Over the last few decades, researchers have made considerable efforts to make decision support more accessible for small and medium enterprises by reducing the cost of designing, developing and maintaining automated decision support systems. However, due to the diversity of the underlying combinatorial optimisation problems, reusability of such systems has been limited; in most cases, expensive expertise has been required to implement bespoke software components. We explore the feasibility of fully automated generation of combinatorial optimisation systems using large language models (LLMs). An LLM will be responsible for interpreting the user-provided problem description in natural language and designing and implementing problem-specific software components. We discuss the principles of fully automated LLM-based optimisation system generation, and evaluate several proof-of-concept generators, comparing their performance on four optimisation problems.