The study analyzes the capacity of Large Language Models (LLMs) to respond to inquiries concerning flow shop scheduling challenges, a common issue in combinatorial optimization with practical applications in manufacturing and service sectors. The study assesses the capacity of LLMs to produce job sequencing solutions that surpass the usual First In, First Out (FIFO) scheduling norm. The research examines two heuristic approaches, Shortest Processing Time (SPT) and Longest Processing Time (LPT), utilizing Taillard benchmark instances. The results demonstrate the differing efficacy of LLMs such as ChatGPT, Copilot, DeepSeek, and Gemini in sequence generation and makespan computation, unveiling that LLMs need further developments for daily use, impairing practitioners, lecturers, and students.