, on the plane. Each location will generate a certain revenue stream for the service provider if it is acquired. In addition, once a location has been acquired (i.e. served), it may be less expensive to acquire other nearby locations. The problem addressed in this paper is: Given a finite budget for acquisitions and a model for the acquisition costs, how to sequence the acquisitions to maximize the total new revenue from the locations acquired? A specific cost model is proposed, an integer programming formulation of the problem and its transformations presented. Properties of the models and of the optimal solution axe discussed. Finally, an effective heuristic method intended for applications is developed. Features of the solutions are demonstrated by a numerical study.