  Business optimisation refers to the process of finding and implementing
efficient and cost-effective means of operation to bring a competitive
advantage for businesses. Synthesizing problem formulations is an integral part
of business optimisation, which relies on human expertise to construct problem
formulations using optimisation languages. Interestingly, with advancements in
Large Language Models (LLMs), the human expertise needed in problem formulation
can be minimized. However, developing an LLM for problem formulation is
challenging, due to training data, token limitations, and lack of appropriate
performance metrics. For the requirement of training data, recent attention has
been directed towards fine-tuning pre-trained LLMs for downstream tasks rather
than training an LLM from scratch for a specific task. In this paper, we adopt
an LLM fine-tuning approach and propose an AI-Copilot for business optimisation
problem formulation. For token limitations, we introduce modularization and
prompt engineering techniques to synthesize complex problem formulations as
modules that fit into the token limits of LLMs. Additionally, we design
performance evaluation metrics that are better suited for assessing the
accuracy and quality of problem formulations. The experiment results
demonstrate that with this approach we can synthesize complex and large problem
formulations for a typical business optimisation problem in production
scheduling.
