Wireless sensor networks face significant challenges in large-scale multitask scenarios (LSM-WSNs), where traditional data collection methods lead to high energy consumption and packet collisions. Mobile data collection, employing mobile collectors, mitigates these issues but introduces electricity shortages due to limited battery capacity. This paper addresses the core research problem of minimizing charger deployment costs while ensuring uninterrupted power for mobile collectors in long-running LSM-WSNs. We formulate the Minimum-Cost Charger Deployment (MCCD) problem, prove its NP-hardness, and establish its equivalence to the Overflow-Free MCCD (OF-MCCD) problem. By refining constraints and transforming OF-MCCD into a Minimum-Cost Submodular Cover (MCSC) problem, we propose a greedy algorithm with an approximation ratio of$ln\gamma +1$, where$\gamma$is a system parameter. Further, we extend MCCD problem to adjustable power allocation case, showing that continuous power allocation reduces to linear programming, while discrete power allocation remains NP-hard, for which we devise an efficient$ln\gamma +1$-approximation solution. Additionally, we tackle the Charger Deployment Extension (CDE) problem for evolving network requirements. The unique contributions include the first systematic study of cost-optimal charger deployment for LSM-WSNs, novel problem formulations, and theoretically grounded algorithms with provable guarantees. Simulations validate that our solutions outperform baselines across diverse scenarios.