With the accelerated development of Industry 4.0, intelligent manufacturing systems increasingly require efficient task allocation and scheduling in multi-robot systems. However, existing methods rely on domain expertise and face challenges in adapting to dynamic production constraints. Additionally, enterprises have high privacy requirements for production scheduling data, which prevents the use of cloud-based large language models (LLMs) for solution development. To address these challenges, there is an urgent need for an automated modeling solution that meets data privacy requirements. This study proposes a knowledge-augmented mixed integer linear programming (MILP) automated formulation framework, integrating local LLMs with domain-specific knowledge bases to generate executable code from natural language descriptions automatically. The framework employs a knowledge-guided DeepSeek-R1-Distill-Qwen-32B model to extract complex spatiotemporal constraints (82% average accuracy) and leverages a supervised fine-tuned Qwen2.5-Coder-7B-Instruct model for efficient MILP code generation (90% average accuracy). Experimental results demonstrate that the framework successfully achieves automatic modeling in the aircraft skin manufacturing case while ensuring data privacy and computational efficiency. This research provides a low-barrier and highly reliable technical path for modeling in complex industrial scenarios.