Résumé
IntroductionNew bandwidth-consuming usages and the increase in the number of users induce an expo- nential growth of mobile traffic [4]. Facing this traffic growth, telecommunication companies are hence pushed to expand their network through important investments (several billion e to improve the mobile network in the last six years, see [6]). This network design problem has two specific features. First, a fast roll-out between mobile networks generation and a highly competitive environment that encourage operators to invest in the newest technology available. Second, telecommunication companies are often both infrastructure operators, planning their network expansion, and service providers, designing the offers proposed to the subscribers.Through marketing investments, the operator is able to control the demand on its different technologies and avoid over-dimensioning, hence reducing its investments in network design. Reversely, the efficiency of such investments over a given year is also dependent on the network deployment performed in the previous years: subscribers will be more reluctant to shift towards the newest technology if no investments on it have been performed. This trade-off between network and subscribers dynamic can be financially more interesting than a separate optimiza- tion of the two problems. Moreover, an operator fixes strategical guidelines on its network for remaining competitive. Some of these indicators (for example, throughput) depend on both network and subscriber performances. Investments in subscribers and networks should hence be jointly optimized over the whole time-horizon of a strategical planning, which is typically 5 years for a telecommunication operator.This enlightens that subscriber and network dynamics are intertwined. However, to the best of our knowledge, these dynamics have been until now studied separately. To represent the subscriber dynamic, we consider in this work discrete subsidies that represent different possible marketing savings on a new phone required to access the new service. In order to model how the subscribers react to such subsidies, we choose in this article to use the well-studied Bass model (see [1] for the original paper, [5] for a model with the notion of generations, and [2] for applications to telecommunication context). Adapting this model for our context (see the extended version of the article [3] for more details), we assume that subscribers react according to both the subsidy amount proposed and an indicator of the network deployment.Our contribution is two-fold. First, we provide a modeling of the subscribers’ behavior and incorporate it in a linear Mixed-Integer Programming (MIP) formulation. Second, we im- prove the performance of the model through (i) the strengthening of the MIP with several families of valid inequalities, and (ii) a heuristic algorithm that assigns fixed values of the deci-sion variables (subsidies and coverage) and solves the resulting problem as a knapsack problem.The remainder of this article is organized as follows. Section 2 introduces our Mobile Master Plan problem (MMP) for two technologies, for which a mixed-integer formulation is provided and linearized. Section 3 introduces the aforementioned valid inequalities and heuristic algo- rithm. Numerical experiments assess these methods in Section 4. Concluding remarks are given in Section 5.