The growing demand for electric vehicle (EV) charging infrastructure presents significant planning challenges, requiring efficient strategies for investment and operation to deliver cost-effective charging services. However, the potential benefits of EV charging assignment, particularly in response to varying spatial-temporal patterns of charging demand, remain under-explored in infrastructure planning. This paper proposes an integrated approach that jointly optimizes investment decisions and charging assignments while accounting for spatial-temporal demand dynamics and their interdependencies. To support efficient model development, we leverage a large language model (LLM) to assist in generating and refining the mathematical formulation from structured natural-language descriptions, significantly reducing the modeling burden. The resulting optimization model enables optimal joint decision-making for investment and operation. Additionally, we propose a distributed optimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) to address computational complexity in high-dimensional scenarios, which can be executed on standard computing platforms. We validate our approach through a case study using 1.5 million real-world travel records from Chengdu, China, demonstrating a 30% reduction in total cost compared to a baseline without EV assignment.