Résumé
An increase in the number of users as well as in users demands leads to exponential traffic growth. This traffic growth pushes telecommunication companies to expand their network through important investments (several billion to improve the mobile network in the last six years). They want indeed to satisfy the request of their subscribers in speed and volume to remain competitive. However, excessive or useless investments over the time horizon should be avoided. As a service provider, operators can use subsidies to avoid unnecessary investments. This has led to the design of mobile master plans, whose modeling under a Mixed Integer Linear formulation has been studied in [3]. This modeling integrate both subscriber and network investments. They consider two types of network investments: densification (new pieces of equipment on an existing site) and coverage extension by installing the new technology. These three types of investments are jointly optimized at each period of the time-horizon while satisfying capacity and strategical guidelines constraints (see [2]). The model from [3] tackles the case of a new generation to be installed on existing sites, which is the current case for the French affiliate. However, new sites are installed in other contexts. In particular, 5G arrival comes with a change of paradigm and the migration from a macro-cell network to a multi-scaled cell network, with new microcell networks sites being cheaper but far more numerous in order to cover the whole territory. Another limitation of [3] is that each telecommunication site is associated with its own pool of subscribers, which assumes that there is no overlapping between sites coverage. This assumption leads to overdimensioning since sites coverage overlapping exists in real networks and hence a technology installed on a neighbor site could have been sufficient to serve the subscribers. Allowing the possibility of installing new sites and assessing the earnings due to sites coverage overlapping in dimensionning, are hence important stakes for an operator. Our modeling contribution over our previous work [3] is twofold. We model the sites coverage overlapping and the possibility of installing new sites (equipped only with the newest technology) on the areas not yet equipped. We provide a mixed integer formulation that tackles the two cases, and linearize it in a classical way. We reinforce the model with several valid inequalities and adapt the heuristics from our previous works. We prove the NP-hardness of our formulation, even in the case of a single generation, single module and mono period framework, by a reduction to the set covering problem.