Crowd management and analysis (CMA) systems have gained a lot of interest in the vulgarization of unmanned aerial vehicles (UAVs) use. Crowd tracking using UAVs is among the most important services provided by a CMA. In this paper, we studied the periodic crowd-tracking (PCT) problem. It consists in using UAVs to follow-up crowds, during the life-cycle of an open crowded area (OCA). Two criteria were considered for this purpose. The first is related to the CMA initial investment, while the second is to guarantee the quality of service (QoS). The existing works focus on very specified assumptions that are highly committed to CMAs applications context. This study outlined a new binary linear programming (BLP) model to optimally solve the PCT motivated by a real-world application study taking into consideration the high level of abstraction. To closely approach different real-world contexts, we carefully defined and investigated a set of parameters related to the OCA characteristics, behaviors, and the CMA initial infrastructure investment (e.g., UAVs, charging stations (CSs)). In order to periodically update the UAVs/crowds and UAVs/CSs assignments, the proposed BLP was integrated into a linear algorithm called PCTs solver. Our main objective was to study the PCT problem from both theoretical and numerical viewpoints. To prove the PCTs solver effectiveness, we generated a diversified set of PCTs instances with different scenarios for simulation purposes. The empirical results analysis enabled us to validate the BLP model and the PCTs solver, and to point out a set of new challenges for future research directions.